From 1ebf8782fe6e8a8e1ec28092246001c545c890d0 Mon Sep 17 00:00:00 2001 From: alaudens <147085052+alaudens@users.noreply.github.com> Date: Sun, 29 Oct 2023 20:09:59 -0400 Subject: [PATCH 1/4] Add files via upload AL Semester Project - Edited Notebook --- ...ted_Fraction_of_Molecular_Collisions.ipynb | 1241 +++++++++++++++++ 1 file changed, 1241 insertions(+) create mode 100644 notebooks/contrib/Edited_Fraction_of_Molecular_Collisions.ipynb diff --git a/notebooks/contrib/Edited_Fraction_of_Molecular_Collisions.ipynb b/notebooks/contrib/Edited_Fraction_of_Molecular_Collisions.ipynb new file mode 100644 index 00000000..bba848ac --- /dev/null +++ b/notebooks/contrib/Edited_Fraction_of_Molecular_Collisions.ipynb @@ -0,0 +1,1241 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "m2aSfAcfI2b3" + }, + "source": [ + "# Calculating Fraction of Molecular Collisions that Lead to Reactions #\n", + "\n", + "\n", + "CBE 60535, University of Notre Dame\n", + "\n", + "Problem 3.4 ( pg. 99 ) from Elements of Chemical Reaction Engineering by H. Scott Fogler, Fifth edition, 2016, ISBN: 978-0-13-388751-8.\n", + "\n", + "\n", + "Prepared by:\n", + "\n", + "Yun Young Choi ychoi3@nd.edu\n", + "\n", + "Bingxin Yang byang3@nd.edu" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ePnjXaXiOZSd" + }, + "source": [ + "## Learning Objectives:\n", + "\n", + "After completing this assignment, you should be able to:\n", + "\n", + "\n", + "* Apply integration techniques to Ordinary Differential Equations using Python\n", + "* Plot multiple data on a single graph\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3CGxT9KpPPmz" + }, + "source": [ + "## Intended Audience:\n", + "\n", + "This problem is intended for undergraduate students in Chemical and Biomolecular Engineering students from the University of Notre Dame who have taken Chemical Reaction Engineering." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "i-R3Uyl8nF0a" + }, + "source": [ + "**Useful links to review library:**\n", + "\n", + "1. Plotting with matplotlib\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html?highlight=plot\n", + "\n", + "2. Documentation for scipy.integrate\n", + "\n", + " https://docs.scipy.org/doc/scipy/tutorial/integrate.html\n", + "\n", + "3. Midpoint Rule\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/07/Intro-and-Newton-Cotes.html#midpoint-rule\n", + "\n", + "4. Trapezoid Rule with Multiple Pieces\n", + " https://ndcbe.github.io/data-and-computing/notebooks/07/Intro-and-Newton-Cotes.html#trapezoid-rule-with-multiple-pieces\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "eDHI0yKm5taD" + }, + "source": [ + "## Problem Statement:\n", + "To undergo a reaction, molecules must collide and overcome a certain activation energy. Whether or not the collision will overcome the activation energy depends on the relative velocities of the molecules involved. Our goal is to calculate the fraction of molecular collisions with enough energy to overcome the activation energy and undergo a reaction.\n", + "\n", + "For reactions in the gas phase, we know the relative velocity of each molecule, $U$. We also know the Maxwell-Boltzmann distribution, $f(U, T)$, which estimates the relative velocities of gas molecules at a given temperature.\n", + "\n", + "\\begin{equation}\n", + "f(U,T) = 4π(\\frac{m}{2πk_BT})^{3/2}exp(\\frac{-mU^2}{2k_BT})U^2....(Eq.1)\n", + "\\end{equation}\n", + "\n", + "$K_B$ = Boltzmann's constant = 3.29 E-24 (cal/molecule/$K$)\n", + "\n", + "$m$ = Reduced mass $(g)$\n", + "\n", + "$U$ = Relative velocity $(m/s)$\n", + "\n", + "$T$= Absolute Temperature $(K)$\n", + "\n", + "$e$ = Energy (kcal/molecule)\n", + "\n", + "$E$ = Kinetic energy (kcal/mol)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4ndRniZECa6l" + }, + "source": [ + "Since we are comparing the energy of a collision to activation energy, it is useful to rewrite the Maxwell-Boltzmann distribution in terms of energy. Equation 2 describes the relationship between kinetic energy and velocity and can be substituted into the $f(U, T)$.\n", + "\n", + "\\begin{equation}\n", + "e = \\frac{1}{2}mU^{2}....(Eq.2)\n", + "\\end{equation}\n", + "\n", + "After substitution, the Maxwell Boltzmann probability distribution of collision with energy $e$ $(cal/molecule)$ at temperature $T$ becomes\n", + "\n", + "\\begin{equation}\n", + "f(e,T) = 2π(\\frac{1}{πk_BT})^{3/2}e^{1/2}exp(\\frac{-e}{k_BT})....(Eq. 3)\n", + "\\end{equation}\n", + "\n", + "In terms of energy per mole, $E$, instead of energy per molecule, $e$ ,we have:\n", + "\n", + "\\begin{equation}\n", + "f(E,T) = 2π(\\frac{1}{πRT})^{3/2}E^{1/2}exp(\\frac{-E}{RT})....(Eq.4)\n", + "\\end{equation}\n", + "\n", + "where $E$ is in $(cal/mol)$, $R$ is in $(cal/mol/K)$, and $f(E,T)$ is in $(mol/cal)$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "O43g8sWBFFa2" + }, + "source": [ + "The distribution function $f(E,T)$ is easiest to interpret when it is integrated. Integrating $f(E,T)$ over an energy interval $dE$ is the **Fraction of Collisions** with energies between $E$ and $E + dE$, as shown in Equation 5.\n", + "\n", + "\\begin{equation}\n", + "\\int_{E}^{E + dE} f(E,T)dE....(Eq.5)\n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uOz-fAkiOwjb" + }, + "source": [ + "## Import Libraries:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "id": "Z_Jn-nkBKOGO" + }, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import integrate\n", + "from matplotlib.patches import Polygon" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Grbj_M0lB1j1" + }, + "source": [ + "## 1. Visualizing Fraction of Collisions that Lead to Reactions\n", + "\n", + "Plot the fraction of collisions that lead to reactons versus energy per mole from 0 to 30 $kcal/mol$ for different given temperatures (T = 300, 500, 800 and 1200K).\n", + "\n", + "*Hint: use Equation 4 to get the distribution of collisions that react as a function of energy per mole*\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 442 + }, + "id": "8nONGxJPIYOe", + "outputId": "87777f91-b2bc-48d6-e34f-9211fffcbe90" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "# Gas constant needs to be converted into cal/k mol\n", + "R = 8.314*0.000239\n", + "\n", + "# Generate an array of temperatures for calculation based on the requirements\n", + "T = np.array([300,500,800,1200]) #unit: K\n", + "# Create an empty list to store fraction of collisions\n", + "F = []\n", + "\n", + "pi = math.pi\n", + "\n", + "plt.figure(figsize=(6.4,4), dpi=100) #Plot figure size 6.4x4 with 300 DPi\n", + "\n", + "#add your solution here\n", + "### BEGIN SOLUTION\n", + "\n", + "# Create a for loop for fraction of collisions calculation at different temperatures from 0 to 30 kcal/mol\n", + "for i in range(len(T)):\n", + " E = np.arange(0,30,.1) # range for x-axis\n", + " F = 2*pi*(1/(pi*R*T[i]))**1.5*E**0.5*np.exp(-E/(R*T[i]))\n", + " plt.plot(E,F,linewidth=3, label=str(T[i])+\"K\")\n", + "\n", + "### END SOLUTION\n", + "\n", + "# Plot\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look crowded, so left out\n", + "plt.grid()\n", + "plt.xlabel('E[kcal/mol]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", + "plt.ylabel('f[(mol/kcal)]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", + "plt.legend()\n", + "plt.title(\"Distribution of the Fraction of Molecules that React as a \\nFunction of Kinetic Energy for Various Temperatures\", fontsize=16, fontweight = 'bold')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XWenw1DHCA8A" + }, + "source": [ + "**Discussion:** Explain how the fraction of collisions that lead to reactions change as a function of temperature." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5g0fsad0CJVo" + }, + "source": [ + "**Answer**: For a given activation energy, the higher temperature systems will always have a higher fraction of collisions that overcome the activation energy because their distribution is skewed towards larger energies. For example, if the activation were 5 kcal/mol, the integral from 5 kcal/mol to infinity would be the largest for the higher temperatures and lowest for the lower temperatures." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dL7XwxciCJ57" + }, + "source": [ + "## 2. Determining the Fraction of Molecules\n", + "Write a function that takes in an array of temperatures, a lower bound of integration (activation energy), and an upper bound of integration (infinity unless given) and returns the fraction of collisions that can overcome an activation energy.\n", + "\n", + "*Hint: use integrate.quad. Look up documentation to see its output*" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "id": "h6z_ScYVD1sj" + }, + "outputs": [], + "source": [ + "# Regenerate an array of temperatures for calculation based on the requirements\n", + "\n", + "# Define a function for fraction of molecules that have sufficient energy to pass over an energy barrier calculation\n", + "def fraction(T, low, upp):\n", + " \"\"\"Using integration to calculate the fraction of molecules from 0 to 25 kcal\n", + " Args:\n", + " T: array of temperatures (K)\n", + " low: lower bound of integration (minimum energy barrier)\n", + " upp: upper bound of integration (infinity or a given value)\n", + " E: Energy (per mole)\n", + " Returns:\n", + " f: f(E,T), distribution of collision for energy per mole (mol/cal)\n", + " \"\"\"\n", + "\n", + " # Store fraction of molecules that have sufficient energy to pass over an energy barrier equal to low\n", + " f = []\n", + "\n", + " # Add your solution here\n", + " ### BEGIN SOLUTION\n", + " # Create a for loop for integration calculation at different temperatures\n", + " for i in range(len(T)):\n", + " result,error = integrate.quad(lambda E: 2*pi*(1/(pi*R*T[i]))**1.5*E**0.5*np.exp(-E/(R*T[i])),low,upp)\n", + " f.append(result)\n", + "\n", + " ### END SOLUTION\n", + "\n", + " return f" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LFV8PSZ6Ur_o" + }, + "source": [ + "What is the fraction of molecules that have sufficient energy to pass over an energy barrier of 25 kcal at 300, 500, 800 and 1200K? Print your results.\n", + "\n", + "*Hint: integrate $f(E,T)$ from 25 to infinity (100 is sufficiently large) using function defined above*" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "sf_QPxSqEHvx", + "outputId": "4931efbc-e815-4aba-bd6b-427d4cfa36df" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Fraction of Molecules with Sufficient Energy to Overcome an Energy Barrier of 25 kcal/mol\n", + "300 K: 4.5214316303312536e-18\n", + "500 K: 6.808923611608622e-11\n", + "800 K: 6.821634331731523e-07\n", + "1200 K: 0.00010684065902266493\n" + ] + } + ], + "source": [ + "# calculate fraction of molecules\n", + "frac = fraction(T, 25, 100)\n", + "\n", + "# print fraction of molecules for each T\n", + "print(\"Fraction of Molecules with Sufficient Energy to Overcome an Energy Barrier of 25 kcal/mol\")\n", + "for i in range(len(T)):\n", + " print(\"{} K: {}\".format(T[i], frac[i]))" + ] + }, + { + "cell_type": "markdown", + "source": [ + "**Discussion**: what can we see about the relationship between temperature and fraction of molecules that can overcome an arbitrary activation energy?" + ], + "metadata": { + "id": "d2bm9-jWjwhA" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer**: we can see that as temperature increases, the fraction of molecules that overcome the activation energy increases" + ], + "metadata": { + "id": "GdkcXSDbj6Ly" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kxEt3olsCxVb" + }, + "source": [ + "## 3. Calculating the Ratio of the Fraction of Molecules that React\n", + "Calculate the fraction of molecules that react between 0 and 25 kcal/mol for 300 K and 1200 K. Store your results in a list called $I$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "_LjTklXOIHze", + "outputId": "3f697c15-a493-4f62-e632-9246c77b2397" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Fraction of Collisions that React with Barrier Height between 0-25 kcal/mol from 300 K to 1200 K: \n", + " [0.9999999999999933, 0.9998931593409495]\n" + ] + } + ], + "source": [ + "# Define Temperature in a list T1 (300K and 1200K)\n", + "T1 = np.array([300,1200])\n", + "\n", + "# Store the fraction from the integration in I to obtain the fraction at given temperatures\n", + "# Create an empty list I2\n", + "I = []\n", + "# Add your solution here\n", + "### BEGIN SOLUTION\n", + "\n", + "I = fraction(T1, 0, 25)\n", + "\n", + "### END SOLUTION\n", + "\n", + "# print data\n", + "print(\"Fraction of Collisions that React with Barrier Height between 0-25 kcal/mol from 300 K to 1200 K: \\n\", I)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QnnncXwWU0Oz" + }, + "source": [ + "Now, obtain the ratio using the `I` obtained above comparing 300 K to 1200 K." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "F2-u8fBRTXce", + "outputId": "ee098fd3-ed2b-47ff-d41d-e3a7105ac68d" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Baseline resistance = 1.0000\n" + ] + } + ], + "source": [ + "#Add your solution here that will calculate and show the ratio here\n", + "### BEGIN SOLUTION\n", + "R = I[0]//I[1]\n", + "\n", + "### END SOLUTION\n", + "\n", + "# print the obtained ratio\n", + "print(\"Baseline resistance = {0:0.4f}\".format(R))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "aY2GkD4iXtXI" + }, + "source": [ + "### Additional Analysis\n", + "\n", + "As mentioned above, The distribution function $f(E,T)$ is most easily interpreted by recognizing that integrating $f(E,T)$ over a change dE is the **Fraction of Collisions** with energies between $E$ and $E + dE$\n", + "\n", + "\n", + "\\begin{equation}\n", + "\\int_{E}^{E + dE} f(E,T)dE....(Eq.5)\n", + "\\end{equation}\n", + "\n", + "\n", + "\n", + "\n", + "The **Reaction of Collisions** can be found by setting the lower integration limit equal to activation energy, $E_{A}$, and the upper integration limit to infinity as shown in Equation 6.\n", + "\n", + "\\begin{equation}\n", + "F(E>E_A,T) = \\int_{E_A}^{∞} f(E,T)dE....(Eq.6)\n", + "\\end{equation}\n", + "\n", + "\n", + "\n", + "\n", + "For $E_{A}$ > 3$RT$, an analytical approximation for the fraction of collision with energies greater than $E_{A}$ can be obtained by integrating Equation 5 from $E_{A}$ to infinity to get:\n", + "\n", + "\\begin{equation}\n", + "F(E>E_A,T) = (\\frac{2}{{π}^{0.5}})(\\frac{E_A}{RT})^{1/2}exp(\\frac{-E_A}{RT})....(Eq.7)\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zg5GdAq-C8yF" + }, + "source": [ + "## 4. Fraction of Collisions that have Energies Greater Than a Certain Value, $E_A$.\n", + "\n", + "### 4a. Manually integrate Equation 5 from $E_A$ to infinity and to get Equation 7.\n", + "\n", + "*Hint: the constants in the equation can be grouped and substituted with constant such as A and/or B for simplification*\n", + "\n", + "*Hint: use u-substition*\n", + "\n", + "Submit the written work via ***Gradescope***." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "qmx3mCg4DedZ" + }, + "source": [ + "### 4b. Numeric Integration\n", + "\n", + "Numerically integrate Equation 5 and evaluate at $E_A$ for $E_A$ ranging from 0 to 40." + ] + }, + { + "cell_type": "code", + "source": [ + "# gas constant needs to be converted into cal/k mol\n", + "R = 8.314*0.000239\n", + "\n", + "#add solution here\n", + "\n", + "# define energy range from 0 to 40 kcal\n", + "E_A = np.arange(.0,40,.1) # range for x-axis\n", + "\n", + "# temperature\n", + "T2 = 700 # units: K\n", + "\n", + "#define equation 7 as F_C\n", + "def F_C(E_A, T):\n", + " \"\"\"Calculating the fraction of collisions\n", + " Args:\n", + " E_A: activation energy (kcal/mol)\n", + " T: temperature (K)\n", + " Returns:\n", + " y: fraction of collisions with energy greater than E_A\n", + " \"\"\"\n", + " pi = math.pi\n", + " # calculation of fraction of collision\n", + " y = 2*pi*(1/(pi*R*T))**1.5*E_A**0.5*np.exp(-E_A/(R*T))\n", + "\n", + " return y" + ], + "metadata": { + "id": "kEJ0Ap_YpfEz" + }, + "execution_count": 10, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uH8g2S2yDksx" + }, + "source": [ + "### 4c. Visualization:\n", + "\n", + "Graph using the equation you have obtained from 4b for 700K." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 446 + }, + "id": "GB99P_10HcIx", + "outputId": "7b2a95da-b1ff-44ca-d0ac-efaf4cef7d9e" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "# plot the data\n", + "plt.figure(figsize=(6.4,4), dpi=100)\n", + "plt.grid()\n", + "plt.semilogy(E_A, F_C(E_A,T2), linewidth=3, label=\"Fraction of Collision\")\n", + "plt.ylim([10E-12,1])\n", + "plt.xlim([20,40])\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", + "plt.xlabel('$E_A$ [kcal/mol]',fontsize=16, fontweight = 'bold')\n", + "plt.ylabel('Fraction of Collisions that \\nLead to Reactions [(mol/kcal)]',fontsize=16, fontweight = 'bold')\n", + "plt.title('Fraction of Collisions that Lead to Reactions \\nversus Activation Energy', fontsize=16, fontweight = 'bold')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "source": [ + "### What does the plot above tell us?\n", + "\n", + "**Answer:** it tells us that as the activation energy increases, the amount of collisions that lead to reactions decreases. The relationship is linear" + ], + "metadata": { + "id": "VsF6GaKJ_1ld" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "bMRynDq0DpS9" + }, + "source": [ + "### 4d. What fraction of collisions have energies greater than $E$ = 25 kcal/mol?\n", + "\n", + "Hint: What is the y axis value when x = 25 kcal?" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "BbXq2KFny_Vd", + "outputId": "0b776635-750d-4a98-8a85-613ad91105d4" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Fraction of collisions have energies greater than E = 25 kcal/mol at 700K: \n", + " 5.37835222623192e-08 when E = 25 kcal\n" + ] + } + ], + "source": [ + "# Define constants\n", + "E_A1 = 25 # unit: kcal\n", + "\n", + "# Call the function F_C and calculate the fraction of collisions at 700K.\n", + "### BEGIN SOLUTION\n", + "F_C(E_A1,T2)\n", + "\n", + "### END SOLUTION\n", + "print(\"Fraction of collisions have energies greater than E = 25 kcal/mol at 700K: \\n\",F_C(E_A1,T2),\"when E = 25 kcal\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8htz9cwyD17l" + }, + "source": [ + "### 4e. Visualization at different temperature:\n", + "\n", + "Graph using the code you have obtained from 4b for 500K." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 423 + }, + "id": "j998WfmAHeI8", + "outputId": "32f4a252-3c41-435a-8d59-6359e3afe36a" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ], + "source": [ + "#add your solution here to get the graph shown below\n", + "E_A2 = np.arange(0,40,0.01)\n", + "# define temperature for this problem\n", + "T3 = 500 #unit: K\n", + "\n", + "# Call the funcation and calculate the fraction of collisions and create a semilog plot as shown in 4c.\n", + "#Add your solution here\n", + "### BEGIN SOLUTION\n", + "F_C(E_A2, T3)\n", + "\n", + "#Plot\n", + "plt.figure(figsize=(6.4,4), dpi=100)\n", + "plt.grid()\n", + "plt.semilogy(E_A2, F_C(E_A2,T3), linewidth=3, label=\"Fraction of Molecule\")\n", + "plt.xlabel('$E_A$ [kcal/mol]', fontsize=16, fontweight = 'bold')\n", + "plt.ylabel('Fraction of Molecule[(mol/kcal)]', fontsize=16, fontweight = 'bold')\n", + "plt.title('Fraction of Molecule graph', fontsize=16, fontweight = 'bold')\n", + "plt.ylim([10E-12,1])\n", + "plt.xlim([10,25])\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", + "plt.legend()\n", + "plt.show()\n", + "### END SOLUTION" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VraTYxTzD9vY" + }, + "source": [ + "### 4f. What fraction of molecules have collision energies greater than 15 kcal/mol at 500K?" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "0vPCNSoUHet-", + "outputId": "e46361cd-562d-4941-dcf3-351e12b9cb75" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "F_500 is 6.722248169794792e-11 when E_A = 15\n" + ] + } + ], + "source": [ + "# Find F_500 when E = 25\n", + "### BEGIN SOLUTION\n", + "F_C(E_A1, T3)\n", + "### END SOLUTION\n", + "\n", + "print(\"F_500 is\",F_C(E_A1, T3),\"when E_A = 15\")" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "8uS26QLefXAn", + "outputId": "c83f0db1-31d2-412f-bd99-5d4acfbe095b" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "F_700 is 5.37835222623192e-08 when E_A = 15\n" + ] + } + ], + "source": [ + "# Find F_700 when E = 25\n", + "### BEGIN SOLUTION\n", + "F_C(E_A1, T2)\n", + "\n", + "### END SOLUTION\n", + "\n", + "print(\"F_700 is\",F_C(E_A1, T2),\"when E_A = 15\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "swiSvh-OkQpr" + }, + "source": [ + "**Discussion:**\n", + "Compare fraction of collision that overcome an activation energy of 25 kcal/mol at 500 K and 700 K." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "wgP-3ca_kWdX" + }, + "source": [ + "**Answer**:\n", + "The fraction of collisions that overcome 25 kcal/mol increases 3 orders of magnitude from 500 K to 700 K." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ApAGEMY0kFyw" + }, + "source": [ + "## 5. Fraction of Collisions at Various Temperatures" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "npM5ktX3EGNp" + }, + "source": [ + "### 5a. Graph $f(E > E_A,T)$ versus $T$ for $E_A$ = 3, 10, 25 and 40 kcal/mol. Assume T varies from 1 K to 120 K. Use a semilog plot for the y-axis.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 442 + }, + "id": "ngJ4qqxfGduS", + "outputId": "a1fdeec5-524b-44c7-b115-69008d65bdd9" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "# define constants and data storage\n", + "# make a list for fraction storage\n", + "F3 = []\n", + "# redefine the range of temperature\n", + "T4 = np.arange(1,120,0.1) # Unit: K\n", + "# make a list for energy\n", + "EA3 = [3,10,25,40] #unit: kcal\n", + "pi = math.pi\n", + "\n", + "plt.figure(figsize=(6.4,4), dpi=100) #Figure size 4x4 with 300 DPi\n", + "# Create a loop for fraction calculation for different temperatures and to graph a semilog graph\n", + "# enter equation here\n", + "### BEGIN SOLUTION\n", + "for i in range(len(EA3)):\n", + " F3 = 2*pi**(-0.5)*((EA3[i]/(R*T4))**0.5)*np.exp(-EA3[i]/(R*T4))\n", + " plt.semilogy(T4, F3, label=str(EA3[i])+\" kcal/mol\",linewidth=3)\n", + "### END SOLUTION\n", + "\n", + "# plot\n", + "plt.grid()\n", + "plt.ylim([10E-292,1])\n", + "plt.xlim([0,120])\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", + "plt.xlabel('T [K]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", + "plt.ylabel('f($E > E_A$)[(mol/kcal)]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", + "plt.title(\"Fraction of Molecules that React as a Function of \\nTemperature at Various Activation Energies\", fontsize=16, fontweight = 'bold')\n", + "\n", + "\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "TeWOvx69ihEl" + }, + "source": [ + "**Discussion:** What does the graph above show?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QcYMcmh-ij0l" + }, + "source": [ + "**Answer**: As temperature increases, the fraction of molecules that react increases. Additionally, a lower activation energy leads to a higher fraction of molecules that react. The largest fraction of molecules will react at the highest temperature and with the lowest activation energy.\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## 6. Comparing Midpoint Rule to Gass Quadruture" + ], + "metadata": { + "id": "lCEsXaRC9q2c" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Our goal is to determine the amount of segments it takes before midpoint rule is approximately as good of an estimator as Gauss Quadrature." + ], + "metadata": { + "id": "LPhMFvjzvZck" + } + }, + { + "cell_type": "markdown", + "source": [ + "###6a. By hand, write out the midpoint rule and sketch an image describing the process" + ], + "metadata": { + "id": "QnVhVVRh9x3V" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer:** I_midpoint = $h*f((a+b)/2)$. For multiple pieces, sum up all the I_midpoints. A picture should show a rectangle (or several) that are centered at a given point and have width b-a." + ], + "metadata": { + "id": "l9a3Jztv-NvL" + } + }, + { + "cell_type": "markdown", + "source": [ + "### 6b. Write a function to numerically integrate the fraction of collisions using the midpoint rule. Evaluate at T = 800 K. Use E between 0 to 15 kcal/mol.\n", + "*Hint: this is similar to the midpoint code from the class website and trapezoid rule with multiple pieces. Basically, you are writing the midpoint rule with multiple pieces*\n" + ], + "metadata": { + "id": "oGKEYVdM-wNI" + } + }, + { + "cell_type": "code", + "source": [ + "# define and plot function\n", + "def midpoint_integration(N, plot = True):\n", + " \"\"\"\n", + " Args:\n", + " N = the number of rectangles\n", + " plot = a boolean that determines whether to generate plots or return the result of the integration\n", + " *This is useful because for visual purposes, you create a plot. For calculating errors, you will return the\n", + " integration result instead\n", + " Returns:\n", + " Imid = the approximate result of the integral (if !plot)\n", + " OR\n", + " generates a plot of the midpoint rule applied to the distribution of the fraction of collisions (if plot)\n", + " \"\"\"\n", + "\n", + " T = 800\n", + " E = np.linspace(0,15,100)\n", + "\n", + " # update the equation to represent the fraction of collisions\n", + " ### BEGIN SOLUTION ###\n", + " f = lambda E: 2*pi*(1/(pi*R*T))**1.5*E**0.5*np.exp(-E/(R*T))\n", + " ### END SOLUTION ###\n", + "\n", + " if plot:\n", + " plt.plot(E,f(E),label=\"f(x)\",color=\"blue\")\n", + " ax = plt.gca()\n", + "\n", + " # bounding a and b, finding width of each rectangle\n", + " far_left = 0\n", + " far_right = 15\n", + " width = (far_right - far_left)/N\n", + "\n", + " # initializing counter\n", + " Imid = 0\n", + "\n", + " # create a loop that approximates the integration using midpoint rule\n", + " # hint: a and b must update each iteration. The width between them is constant.\n", + " # hint: calculate the value of the function, plug into Imid formula, and add Imid to an accumulator\n", + " # call the evaluation of the function at (a+b)/2 \"mid\" for coherence with rectangle drawing code\n", + " ### BEGIN SOLUTION ###\n", + " for i in range(N):\n", + " a = i*width\n", + " b = i*width + width\n", + " mid = f((a + b)/2)\n", + " Imid += width*mid\n", + " ### END SOLUTION\n", + "\n", + " # draw rectangle\n", + " if plot:\n", + " verts = [(a,0),(a,mid), (b,mid),(b,0)]\n", + " poly = Polygon(verts, facecolor='0.8', edgecolor='k')\n", + " ax.add_patch(poly)\n", + "\n", + " if plot:\n", + " print(\"Integral estimate = \",Imid)\n", + "\n", + " if (plot == False):\n", + " return Imid\n", + "\n", + " if plot:\n", + " # add labels\n", + " plt.xlabel(\"x\")\n", + " plt.ylabel(\"f(x)\")\n", + " plt.title(\"Midpoint Rule\")\n", + " plt.show()" + ], + "metadata": { + "id": "BAny4QTJ_U0C" + }, + "execution_count": 17, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# call function to test\n", + "midpoint_integration(30)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 490 + }, + "id": "bofqzNpBDbDh", + "outputId": "8a78a157-deb8-46ea-e85f-772c169efdf8" + }, + "execution_count": 18, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Integral estimate = 1.0107343121299819\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 6c. Use scipy.integrate.quad to evaluate the same equation and bounds as in 6b.\n", + "*hint: this will produce an integer*\n" + ], + "metadata": { + "id": "8v3lyakT-6jS" + } + }, + { + "cell_type": "code", + "source": [ + "## finding integral of this function using scipy.integrate.quad\n", + "T = 800\n", + "result,error = integrate.quad(lambda E: 2*pi*(1/(pi*R*T))**1.5*E**0.5*np.exp(-E/(R*T)),0,15)\n", + "print(result)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "H2kF4ZmGyl5n", + "outputId": "25a76a88-d72e-43fb-bc54-7c1b0ae199b4" + }, + "execution_count": 21, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "0.9997094573570767\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 6d. Comparing Midpoint Rule to Gauss Quadrature.\n", + "\n", + "Evaluate the integral using the function from 6b over a range of N (between 1 and 50). This is the \"midpoint result\". Store the midpoint result in a vector. Next, subtract the Gauss Quadrature result from each midpoint result. Store the difference in a vector called compare.\n", + "*hint: cast N[i] as an int*\n", + "\n", + "*hint: set plot = False*" + ], + "metadata": { + "id": "8YyCm6seysSw" + } + }, + { + "cell_type": "code", + "source": [ + "points = 50\n", + "N = np.linspace(1, 50, points)\n", + "compare = np.zeros(points)\n", + "\n", + "### BEGIN SOLUTION\n", + "for i in range(points):\n", + " i = int(i)\n", + " compare[i] = midpoint_integration(int(N[i]), False)\n", + " compare[i] -= result\n", + "### END SOLUTION\n", + "\n", + "print(compare)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "p-tjM_UgyzOQ", + "outputId": "a89b29f8-60c4-4350-83d1-1957f26f5377" + }, + "execution_count": 24, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "[-0.79312238 -0.21494489 -0.00351488 0.05427425 0.06668412 0.06553709\n", + " 0.06051562 0.05475037 0.0492623 0.04434694 0.04004378 0.03630544\n", + " 0.03306072 0.03023791 0.02777264 0.02560982 0.02370324 0.02201446\n", + " 0.02051161 0.01916824 0.01796231 0.0168754 0.01589206 0.01499924\n", + " 0.01418588 0.01344258 0.01276129 0.01213509 0.011558 0.01102485\n", + " 0.01053115 0.01007296 0.00964683 0.00924973 0.00887898 0.00853222\n", + " 0.00820733 0.00790246 0.00761591 0.0073462 0.00709197 0.00685202\n", + " 0.00662525 0.00641067 0.0062074 0.0060146 0.00583156 0.00565759\n", + " 0.00549207 0.00533445]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 6e. Plotting\n", + "Plot compare versus N. Make a publication quality figure.\n" + ], + "metadata": { + "id": "jOihDdotyjXG" + } + }, + { + "cell_type": "code", + "source": [ + "# plot the data\n", + "plt.figure(figsize=(6.4,4), dpi=100)\n", + "plt.grid()\n", + "\n", + "# write line that plots compare vs N\n", + "### BEGIN SOLUTION\n", + "plt.plot(N, compare, linewidth=3, label=\"Difference Between Gauss \\nQuadrature and Midpoint Rule\")\n", + "### END SOLUTION\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick direction: in\n", + "plt.xlabel('Number of Midpoint Rule Rectangles',fontsize=16, fontweight = 'bold')\n", + "plt.ylabel('Difference Between Midpoint \\nRule and Gauss Quadrature \\nIntegral Results',fontsize=16, fontweight = 'bold')\n", + "plt.title('Difference Between Midpoint Rule and Gauss \\nQuadrature for Varying Number of \\nMidpoint Rectangles', fontsize=16, fontweight = 'bold')\n", + "plt.legend()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 466 + }, + "id": "yheaT0CC-600", + "outputId": "c135ac4b-d8b3-4556-d6d0-6d6f01898019" + }, + "execution_count": 35, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "**Discussion**: What do you notice about the errors? At what value of N are the integral approximations roughly equal?" + ], + "metadata": { + "id": "69Ahz9usJxrc" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer**: For N > ~4, the difference approaches 0. The error becomes approximately 0 for N > 30, but for values of N > 10 is probably small enough." + ], + "metadata": { + "id": "KZEUKWaTJ7Lw" + } + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file From d040d08c0995e0fe62d3c46f4b2cc58caee7a596 Mon Sep 17 00:00:00 2001 From: alaudens <147085052+alaudens@users.noreply.github.com> Date: Sun, 29 Oct 2023 20:18:51 -0400 Subject: [PATCH 2/4] Add files via upload --- ...ted_Fraction_of_Molecular_Collisions.ipynb | 1241 +++++++++++++++++ 1 file changed, 1241 insertions(+) create mode 100644 notebooks/contrib-dev/Edited_Fraction_of_Molecular_Collisions.ipynb diff --git a/notebooks/contrib-dev/Edited_Fraction_of_Molecular_Collisions.ipynb b/notebooks/contrib-dev/Edited_Fraction_of_Molecular_Collisions.ipynb new file mode 100644 index 00000000..bba848ac --- /dev/null +++ b/notebooks/contrib-dev/Edited_Fraction_of_Molecular_Collisions.ipynb @@ -0,0 +1,1241 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "m2aSfAcfI2b3" + }, + "source": [ + "# Calculating Fraction of Molecular Collisions that Lead to Reactions #\n", + "\n", + "\n", + "CBE 60535, University of Notre Dame\n", + "\n", + "Problem 3.4 ( pg. 99 ) from Elements of Chemical Reaction Engineering by H. Scott Fogler, Fifth edition, 2016, ISBN: 978-0-13-388751-8.\n", + "\n", + "\n", + "Prepared by:\n", + "\n", + "Yun Young Choi ychoi3@nd.edu\n", + "\n", + "Bingxin Yang byang3@nd.edu" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ePnjXaXiOZSd" + }, + "source": [ + "## Learning Objectives:\n", + "\n", + "After completing this assignment, you should be able to:\n", + "\n", + "\n", + "* Apply integration techniques to Ordinary Differential Equations using Python\n", + "* Plot multiple data on a single graph\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3CGxT9KpPPmz" + }, + "source": [ + "## Intended Audience:\n", + "\n", + "This problem is intended for undergraduate students in Chemical and Biomolecular Engineering students from the University of Notre Dame who have taken Chemical Reaction Engineering." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "i-R3Uyl8nF0a" + }, + "source": [ + "**Useful links to review library:**\n", + "\n", + "1. Plotting with matplotlib\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html?highlight=plot\n", + "\n", + "2. Documentation for scipy.integrate\n", + "\n", + " https://docs.scipy.org/doc/scipy/tutorial/integrate.html\n", + "\n", + "3. Midpoint Rule\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/07/Intro-and-Newton-Cotes.html#midpoint-rule\n", + "\n", + "4. Trapezoid Rule with Multiple Pieces\n", + " https://ndcbe.github.io/data-and-computing/notebooks/07/Intro-and-Newton-Cotes.html#trapezoid-rule-with-multiple-pieces\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "eDHI0yKm5taD" + }, + "source": [ + "## Problem Statement:\n", + "To undergo a reaction, molecules must collide and overcome a certain activation energy. Whether or not the collision will overcome the activation energy depends on the relative velocities of the molecules involved. Our goal is to calculate the fraction of molecular collisions with enough energy to overcome the activation energy and undergo a reaction.\n", + "\n", + "For reactions in the gas phase, we know the relative velocity of each molecule, $U$. We also know the Maxwell-Boltzmann distribution, $f(U, T)$, which estimates the relative velocities of gas molecules at a given temperature.\n", + "\n", + "\\begin{equation}\n", + "f(U,T) = 4π(\\frac{m}{2πk_BT})^{3/2}exp(\\frac{-mU^2}{2k_BT})U^2....(Eq.1)\n", + "\\end{equation}\n", + "\n", + "$K_B$ = Boltzmann's constant = 3.29 E-24 (cal/molecule/$K$)\n", + "\n", + "$m$ = Reduced mass $(g)$\n", + "\n", + "$U$ = Relative velocity $(m/s)$\n", + "\n", + "$T$= Absolute Temperature $(K)$\n", + "\n", + "$e$ = Energy (kcal/molecule)\n", + "\n", + "$E$ = Kinetic energy (kcal/mol)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4ndRniZECa6l" + }, + "source": [ + "Since we are comparing the energy of a collision to activation energy, it is useful to rewrite the Maxwell-Boltzmann distribution in terms of energy. Equation 2 describes the relationship between kinetic energy and velocity and can be substituted into the $f(U, T)$.\n", + "\n", + "\\begin{equation}\n", + "e = \\frac{1}{2}mU^{2}....(Eq.2)\n", + "\\end{equation}\n", + "\n", + "After substitution, the Maxwell Boltzmann probability distribution of collision with energy $e$ $(cal/molecule)$ at temperature $T$ becomes\n", + "\n", + "\\begin{equation}\n", + "f(e,T) = 2π(\\frac{1}{πk_BT})^{3/2}e^{1/2}exp(\\frac{-e}{k_BT})....(Eq. 3)\n", + "\\end{equation}\n", + "\n", + "In terms of energy per mole, $E$, instead of energy per molecule, $e$ ,we have:\n", + "\n", + "\\begin{equation}\n", + "f(E,T) = 2π(\\frac{1}{πRT})^{3/2}E^{1/2}exp(\\frac{-E}{RT})....(Eq.4)\n", + "\\end{equation}\n", + "\n", + "where $E$ is in $(cal/mol)$, $R$ is in $(cal/mol/K)$, and $f(E,T)$ is in $(mol/cal)$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "O43g8sWBFFa2" + }, + "source": [ + "The distribution function $f(E,T)$ is easiest to interpret when it is integrated. Integrating $f(E,T)$ over an energy interval $dE$ is the **Fraction of Collisions** with energies between $E$ and $E + dE$, as shown in Equation 5.\n", + "\n", + "\\begin{equation}\n", + "\\int_{E}^{E + dE} f(E,T)dE....(Eq.5)\n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uOz-fAkiOwjb" + }, + "source": [ + "## Import Libraries:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "id": "Z_Jn-nkBKOGO" + }, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import integrate\n", + "from matplotlib.patches import Polygon" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Grbj_M0lB1j1" + }, + "source": [ + "## 1. Visualizing Fraction of Collisions that Lead to Reactions\n", + "\n", + "Plot the fraction of collisions that lead to reactons versus energy per mole from 0 to 30 $kcal/mol$ for different given temperatures (T = 300, 500, 800 and 1200K).\n", + "\n", + "*Hint: use Equation 4 to get the distribution of collisions that react as a function of energy per mole*\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 442 + }, + "id": "8nONGxJPIYOe", + "outputId": "87777f91-b2bc-48d6-e34f-9211fffcbe90" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ], + "source": [ + "# Gas constant needs to be converted into cal/k mol\n", + "R = 8.314*0.000239\n", + "\n", + "# Generate an array of temperatures for calculation based on the requirements\n", + "T = np.array([300,500,800,1200]) #unit: K\n", + "# Create an empty list to store fraction of collisions\n", + "F = []\n", + "\n", + "pi = math.pi\n", + "\n", + "plt.figure(figsize=(6.4,4), dpi=100) #Plot figure size 6.4x4 with 300 DPi\n", + "\n", + "#add your solution here\n", + "### BEGIN SOLUTION\n", + "\n", + "# Create a for loop for fraction of collisions calculation at different temperatures from 0 to 30 kcal/mol\n", + "for i in range(len(T)):\n", + " E = np.arange(0,30,.1) # range for x-axis\n", + " F = 2*pi*(1/(pi*R*T[i]))**1.5*E**0.5*np.exp(-E/(R*T[i]))\n", + " plt.plot(E,F,linewidth=3, label=str(T[i])+\"K\")\n", + "\n", + "### END SOLUTION\n", + "\n", + "# Plot\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look crowded, so left out\n", + "plt.grid()\n", + "plt.xlabel('E[kcal/mol]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", + "plt.ylabel('f[(mol/kcal)]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", + "plt.legend()\n", + "plt.title(\"Distribution of the Fraction of Molecules that React as a \\nFunction of Kinetic Energy for Various Temperatures\", fontsize=16, fontweight = 'bold')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XWenw1DHCA8A" + }, + "source": [ + "**Discussion:** Explain how the fraction of collisions that lead to reactions change as a function of temperature." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5g0fsad0CJVo" + }, + "source": [ + "**Answer**: For a given activation energy, the higher temperature systems will always have a higher fraction of collisions that overcome the activation energy because their distribution is skewed towards larger energies. For example, if the activation were 5 kcal/mol, the integral from 5 kcal/mol to infinity would be the largest for the higher temperatures and lowest for the lower temperatures." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dL7XwxciCJ57" + }, + "source": [ + "## 2. Determining the Fraction of Molecules\n", + "Write a function that takes in an array of temperatures, a lower bound of integration (activation energy), and an upper bound of integration (infinity unless given) and returns the fraction of collisions that can overcome an activation energy.\n", + "\n", + "*Hint: use integrate.quad. Look up documentation to see its output*" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "id": "h6z_ScYVD1sj" + }, + "outputs": [], + "source": [ + "# Regenerate an array of temperatures for calculation based on the requirements\n", + "\n", + "# Define a function for fraction of molecules that have sufficient energy to pass over an energy barrier calculation\n", + "def fraction(T, low, upp):\n", + " \"\"\"Using integration to calculate the fraction of molecules from 0 to 25 kcal\n", + " Args:\n", + " T: array of temperatures (K)\n", + " low: lower bound of integration (minimum energy barrier)\n", + " upp: upper bound of integration (infinity or a given value)\n", + " E: Energy (per mole)\n", + " Returns:\n", + " f: f(E,T), distribution of collision for energy per mole (mol/cal)\n", + " \"\"\"\n", + "\n", + " # Store fraction of molecules that have sufficient energy to pass over an energy barrier equal to low\n", + " f = []\n", + "\n", + " # Add your solution here\n", + " ### BEGIN SOLUTION\n", + " # Create a for loop for integration calculation at different temperatures\n", + " for i in range(len(T)):\n", + " result,error = integrate.quad(lambda E: 2*pi*(1/(pi*R*T[i]))**1.5*E**0.5*np.exp(-E/(R*T[i])),low,upp)\n", + " f.append(result)\n", + "\n", + " ### END SOLUTION\n", + "\n", + " return f" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LFV8PSZ6Ur_o" + }, + "source": [ + "What is the fraction of molecules that have sufficient energy to pass over an energy barrier of 25 kcal at 300, 500, 800 and 1200K? Print your results.\n", + "\n", + "*Hint: integrate $f(E,T)$ from 25 to infinity (100 is sufficiently large) using function defined above*" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "sf_QPxSqEHvx", + "outputId": "4931efbc-e815-4aba-bd6b-427d4cfa36df" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Fraction of Molecules with Sufficient Energy to Overcome an Energy Barrier of 25 kcal/mol\n", + "300 K: 4.5214316303312536e-18\n", + "500 K: 6.808923611608622e-11\n", + "800 K: 6.821634331731523e-07\n", + "1200 K: 0.00010684065902266493\n" + ] + } + ], + "source": [ + "# calculate fraction of molecules\n", + "frac = fraction(T, 25, 100)\n", + "\n", + "# print fraction of molecules for each T\n", + "print(\"Fraction of Molecules with Sufficient Energy to Overcome an Energy Barrier of 25 kcal/mol\")\n", + "for i in range(len(T)):\n", + " print(\"{} K: {}\".format(T[i], frac[i]))" + ] + }, + { + "cell_type": "markdown", + "source": [ + "**Discussion**: what can we see about the relationship between temperature and fraction of molecules that can overcome an arbitrary activation energy?" + ], + "metadata": { + "id": "d2bm9-jWjwhA" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer**: we can see that as temperature increases, the fraction of molecules that overcome the activation energy increases" + ], + "metadata": { + "id": "GdkcXSDbj6Ly" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kxEt3olsCxVb" + }, + "source": [ + "## 3. Calculating the Ratio of the Fraction of Molecules that React\n", + "Calculate the fraction of molecules that react between 0 and 25 kcal/mol for 300 K and 1200 K. Store your results in a list called $I$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "_LjTklXOIHze", + "outputId": "3f697c15-a493-4f62-e632-9246c77b2397" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Fraction of Collisions that React with Barrier Height between 0-25 kcal/mol from 300 K to 1200 K: \n", + " [0.9999999999999933, 0.9998931593409495]\n" + ] + } + ], + "source": [ + "# Define Temperature in a list T1 (300K and 1200K)\n", + "T1 = np.array([300,1200])\n", + "\n", + "# Store the fraction from the integration in I to obtain the fraction at given temperatures\n", + "# Create an empty list I2\n", + "I = []\n", + "# Add your solution here\n", + "### BEGIN SOLUTION\n", + "\n", + "I = fraction(T1, 0, 25)\n", + "\n", + "### END SOLUTION\n", + "\n", + "# print data\n", + "print(\"Fraction of Collisions that React with Barrier Height between 0-25 kcal/mol from 300 K to 1200 K: \\n\", I)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QnnncXwWU0Oz" + }, + "source": [ + "Now, obtain the ratio using the `I` obtained above comparing 300 K to 1200 K." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "F2-u8fBRTXce", + "outputId": "ee098fd3-ed2b-47ff-d41d-e3a7105ac68d" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Baseline resistance = 1.0000\n" + ] + } + ], + "source": [ + "#Add your solution here that will calculate and show the ratio here\n", + "### BEGIN SOLUTION\n", + "R = I[0]//I[1]\n", + "\n", + "### END SOLUTION\n", + "\n", + "# print the obtained ratio\n", + "print(\"Baseline resistance = {0:0.4f}\".format(R))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "aY2GkD4iXtXI" + }, + "source": [ + "### Additional Analysis\n", + "\n", + "As mentioned above, The distribution function $f(E,T)$ is most easily interpreted by recognizing that integrating $f(E,T)$ over a change dE is the **Fraction of Collisions** with energies between $E$ and $E + dE$\n", + "\n", + "\n", + "\\begin{equation}\n", + "\\int_{E}^{E + dE} f(E,T)dE....(Eq.5)\n", + "\\end{equation}\n", + "\n", + "\n", + "\n", + "\n", + "The **Reaction of Collisions** can be found by setting the lower integration limit equal to activation energy, $E_{A}$, and the upper integration limit to infinity as shown in Equation 6.\n", + "\n", + "\\begin{equation}\n", + "F(E>E_A,T) = \\int_{E_A}^{∞} f(E,T)dE....(Eq.6)\n", + "\\end{equation}\n", + "\n", + "\n", + "\n", + "\n", + "For $E_{A}$ > 3$RT$, an analytical approximation for the fraction of collision with energies greater than $E_{A}$ can be obtained by integrating Equation 5 from $E_{A}$ to infinity to get:\n", + "\n", + "\\begin{equation}\n", + "F(E>E_A,T) = (\\frac{2}{{π}^{0.5}})(\\frac{E_A}{RT})^{1/2}exp(\\frac{-E_A}{RT})....(Eq.7)\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zg5GdAq-C8yF" + }, + "source": [ + "## 4. Fraction of Collisions that have Energies Greater Than a Certain Value, $E_A$.\n", + "\n", + "### 4a. Manually integrate Equation 5 from $E_A$ to infinity and to get Equation 7.\n", + "\n", + "*Hint: the constants in the equation can be grouped and substituted with constant such as A and/or B for simplification*\n", + "\n", + "*Hint: use u-substition*\n", + "\n", + "Submit the written work via ***Gradescope***." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "qmx3mCg4DedZ" + }, + "source": [ + "### 4b. Numeric Integration\n", + "\n", + "Numerically integrate Equation 5 and evaluate at $E_A$ for $E_A$ ranging from 0 to 40." + ] + }, + { + "cell_type": "code", + "source": [ + "# gas constant needs to be converted into cal/k mol\n", + "R = 8.314*0.000239\n", + "\n", + "#add solution here\n", + "\n", + "# define energy range from 0 to 40 kcal\n", + "E_A = np.arange(.0,40,.1) # range for x-axis\n", + "\n", + "# temperature\n", + "T2 = 700 # units: K\n", + "\n", + "#define equation 7 as F_C\n", + "def F_C(E_A, T):\n", + " \"\"\"Calculating the fraction of collisions\n", + " Args:\n", + " E_A: activation energy (kcal/mol)\n", + " T: temperature (K)\n", + " Returns:\n", + " y: fraction of collisions with energy greater than E_A\n", + " \"\"\"\n", + " pi = math.pi\n", + " # calculation of fraction of collision\n", + " y = 2*pi*(1/(pi*R*T))**1.5*E_A**0.5*np.exp(-E_A/(R*T))\n", + "\n", + " return y" + ], + "metadata": { + "id": "kEJ0Ap_YpfEz" + }, + "execution_count": 10, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uH8g2S2yDksx" + }, + "source": [ + "### 4c. Visualization:\n", + "\n", + "Graph using the equation you have obtained from 4b for 700K." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 446 + }, + "id": "GB99P_10HcIx", + "outputId": "7b2a95da-b1ff-44ca-d0ac-efaf4cef7d9e" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "# plot the data\n", + "plt.figure(figsize=(6.4,4), dpi=100)\n", + "plt.grid()\n", + "plt.semilogy(E_A, F_C(E_A,T2), linewidth=3, label=\"Fraction of Collision\")\n", + "plt.ylim([10E-12,1])\n", + "plt.xlim([20,40])\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", + "plt.xlabel('$E_A$ [kcal/mol]',fontsize=16, fontweight = 'bold')\n", + "plt.ylabel('Fraction of Collisions that \\nLead to Reactions [(mol/kcal)]',fontsize=16, fontweight = 'bold')\n", + "plt.title('Fraction of Collisions that Lead to Reactions \\nversus Activation Energy', fontsize=16, fontweight = 'bold')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "source": [ + "### What does the plot above tell us?\n", + "\n", + "**Answer:** it tells us that as the activation energy increases, the amount of collisions that lead to reactions decreases. The relationship is linear" + ], + "metadata": { + "id": "VsF6GaKJ_1ld" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "bMRynDq0DpS9" + }, + "source": [ + "### 4d. What fraction of collisions have energies greater than $E$ = 25 kcal/mol?\n", + "\n", + "Hint: What is the y axis value when x = 25 kcal?" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "BbXq2KFny_Vd", + "outputId": "0b776635-750d-4a98-8a85-613ad91105d4" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Fraction of collisions have energies greater than E = 25 kcal/mol at 700K: \n", + " 5.37835222623192e-08 when E = 25 kcal\n" + ] + } + ], + "source": [ + "# Define constants\n", + "E_A1 = 25 # unit: kcal\n", + "\n", + "# Call the function F_C and calculate the fraction of collisions at 700K.\n", + "### BEGIN SOLUTION\n", + "F_C(E_A1,T2)\n", + "\n", + "### END SOLUTION\n", + "print(\"Fraction of collisions have energies greater than E = 25 kcal/mol at 700K: \\n\",F_C(E_A1,T2),\"when E = 25 kcal\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8htz9cwyD17l" + }, + "source": [ + "### 4e. Visualization at different temperature:\n", + "\n", + "Graph using the code you have obtained from 4b for 500K." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 423 + }, + "id": "j998WfmAHeI8", + "outputId": "32f4a252-3c41-435a-8d59-6359e3afe36a" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ], + "source": [ + "#add your solution here to get the graph shown below\n", + "E_A2 = np.arange(0,40,0.01)\n", + "# define temperature for this problem\n", + "T3 = 500 #unit: K\n", + "\n", + "# Call the funcation and calculate the fraction of collisions and create a semilog plot as shown in 4c.\n", + "#Add your solution here\n", + "### BEGIN SOLUTION\n", + "F_C(E_A2, T3)\n", + "\n", + "#Plot\n", + "plt.figure(figsize=(6.4,4), dpi=100)\n", + "plt.grid()\n", + "plt.semilogy(E_A2, F_C(E_A2,T3), linewidth=3, label=\"Fraction of Molecule\")\n", + "plt.xlabel('$E_A$ [kcal/mol]', fontsize=16, fontweight = 'bold')\n", + "plt.ylabel('Fraction of Molecule[(mol/kcal)]', fontsize=16, fontweight = 'bold')\n", + "plt.title('Fraction of Molecule graph', fontsize=16, fontweight = 'bold')\n", + "plt.ylim([10E-12,1])\n", + "plt.xlim([10,25])\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", + "plt.legend()\n", + "plt.show()\n", + "### END SOLUTION" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VraTYxTzD9vY" + }, + "source": [ + "### 4f. What fraction of molecules have collision energies greater than 15 kcal/mol at 500K?" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "0vPCNSoUHet-", + "outputId": "e46361cd-562d-4941-dcf3-351e12b9cb75" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "F_500 is 6.722248169794792e-11 when E_A = 15\n" + ] + } + ], + "source": [ + "# Find F_500 when E = 25\n", + "### BEGIN SOLUTION\n", + "F_C(E_A1, T3)\n", + "### END SOLUTION\n", + "\n", + "print(\"F_500 is\",F_C(E_A1, T3),\"when E_A = 15\")" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "8uS26QLefXAn", + "outputId": "c83f0db1-31d2-412f-bd99-5d4acfbe095b" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "F_700 is 5.37835222623192e-08 when E_A = 15\n" + ] + } + ], + "source": [ + "# Find F_700 when E = 25\n", + "### BEGIN SOLUTION\n", + "F_C(E_A1, T2)\n", + "\n", + "### END SOLUTION\n", + "\n", + "print(\"F_700 is\",F_C(E_A1, T2),\"when E_A = 15\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "swiSvh-OkQpr" + }, + "source": [ + "**Discussion:**\n", + "Compare fraction of collision that overcome an activation energy of 25 kcal/mol at 500 K and 700 K." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "wgP-3ca_kWdX" + }, + "source": [ + "**Answer**:\n", + "The fraction of collisions that overcome 25 kcal/mol increases 3 orders of magnitude from 500 K to 700 K." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ApAGEMY0kFyw" + }, + "source": [ + "## 5. Fraction of Collisions at Various Temperatures" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "npM5ktX3EGNp" + }, + "source": [ + "### 5a. Graph $f(E > E_A,T)$ versus $T$ for $E_A$ = 3, 10, 25 and 40 kcal/mol. Assume T varies from 1 K to 120 K. Use a semilog plot for the y-axis.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 442 + }, + "id": "ngJ4qqxfGduS", + "outputId": "a1fdeec5-524b-44c7-b115-69008d65bdd9" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "# define constants and data storage\n", + "# make a list for fraction storage\n", + "F3 = []\n", + "# redefine the range of temperature\n", + "T4 = np.arange(1,120,0.1) # Unit: K\n", + "# make a list for energy\n", + "EA3 = [3,10,25,40] #unit: kcal\n", + "pi = math.pi\n", + "\n", + "plt.figure(figsize=(6.4,4), dpi=100) #Figure size 4x4 with 300 DPi\n", + "# Create a loop for fraction calculation for different temperatures and to graph a semilog graph\n", + "# enter equation here\n", + "### BEGIN SOLUTION\n", + "for i in range(len(EA3)):\n", + " F3 = 2*pi**(-0.5)*((EA3[i]/(R*T4))**0.5)*np.exp(-EA3[i]/(R*T4))\n", + " plt.semilogy(T4, F3, label=str(EA3[i])+\" kcal/mol\",linewidth=3)\n", + "### END SOLUTION\n", + "\n", + "# plot\n", + "plt.grid()\n", + "plt.ylim([10E-292,1])\n", + "plt.xlim([0,120])\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", + "plt.xlabel('T [K]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", + "plt.ylabel('f($E > E_A$)[(mol/kcal)]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", + "plt.title(\"Fraction of Molecules that React as a Function of \\nTemperature at Various Activation Energies\", fontsize=16, fontweight = 'bold')\n", + "\n", + "\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "TeWOvx69ihEl" + }, + "source": [ + "**Discussion:** What does the graph above show?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QcYMcmh-ij0l" + }, + "source": [ + "**Answer**: As temperature increases, the fraction of molecules that react increases. Additionally, a lower activation energy leads to a higher fraction of molecules that react. The largest fraction of molecules will react at the highest temperature and with the lowest activation energy.\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## 6. Comparing Midpoint Rule to Gass Quadruture" + ], + "metadata": { + "id": "lCEsXaRC9q2c" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Our goal is to determine the amount of segments it takes before midpoint rule is approximately as good of an estimator as Gauss Quadrature." + ], + "metadata": { + "id": "LPhMFvjzvZck" + } + }, + { + "cell_type": "markdown", + "source": [ + "###6a. By hand, write out the midpoint rule and sketch an image describing the process" + ], + "metadata": { + "id": "QnVhVVRh9x3V" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer:** I_midpoint = $h*f((a+b)/2)$. For multiple pieces, sum up all the I_midpoints. A picture should show a rectangle (or several) that are centered at a given point and have width b-a." + ], + "metadata": { + "id": "l9a3Jztv-NvL" + } + }, + { + "cell_type": "markdown", + "source": [ + "### 6b. Write a function to numerically integrate the fraction of collisions using the midpoint rule. Evaluate at T = 800 K. Use E between 0 to 15 kcal/mol.\n", + "*Hint: this is similar to the midpoint code from the class website and trapezoid rule with multiple pieces. Basically, you are writing the midpoint rule with multiple pieces*\n" + ], + "metadata": { + "id": "oGKEYVdM-wNI" + } + }, + { + "cell_type": "code", + "source": [ + "# define and plot function\n", + "def midpoint_integration(N, plot = True):\n", + " \"\"\"\n", + " Args:\n", + " N = the number of rectangles\n", + " plot = a boolean that determines whether to generate plots or return the result of the integration\n", + " *This is useful because for visual purposes, you create a plot. For calculating errors, you will return the\n", + " integration result instead\n", + " Returns:\n", + " Imid = the approximate result of the integral (if !plot)\n", + " OR\n", + " generates a plot of the midpoint rule applied to the distribution of the fraction of collisions (if plot)\n", + " \"\"\"\n", + "\n", + " T = 800\n", + " E = np.linspace(0,15,100)\n", + "\n", + " # update the equation to represent the fraction of collisions\n", + " ### BEGIN SOLUTION ###\n", + " f = lambda E: 2*pi*(1/(pi*R*T))**1.5*E**0.5*np.exp(-E/(R*T))\n", + " ### END SOLUTION ###\n", + "\n", + " if plot:\n", + " plt.plot(E,f(E),label=\"f(x)\",color=\"blue\")\n", + " ax = plt.gca()\n", + "\n", + " # bounding a and b, finding width of each rectangle\n", + " far_left = 0\n", + " far_right = 15\n", + " width = (far_right - far_left)/N\n", + "\n", + " # initializing counter\n", + " Imid = 0\n", + "\n", + " # create a loop that approximates the integration using midpoint rule\n", + " # hint: a and b must update each iteration. The width between them is constant.\n", + " # hint: calculate the value of the function, plug into Imid formula, and add Imid to an accumulator\n", + " # call the evaluation of the function at (a+b)/2 \"mid\" for coherence with rectangle drawing code\n", + " ### BEGIN SOLUTION ###\n", + " for i in range(N):\n", + " a = i*width\n", + " b = i*width + width\n", + " mid = f((a + b)/2)\n", + " Imid += width*mid\n", + " ### END SOLUTION\n", + "\n", + " # draw rectangle\n", + " if plot:\n", + " verts = [(a,0),(a,mid), (b,mid),(b,0)]\n", + " poly = Polygon(verts, facecolor='0.8', edgecolor='k')\n", + " ax.add_patch(poly)\n", + "\n", + " if plot:\n", + " print(\"Integral estimate = \",Imid)\n", + "\n", + " if (plot == False):\n", + " return Imid\n", + "\n", + " if plot:\n", + " # add labels\n", + " plt.xlabel(\"x\")\n", + " plt.ylabel(\"f(x)\")\n", + " plt.title(\"Midpoint Rule\")\n", + " plt.show()" + ], + "metadata": { + "id": "BAny4QTJ_U0C" + }, + "execution_count": 17, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# call function to test\n", + "midpoint_integration(30)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 490 + }, + "id": "bofqzNpBDbDh", + "outputId": "8a78a157-deb8-46ea-e85f-772c169efdf8" + }, + "execution_count": 18, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Integral estimate = 1.0107343121299819\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 6c. Use scipy.integrate.quad to evaluate the same equation and bounds as in 6b.\n", + "*hint: this will produce an integer*\n" + ], + "metadata": { + "id": "8v3lyakT-6jS" + } + }, + { + "cell_type": "code", + "source": [ + "## finding integral of this function using scipy.integrate.quad\n", + "T = 800\n", + "result,error = integrate.quad(lambda E: 2*pi*(1/(pi*R*T))**1.5*E**0.5*np.exp(-E/(R*T)),0,15)\n", + "print(result)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "H2kF4ZmGyl5n", + "outputId": "25a76a88-d72e-43fb-bc54-7c1b0ae199b4" + }, + "execution_count": 21, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "0.9997094573570767\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 6d. Comparing Midpoint Rule to Gauss Quadrature.\n", + "\n", + "Evaluate the integral using the function from 6b over a range of N (between 1 and 50). This is the \"midpoint result\". Store the midpoint result in a vector. Next, subtract the Gauss Quadrature result from each midpoint result. Store the difference in a vector called compare.\n", + "*hint: cast N[i] as an int*\n", + "\n", + "*hint: set plot = False*" + ], + "metadata": { + "id": "8YyCm6seysSw" + } + }, + { + "cell_type": "code", + "source": [ + "points = 50\n", + "N = np.linspace(1, 50, points)\n", + "compare = np.zeros(points)\n", + "\n", + "### BEGIN SOLUTION\n", + "for i in range(points):\n", + " i = int(i)\n", + " compare[i] = midpoint_integration(int(N[i]), False)\n", + " compare[i] -= result\n", + "### END SOLUTION\n", + "\n", + "print(compare)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "p-tjM_UgyzOQ", + "outputId": "a89b29f8-60c4-4350-83d1-1957f26f5377" + }, + "execution_count": 24, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "[-0.79312238 -0.21494489 -0.00351488 0.05427425 0.06668412 0.06553709\n", + " 0.06051562 0.05475037 0.0492623 0.04434694 0.04004378 0.03630544\n", + " 0.03306072 0.03023791 0.02777264 0.02560982 0.02370324 0.02201446\n", + " 0.02051161 0.01916824 0.01796231 0.0168754 0.01589206 0.01499924\n", + " 0.01418588 0.01344258 0.01276129 0.01213509 0.011558 0.01102485\n", + " 0.01053115 0.01007296 0.00964683 0.00924973 0.00887898 0.00853222\n", + " 0.00820733 0.00790246 0.00761591 0.0073462 0.00709197 0.00685202\n", + " 0.00662525 0.00641067 0.0062074 0.0060146 0.00583156 0.00565759\n", + " 0.00549207 0.00533445]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### 6e. Plotting\n", + "Plot compare versus N. Make a publication quality figure.\n" + ], + "metadata": { + "id": "jOihDdotyjXG" + } + }, + { + "cell_type": "code", + "source": [ + "# plot the data\n", + "plt.figure(figsize=(6.4,4), dpi=100)\n", + "plt.grid()\n", + "\n", + "# write line that plots compare vs N\n", + "### BEGIN SOLUTION\n", + "plt.plot(N, compare, linewidth=3, label=\"Difference Between Gauss \\nQuadrature and Midpoint Rule\")\n", + "### END SOLUTION\n", + "plt.xticks(fontsize=15) #Tick font size 15\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", + "plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick direction: in\n", + "plt.xlabel('Number of Midpoint Rule Rectangles',fontsize=16, fontweight = 'bold')\n", + "plt.ylabel('Difference Between Midpoint \\nRule and Gauss Quadrature \\nIntegral Results',fontsize=16, fontweight = 'bold')\n", + "plt.title('Difference Between Midpoint Rule and Gauss \\nQuadrature for Varying Number of \\nMidpoint Rectangles', fontsize=16, fontweight = 'bold')\n", + "plt.legend()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 466 + }, + "id": "yheaT0CC-600", + "outputId": "c135ac4b-d8b3-4556-d6d0-6d6f01898019" + }, + "execution_count": 35, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "**Discussion**: What do you notice about the errors? At what value of N are the integral approximations roughly equal?" + ], + "metadata": { + "id": "69Ahz9usJxrc" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer**: For N > ~4, the difference approaches 0. The error becomes approximately 0 for N > 30, but for values of N > 10 is probably small enough." + ], + "metadata": { + "id": "KZEUKWaTJ7Lw" + } + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file From a179855825bc196829bd850f9e82b0bf5d50d763 Mon Sep 17 00:00:00 2001 From: alaudens <147085052+alaudens@users.noreply.github.com> Date: Thu, 2 Nov 2023 10:31:07 -0400 Subject: [PATCH 3/4] Delete notebooks/contrib-dev/Fraction_of_Molecular_Collisions.ipynb --- .../Fraction_of_Molecular_Collisions.ipynb | 1085 ----------------- 1 file changed, 1085 deletions(-) delete mode 100644 notebooks/contrib-dev/Fraction_of_Molecular_Collisions.ipynb diff --git a/notebooks/contrib-dev/Fraction_of_Molecular_Collisions.ipynb b/notebooks/contrib-dev/Fraction_of_Molecular_Collisions.ipynb deleted file mode 100644 index 68ea7754..00000000 --- a/notebooks/contrib-dev/Fraction_of_Molecular_Collisions.ipynb +++ /dev/null @@ -1,1085 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "m2aSfAcfI2b3" - }, - "source": [ - "# Calculating Fraction of Molecular Collisions #\n", - "\n", - "\n", - "CBE 60535, University of Notre Dame \n", - "\n", - "Problem 3.4 ( pg. 99 ) from Elements of Chemical Reaction Engineering by H. Scott Fogler, Fifth edition, 2016, ISBN: 978-0-13-388751-8. \n", - "\n", - "\n", - "Prepared by: \n", - "\n", - "Yun Young Choi ychoi3@nd.edu \n", - "\n", - "Bingxin Yang byang3@nd.edu\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "ePnjXaXiOZSd" - }, - "source": [ - "## Learning Objectives: \n", - "\n", - "After completing this assignment, you should be able to: \n", - "\n", - "\n", - "* Apply integration techniques to Ordinary Differential Equations using Python\n", - "* Plot multiple data on a single graph\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "3CGxT9KpPPmz" - }, - "source": [ - "## Intended Audiences: \n", - "\n", - "This problem is intended for undergraduate students in Chemical and Biomolecular Engineering students from the University of Notre Dame who have taken Chemical Reaction Engineering. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "i-R3Uyl8nF0a" - }, - "source": [ - "**Useful link to review library:**\n", - "\n", - "1. Plot\n", - "\n", - " https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html?highlight=plot\n", - "\n", - "2. Scipy\n", - "\n", - " https://ndcbe.github.io/data-and-computing/notebooks/07/Scipy-Library-Adaptive-Methods-for-Newton-Cotes-and-Gauss-Quadrature.html?highlight=scipy\n", - "\n", - "3. Integral\n", - "\n", - " https://ndcbe.github.io/data-and-computing/notebooks/01/Functions-as-Arguments.html?highlight=integral\n", - "\n", - "4. Ordinary Differential Equations\n", - "\n", - " https://ndcbe.github.io/data-and-computing/notebooks/07/Systems-of-Differential-Equations-and-Scipy.html?highlight=odes\n", - "\n", - "5. Sympy\n", - "\n", - " https://scipy-lectures.org/packages/sympy.html\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "eDHI0yKm5taD" - }, - "source": [ - "## Problem Statement:\n", - "Atoms and molecules have their own unique specific activation energy when undergoing reaction, and have specific minimum energy barriers that it must overcome, also known as barrier height. Now, we must know what fraction of molecular collisions have sufficient energy to cross over the barrier and react.\n", - "\n", - "For reactions in the gas phase, the reacting molecules will not have only one velocity, $U$, but it will also have a distribution of velocities, $f(U,T)$. Some will have high velocities and some will have low velocities as they move around and collide. These velocities are not defined with respect to a fixed coordinate system; these velocities are defined with respect to the other reactant molecules. The Maxwell-Boltzmann distribution of relative velocities is given by the probability function, $f(U,T)$: \n", - "\n", - "\\begin{equation}\n", - "f(U,T) = 4π(\\frac{m}{2πk_BT})^{3/2}exp(\\frac{-mU^2}{2k_BT})U^2....(Eq.1)\n", - "\\end{equation}\n", - "\n", - "$K_B$ = Boltzmann's constnat = 3.29 E-24 (cal/molecule/$K$) \n", - "\n", - "$m$ = Reduced mass $(g)$ \n", - "\n", - "$U$ = Relative velocity $(m/s)$ \n", - "\n", - "$T$= Absolute Temperature $(K)$ \n", - "\n", - "$e$ = Energy (kcal/molecule) \n", - "\n", - "$E$ = Kinetic energy (kcal/mol) \n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "4ndRniZECa6l" - }, - "source": [ - "Rather than using velocities to discuss the fraction of molecules with sufficient energy to cross the barrier, we convert these velocities to energies using the equation for kinetic energy in making this conversion:\n", - "\n", - "\\begin{equation}\n", - "e = \\frac{1}{2}mU^{2}....(Eq.2)\n", - "\\end{equation}\n", - "\n", - "Using this substitute, the Maxwell Boltzmann probability distribution of collision with energy $e$ $(cal/molecule)$ at temperature $T$ is \n", - "\n", - "\\begin{equation}\n", - "f(e,T) = 2π(\\frac{1}{πk_BT})^{3/2}e^{1/2}exp(\\frac{-e}{k_BT})....(Eq. 3)\n", - "\\end{equation}\n", - "\n", - "In terms of energy per mole, $E$, instead of energy per molecule, $e$ ,we have: \n", - "\n", - "\\begin{equation}\n", - "f(E,T) = 2π(\\frac{1}{πRT})^{3/2}E^{1/2}exp(\\frac{-E}{RT})....(Eq.4)\n", - "\\end{equation}\n", - "\n", - "where $E$ is in $(cal/mol)$, $R$ is in $(cal/mol/K)$, and $f(E,T)$ is in $(mol/cal)$." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "O43g8sWBFFa2" - }, - "source": [ - "The distribution function $f(E,T)$ is most easily interpreted by recognizing that $[f(E,T),dE]$ is the **Fraction of Collision** with enerfies between $E$ and $E + dE$\n", - "\n", - "\\begin{equation}\n", - "f(E,T)dE = 2π(\\frac{1}{πk_BT})^{3/2}E^{1/2}exp(\\frac{-E}{k_BT})dE....(Eq.5)\n", - "\\end{equation}\n", - "\n", - "For example, the fraction of collisions with energies between 0.25 and 0.35 kcal/mol would be:\n", - "\n", - "$$\\int_{0.25}^{0.35} f(E,T)dE$$\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "uOz-fAkiOwjb" - }, - "source": [ - "## Import Libraries: " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "id": "Z_Jn-nkBKOGO" - }, - "outputs": [], - "source": [ - "import math\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import pandas as pd\n", - "from sympy.geometry.line import pi_coeff\n", - "from sympy import *\n", - "from scipy import integrate\n", - "from scipy.integrate import quad" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "Grbj_M0lB1j1" - }, - "source": [ - "## 1. Visualizing Fraction of Collisions\n", - "\n", - "Plot the fraction of collision with energy per mole from 0 to 30 $kcal/mol$ for different given temperatures (T = 300, 500, 800 and 1200K). \n", - "\n", - "Hint: Fraction of collision as function of energy per mole, uses equation 4. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 389 - }, - "id": "8nONGxJPIYOe", - "outputId": "c832dc58-fcb9-42d6-ac63-25383d3157f9" - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Gas constant needs to be converted into cal/k mol\n", - "R = 8.314*0.000239\n", - "\n", - "# Generate an array of tempeartures for calculation based on the requirements\n", - "T = np.array([300,500,800,1200]) #unit: K\n", - "# Create an empty list to store Fraction of collions \n", - "F= [] \n", - "\n", - "pi = math.pi\n", - "\n", - "plt.figure(figsize=(6.4,4), dpi=100) #Plot figure size 6.4x4 with 300 DPi\n", - "# Create a for loop for fraction of collisions calculation at different temperatures from 0 to 30 kcal/mol\n", - "#add your solution here\n", - "### BEGIN SOLUTION\n", - "\n", - "for i in range(len(T)):\n", - " E = np.arange(0,30,.1) # range for x-axis \n", - " F= 2*pi*(1/(pi*R*T[i]))**1.5*E**0.5*np.exp(-E/(R*T[i])) \n", - " plt.plot(E,F,linewidth=3, label=\"Temp:\"+str(T[i])+\"K\")\n", - " i += 1\n", - "\n", - "### END SOLUTION\n", - "\n", - "# Plot\n", - "plt.xticks(fontsize=15) #Tick font size 15\n", - "plt.yticks(fontsize=15)\n", - "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", - "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", - "plt.grid()\n", - "plt.xlabel('E[kcal/mol]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", - "plt.ylabel(' f[(mol/kcal)]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "XWenw1DHCA8A" - }, - "source": [ - "Discussion: Explain how the fraction of collisions change as a function of given temperatures as you see on the graph. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "5g0fsad0CJVo" - }, - "source": [ - "**Answer**: When you look at the graph, you can see that fraction of collision increase with increasing temperature at $E$ = 5 kcal/mol. For kinetic energy lower than 5 kcal/mol, lower the temperature, the probability of collision is lower, therefore it will require more energy to get over the activation energy barrier. For higher temperature below $E$ = 5 kcal/mol, it will have more movement within itself that it require less energy." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "dL7XwxciCJ57" - }, - "source": [ - "## 2. Determining the Fraction of Molecules \n", - "What is the fraction of molecules that have sufficient energy to pass over an energy barrier of 25 kcal at 300,500, 800 and 1200K. \n", - "\n", - "Hint: Perform integration of $f(E,T)$ from 0 to 25 kcal?" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "id": "h6z_ScYVD1sj" - }, - "outputs": [], - "source": [ - "# Regenerate an array of tempeartures for calculation based on the requirements\n", - "\n", - "# Define a function for fraction of molecules that has sufficient energy to pass over an energy barrier calculation\n", - "def fraction(T):\n", - " \"\"\"Using integration to calculate the fraction of molecules from 0 to 25 kcal\n", - " Args:\n", - " T: temperature (K)\n", - " E: Energy (per mole)\n", - " Returns:\n", - " f(E,T) : distribution of collision for energy per mole (mol/cal)\n", - " \"\"\"\n", - "\n", - " # Store fraction of molecules that does not have sufficient energy to pass over an energy barrier of 25 kcal in a list\n", - " I = []\n", - "\n", - " # i in terms of the order of temperatures in T\n", - " i = 0\n", - " \n", - " # Create a for loop for integration calculation at different temperatures\n", - " # Add your solution here\n", - " ### BEGIN SOLUTION\n", - " for i in range(len(T)):\n", - " result,error = integrate.quad(lambda E: 2*pi*(1/(pi*R*T[i]))**1.5*E**0.5*np.exp(-E/(R*T[i])),0,25)\n", - " I.append(result)\n", - "\n", - " ### END SOLUTION\n", - "\n", - " return I " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "LFV8PSZ6Ur_o" - }, - "source": [ - "Store the fraction of molecule you integrated above into `I1`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "sf_QPxSqEHvx", - "outputId": "66f9e36f-0820-45d9-a848-58e8e70c04bf" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Fraction from 300 K to 1200 K from intergation: \n", - " [0.9999999999999933, 0.9999999999318481, 0.9999993178365589, 0.9998931593409495]\n" - ] - } - ], - "source": [ - "# Store data in I1 for the fraction\n", - "I1 =[]\n", - "# Add your solution here \n", - "### BEGIN SOLUTION\n", - "I1 = fraction(T)\n", - "\n", - "### END SOLUTION\n", - "\n", - "#Print I1 to confirm\n", - "print(\"Fraction from 300 K to 1200 K from intergation: \\n\", I1)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "W1Y_GkFMtVeM" - }, - "source": [ - "To get over an energy barrier, subtract fraction of molecule obtained from 1. \n", - "Store answers as a list in `F_1`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "A4CioKIeGHnA", - "outputId": "f08eee67-1e68-45fd-e69d-607ef990a1a9" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Fraction of molecules that has sufficient energy to pass over an energy barrier of 25 kcal: \n", - " [6.661338147750939e-15, 6.815192854503493e-11, 6.821634410680844e-07, 0.0001068406590505333]\n" - ] - } - ], - "source": [ - "# Create a list of fraction of molecules that has sufficient energy to pass over an energy barrier of 25 kcal from 300K to 1200 K\n", - "F_1 = [] #create an empty list\n", - "\n", - "# i in terms of the temperature order in T1\n", - "i = 0\n", - "\n", - "# Create a while loop that will calculate the fraction of molecules that has sufficient energy to pass over an energy barrier\n", - "# Add your solution here \n", - "### BEGIN SOLUTION\n", - "while i < 4:\n", - " F1 = 1 - I1[i]\n", - " F_1.append(F1)\n", - "\n", - " i += 1\n", - "\n", - "### END SOLUTION\n", - "\n", - "# Print results\n", - "print(\"Fraction of molecules that has sufficient energy to pass over an energy barrier of 25 kcal: \\n\", F_1)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "kxEt3olsCxVb" - }, - "source": [ - "## 3. Calculating the Ratio of the Fraction of Energies\n", - "\n", - "Create a list that shows fraction of energies between 0 and 25 kcal for 300 K and 1200 K. Store answer in `I2`\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "_LjTklXOIHze", - "outputId": "46f1d33d-4e8c-4f8c-e786-d7a06ebf033e" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Fraction from 300 K to 1200 K from intergation: \n", - " [0.9999999999999933, 0.9998931593409495]\n" - ] - } - ], - "source": [ - "# Define Temperature in a list T2 (300K and 1200K)\n", - "T1 = np.array([300,1200])\n", - "\n", - "# Store the fraction from the integration in I2 to obtain the fraction at differnt given tempeartures\n", - "# Create an empty list I2\n", - "I2 =[]\n", - "# Add your solution here \n", - "### BEGIN SOLUTION\n", - "\n", - "I2 = fraction(T1)\n", - "\n", - "### END SOLUTION\n", - "\n", - "# print data\n", - "print(\"Fraction from 300 K to 1200 K from intergation: \\n\", I2)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "QnnncXwWU0Oz" - }, - "source": [ - "Now, obtain the ratio using the `I2` obtained above comparing 300 K to 1200 K. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "F2-u8fBRTXce", - "outputId": "98c5b049-aad4-4d69-bba0-b4d61606346d" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Baseline resistance = 1.0000\n" - ] - } - ], - "source": [ - "# define a list for ratio data store\n", - "R = []\n", - "\n", - "#Add your solution here that will calculate and show the ratio here\n", - "### BEGIN SOLUTION\n", - "R = I2[0]//I2[1]\n", - "\n", - "### END SOLUTION\n", - "\n", - "# print the obtained ratio\n", - "print(\"Baseline resistance = {0:0.4f}\".format(R))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "aY2GkD4iXtXI" - }, - "source": [ - "### Additional Analysis\n", - "\n", - "As mentioned above, The distribution function $f(E,T)$ is most easily interpreted by recognizing that $[f(E,T)dE]$ is the **Fraction of Collision** with energies between $E$ and $E + dE$\n", - "\n", - "\n", - "\\begin{equation}\n", - "f(E,T)dE = 2π(\\frac{1}{πk_BT})^{3/2}E^{1/2}exp(\\frac{-E}{k_BT})dE....(Eq.5)\n", - "\\end{equation}\n", - "\n", - "\n", - "\n", - "\n", - "The **Reaction of Collision** that have energies greater than a certain value, $E_{A}$ can be expressed as below: \n", - "\n", - "\\begin{equation}\n", - "F(E>E_A,T) = \\int_{E_A}^{∞} f(E,T)dE....(Eq.6)\n", - "\\end{equation}\n", - "\n", - "\n", - "\n", - "\n", - "For $E_{A}$ > 3$RT$, analytical approximation for the fraction of molecules of collision with energies greater than $E_{A}$ as below can be obtained from equation 5 and 6 and integration: \n", - "\n", - "\\begin{equation}\n", - "F(E>E_A,T) = (\\frac{2}{{π}^{0.5}})(\\frac{E_A}{RT})^{1/2}exp(\\frac{-E_A}{RT})....(Eq.7)\n", - "\\end{equation}" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "zg5GdAq-C8yF" - }, - "source": [ - "## 4. Fraction of Collisions that have Energies Greater Than a Certain Value, $E_A$.\n", - "\n", - "### 4a. Manually integrate equation 5 to obtain the equation for fraction of collision from $E_A$ to infinite on your paper to get to equation 7.\n", - "\n", - "Hint: Starting with equation 5, integrate from $E_A$ to infinity (shown as equation 6) and solve to get equation 7.\n", - "\n", - "Hint 2: The constants in the equation can be grouped and substituted with constnat such as A and/or B. \n", - "\n", - "Hint 3: Use u-substition. \n", - "\n", - "Submit the written work via ***Gradescope***." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "qmx3mCg4DedZ" - }, - "source": [ - "### 4b. Numeric Integration \n", - "\n", - "Design a code that will integrate equation 5 to equation 7 for you and compare the equation you have obtained from 4a (written part). " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 61 - }, - "id": "DHKP-61pHbXh", - "outputId": "65440332-d011-458c-fb17-4a3b8492fb8e" - }, - "outputs": [ - { - "data": { - "image/png": "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", - "text/latex": [ - "$\\displaystyle \\int 2 E^{0.5} \\pi \\left(\\frac{1}{R T \\pi}\\right)^{1.5} e^{- \\frac{E}{R T}}\\, dE$" - ], - "text/plain": [ - " / \n", - " | \n", - " | -E \n", - " | 1.5 --- \n", - " | 0.5 / 1 \\ R*T \n", - " | 2*E *pi*|------| *e dE\n", - " | \\R*T*pi/ \n", - " | \n", - "/ " - ] - }, - "execution_count": 158, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Integrate the equation\n", - "#Define symbols\n", - "init_printing(use_unicode=False, wrap_line=False)\n", - "E = Symbol('E')\n", - "pi = Symbol('pi')\n", - "R = Symbol('R')\n", - "T = Symbol('T')\n", - "\n", - "# add your solution that shows integrated equation \n", - "### BEGIN SOLUTION\n", - "Integral((2*pi)*((1/(pi*R*T))**1.5)*(E**0.5)*exp(-E/(R*T)), E)\n", - "### END SOLUTION" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "l5ygVWLsv2PX" - }, - "source": [ - "Hint: you will run into gamma when doing the integration. Gamma is shown below:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "osR7QRywsEVS", - "outputId": "f1c18040-36ab-48e3-ba8b-a050dbc4fbf8" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(E_A/(R*T))**0.5*exp(-E_A/(R*T))\n" - ] - } - ], - "source": [ - "# lower case gamma follows this equation shown below \n", - "z = 1.5\n", - "E_A = Symbol('E_A')\n", - "t = E_A/(R*T)\n", - "gamma = (t**(z-1))*exp(-t)\n", - "print(gamma)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "jHq9sOHfwZ7P" - }, - "source": [ - "Label the integrated equation (eq.7) as `y`" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "id": "h4E4jLR_vUlh" - }, - "outputs": [], - "source": [ - "#define the integrated equation as y \n", - "#Add your solution here\n", - "### BEGIN SOLUTION\n", - "\n", - "y = 2*(pi**(-0.5))*((E_A/(R*T))**0.5)*exp(-E_A/(R*T))\n", - "\n", - "### END SOLUTION" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "uH8g2S2yDksx" - }, - "source": [ - "### 4c. Visualization: \n", - "\n", - "Graph using the equation you have obtained from 4b for 700K." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 453 - }, - "id": "GB99P_10HcIx", - "outputId": "122a548f-27a1-43e0-e982-e49dfb00c110" - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "### BEGIN SOLUTION\n", - "# gas constant needs to be converted into cal/k mol\n", - "R = 8.314*0.000239\n", - "\n", - "#add solution here\n", - "\n", - "# define energy range from 0 to 40 kcal\n", - "E_A = np.arange(.0,40,.1) # range for x-axis \n", - "\n", - "# temperature\n", - "T2 = 700 # units: K\n", - "\n", - "#define equation 7 (aka. y) as F_C\n", - "def F_C(E_A, T):\n", - " \"\"\"Calculating the fraction of collisions\n", - " Args:\n", - " E_A: Energy greater than certain value per mole (kcal/mol)\n", - " T: Temperature (K) \n", - " Returns:\n", - " y: Fraction of Collisions with energy greater than E_A\n", - " \"\"\"\n", - " pi = math.pi\n", - " # calculation of fraction of collision\n", - " y = 2*pi*(1/(pi*R*T))**1.5*E_A**0.5*np.exp(-E_A/(R*T))\n", - "\n", - " return y\n", - "\n", - "\n", - "# plot the data\n", - "plt.figure(figsize=(6.4,4), dpi=100)\n", - "plt.grid()\n", - "plt.semilogy(E_A, F_C(E_A,T2), linewidth=3, label=\"Fraction of Collision\")\n", - "plt.ylim([10E-12,1])\n", - "plt.xlim([20,40])\n", - "plt.xticks(fontsize=15) #Tick font size 15\n", - "plt.yticks(fontsize=15)\n", - "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", - "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", - "plt.xlabel('$E_A$ [kcal/mol]',fontsize=16, fontweight = 'bold') \n", - "plt.ylabel('Fraction of Collisions [(mol/kcal)]',fontsize=16, fontweight = 'bold')\n", - "plt.title('Fraction of Collision Graph', fontsize=16, fontweight = 'bold')\n", - "plt.legend()\n", - "plt.show()\n", - "\n", - "### END SOLUTION" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "bMRynDq0DpS9" - }, - "source": [ - "### 4d. What fraction of collisions have energies greater than $E$ = 25 kcal/mol?\n", - "\n", - "Hint: What is the y axis value when x = 25 kcal?" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "BbXq2KFny_Vd", - "outputId": "b350802f-21ef-4787-e30d-b5c050d75365" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Fraction of collisions have energies greater than E = 25 kcal/mol at 700K: \n", - " 5.37835222623192e-08 when E = 25 kcal\n" - ] - } - ], - "source": [ - "# Define constants\n", - "E_A1 = 25 # unit: kcal\n", - "\n", - "# Call the function F_C and calculate the fraction of collisions at 700K.\n", - "### BEGIN SOLUTION\n", - "F_C(E_A1,T2)\n", - "\n", - "### END SOLUTION\n", - "print(\"Fraction of collisions have energies greater than E = 25 kcal/mol at 700K: \\n\",F_C(E_A1,T2),\"when E = 25 kcal\")" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "8htz9cwyD17l" - }, - "source": [ - "### 4e. Visualization at different temperature:\n", - "\n", - "Graph using the code you have obtained from 4b for 500K." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 442 - }, - "id": "j998WfmAHeI8", - "outputId": "f8f61eb1-7362-46e5-a825-10f8807a7856" - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "#add your solution here to get the graph shown below\n", - "E_A2 = np.arange(0,40,0.01)\n", - "# define temperature for this problem\n", - "T3 = 500 #unit: K\n", - "\n", - "# Call the funcation and calculate the fraction of collisions and create a semilog plot as shown in 4c.\n", - "#Add your solution here\n", - "### BEGIN SOLUTION\n", - "F_C(E_A2, T3)\n", - "\n", - "#Plot \n", - "plt.figure(figsize=(6.4,4), dpi=100)\n", - "plt.grid()\n", - "plt.semilogy(E_A2, F_C(E_A2,T3), linewidth=3, label=\"Fraction of Molecule\")\n", - "plt.xlabel('$E_A$ [kcal/mol]', fontsize=16, fontweight = 'bold') \n", - "plt.ylabel('Fraction of Molecule[(mol/kcal)]', fontsize=16, fontweight = 'bold') \n", - "plt.title('Fraction of Molecule graph', fontsize=16, fontweight = 'bold')\n", - "plt.ylim([10E-12,1])\n", - "plt.xlim([10,25])\n", - "plt.xticks(fontsize=15) #Tick font size 15\n", - "plt.yticks(fontsize=15)\n", - "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", - "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", - "plt.legend()\n", - "plt.show()\n", - "### END SOLUTION" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "VraTYxTzD9vY" - }, - "source": [ - "### 4f. What fraction of molecules have energies greater than 15 kcal/mol at 500K?" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "0vPCNSoUHet-", - "outputId": "4f515c54-4015-4063-f77f-117c7b533b1c" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "F_500 is 6.722248169794792e-11 when E=15\n" - ] - } - ], - "source": [ - "# Find F_500 when E = 25\n", - "### BEGIN SOLUTION\n", - "F_C(E_A1, T3)\n", - "### END SOLUTION\n", - "\n", - "print(\"F_500 is\",F_C(E_A1, T3),\"when E=15\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "8uS26QLefXAn", - "outputId": "fb176454-4b36-491a-8b16-2b5daf68c06a" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "F_700 is 5.37835222623192e-08 when E=15\n" - ] - } - ], - "source": [ - "# Find F_700 when E = 25\n", - "### BEGIN SOLUTION\n", - "F_C(E_A1, T2)\n", - "\n", - "### END SOLUTION\n", - "\n", - "print(\"F_700 is\",F_C(E_A1, T2),\"when E=15\")" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "swiSvh-OkQpr" - }, - "source": [ - "Discussion: \n", - "Compare fraction of collision(of molecules) with energies greater than 25 kcal/mol at 500K and 700K. Explain the results below." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "wgP-3ca_kWdX" - }, - "source": [ - "**Answer**: \n", - "The fraction increases at 700K of 3 order of magnitude. The rate increases with the increasing fraction of collisions that have sufficient energy to cross over the barrier and form products." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "ApAGEMY0kFyw" - }, - "source": [ - "## 5. Fraction of Collisions at Various Temperatures" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "npM5ktX3EGNp" - }, - "source": [ - "### 5a. Graph $f(E > E_A,T)$ versus $T$ for $E_A$ = 3, 10, 25 and 40 kcal/mol.\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 389 - }, - "id": "ngJ4qqxfGduS", - "outputId": "25ac3e44-a7de-4b91-c626-a7cd08e2f854" - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# define constants and data storage\n", - "# make a list for fraction storage\n", - "F3 = []\n", - "# redefine the range of temperature\n", - "T4 = np.arange(1,120,0.1) # Unit: K\n", - "# make a list for energy\n", - "EA3 = [3,10,25,40] #unit: kcal\n", - "\n", - "# i in terms of the order in energy EA3\n", - "i = 0\n", - "\n", - "plt.figure(figsize=(6.4,4), dpi=100) #Figure size 4x4 with 300 DPi\n", - "# Create a loop for fraction calculation for different temperatures and to graph a semilog graph\n", - "# enter equation here \n", - "### BEGIN SOLUTION\n", - "for i in range(len(EA3)):\n", - " pi = math.pi\n", - " F3 = 2*pi**(-0.5)*((EA3[i]/(R*T4))**0.5)*np.exp(-EA3[i]/(R*T4))\n", - " plt.semilogy(T4, F3, label=\"$E_A$:\"+str(EA3[i])+\" [kcal/mol]\",linewidth=3)\n", - " i += 1\n", - "### END SOLUTION\n", - "\n", - "# plot \n", - "plt.grid()\n", - "plt.ylim([10E-292,1])\n", - "plt.xlim([0,120])\n", - "plt.xticks(fontsize=15) #Tick font size 15\n", - "plt.yticks(fontsize=15)\n", - "plt.tick_params(direction=\"in\",top=True, right=True) #Major tick direction: in\n", - "#plt.tick_params(which=\"minor\",direction=\"in\",top=True, right=True) #minor tick will make the graph look more crowded so is left out\n", - "plt.xlabel('T [K]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", - "plt.ylabel('f(E > $E_A$)[(mol/kcal)]', fontsize=16, fontweight = 'bold') #axis label font size: 16, bold\n", - "\n", - "\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "TeWOvx69ihEl" - }, - "source": [ - "Discussion: \n", - "What do you find from the plot from above?" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "QcYMcmh-ij0l" - }, - "source": [ - "**Answer**: \n", - "\n", - "From the graph, it can be seen that any temperature the fraction of collisions with energies greater than certain activation energy $(E_A)$ is inversely proportional to that activation energy. In other words, when activation energy is low, the molecule will need less energy to get over the activation energy barrier. At a higher temperature, the temperature will be the governing rule for $f$. \n" - ] - } - ], - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "display_name": "Python 3", - "name": "python3" - }, - "language_info": { - "name": "python" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} From d740eac76bed7064e4f251d4d517a0e2ed5fece6 Mon Sep 17 00:00:00 2001 From: alaudens <147085052+alaudens@users.noreply.github.com> Date: Thu, 2 Nov 2023 10:31:27 -0400 Subject: [PATCH 4/4] Rename Edited_Fraction_of_Molecular_Collisions.ipynb to Fraction_of_Molecular_Collisions.ipynb --- ..._Collisions.ipynb => Fraction_of_Molecular_Collisions.ipynb} | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) rename notebooks/contrib-dev/{Edited_Fraction_of_Molecular_Collisions.ipynb => Fraction_of_Molecular_Collisions.ipynb} (99%) diff --git a/notebooks/contrib-dev/Edited_Fraction_of_Molecular_Collisions.ipynb b/notebooks/contrib-dev/Fraction_of_Molecular_Collisions.ipynb similarity index 99% rename from notebooks/contrib-dev/Edited_Fraction_of_Molecular_Collisions.ipynb rename to notebooks/contrib-dev/Fraction_of_Molecular_Collisions.ipynb index bba848ac..6fdbf861 100644 --- a/notebooks/contrib-dev/Edited_Fraction_of_Molecular_Collisions.ipynb +++ b/notebooks/contrib-dev/Fraction_of_Molecular_Collisions.ipynb @@ -1238,4 +1238,4 @@ }, "nbformat": 4, "nbformat_minor": 0 -} \ No newline at end of file +}