chemical-kinetics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kinetics and the evolution of a system\n",
    "\n",
    "In this notebook we aim at checking the **order of a reaction** on the basis of data collected and stored in a file. \n",
    "\n",
    "This is going to be applied to any time-evolution of any chemical transformation.\n",
    "\n",
    "## Rate law from the function of concentration\n",
    "\n",
    "The goal is to calculate the order of reaction with respect to a reactant. As an example we will consider the spontaneous decomposition of oxygenated water $H_2O_2$: \n",
    "\n",
    "$$ 2\\,H_2O_2{(aq)} \\longrightarrow 2\\,H_2O_{(l)} \\,+\\, O_2{(aq)} $$\n",
    "\n",
    "we will first focus on the concentration of $[H_2O_2]$, that decreases as the reaction evolves.\n",
    "\n",
    "*The speed of a chemical reaction is to be defined as the change in concentration of a substance divided by the time interval during which this change is observed.*\n",
    "\n",
    "Our first approach will be based on this definition of the speed:\n",
    "\n",
    "\n",
    "$$v = \\frac{1}{V}\\frac{d \\,m_{H_2O_2}}{dt} = \\frac{d[H_2O_2]}{dt}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time (s)</th>\n",
       "      <th>C1 (mol/L)</th>\n",
       "      <th>C2 (mol/L)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>10.00</td>\n",
       "      <td>10.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50</td>\n",
       "      <td>7.94</td>\n",
       "      <td>9.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>6.30</td>\n",
       "      <td>8.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>150</td>\n",
       "      <td>5.00</td>\n",
       "      <td>7.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>200</td>\n",
       "      <td>3.97</td>\n",
       "      <td>6.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>250</td>\n",
       "      <td>3.15</td>\n",
       "      <td>6.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>300</td>\n",
       "      <td>2.50</td>\n",
       "      <td>5.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>350</td>\n",
       "      <td>1.98</td>\n",
       "      <td>4.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>400</td>\n",
       "      <td>1.58</td>\n",
       "      <td>4.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>450</td>\n",
       "      <td>1.25</td>\n",
       "      <td>3.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>500</td>\n",
       "      <td>0.99</td>\n",
       "      <td>3.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>550</td>\n",
       "      <td>0.79</td>\n",
       "      <td>3.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>600</td>\n",
       "      <td>0.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>650</td>\n",
       "      <td>0.50</td>\n",
       "      <td>2.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>700</td>\n",
       "      <td>0.39</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>750</td>\n",
       "      <td>0.31</td>\n",
       "      <td>2.16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Time (s)  C1 (mol/L)  C2 (mol/L)\n",
       "0          0       10.00       10.00\n",
       "1         50        7.94        9.03\n",
       "2        100        6.30        8.15\n",
       "3        150        5.00        7.36\n",
       "4        200        3.97        6.65\n",
       "5        250        3.15        6.00\n",
       "6        300        2.50        5.42\n",
       "7        350        1.98        4.90\n",
       "8        400        1.58        4.42\n",
       "9        450        1.25        3.99\n",
       "10       500        0.99        3.61\n",
       "11       550        0.79        3.26\n",
       "12       600        0.63        2.94\n",
       "13       650        0.50        2.65\n",
       "14       700        0.39        2.40\n",
       "15       750        0.31        2.16"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "C = pd.read_csv('data_kinetics.csv')\n",
    "\n",
    "# two series of experiments have been conducted\n",
    "# C.columns # to display the descriptor of each column\n",
    "C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question 1: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "t,x,y = np.loadtxt(fname='data_kinetics.csv',unpack=True,usecols=(0,1,2),delimiter=\",\",skiprows=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data analysis is one of the most used techniques.\n",
    "\n",
    "Investigate the data above: opening the file can also be done using `numpy` library even if `pandas` is the most used one. Give a precise definition of the following parameters:\n",
    "\n",
    "- fname \n",
    "- unpack\n",
    "- usecols\n",
    "- delimiter\n",
    "- skiprows\n",
    "\n",
    "Answer 1:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The expression of the concentration\n",
    "c1 = C[\"C1 (mol/L)\"]\n",
    "C1 = np.array(c1)\n",
    "\n",
    "\n",
    "# The expression of acquisition time \n",
    "# each times step is 50s from the following\n",
    "t = C[\"Time (s)\"]\n",
    "t = np.array(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we consider a reagent, whose concentration is $[H_2O_2]$ and called `c` in the code, and we acquire such concentrations at equally spaced times $t_i$. For $i$ ranging from `0` to `len(c)-1` the speed is:\n",
    "$$ v_i = - \\dfrac{[H_2O_2]_{i+1}-[H_2O_2]_i}{t_{i+1}-t_i} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Declaration of variables:\n",
    "\n",
    "c = C1 # Fetch c from imported table\n",
    "v = np.diff(c)/50 # calculate the speed\n",
    "c = np.delete(c, len(c)-1, 0) # remove the last point of c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisation of the data\n",
    "t=np.array(C[\"Time (s)\"])\n",
    "t=np.delete(t, len(t)-1, 0)# remove the last point of t\n",
    "# Be careful the array t has been modified\n",
    "\n",
    "plt.plot(t,v,marker= '+',color='blue')\n",
    "plt.xlabel('Time in seconds')\n",
    "plt.ylabel('Volumic speed in (mol/L/s)')\n",
    "plt.title('Time evolution of speed')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The predicted linear model is \"v = a x c + b\" whose characteristics are: \n",
      " a = -0.004123383030417634\n",
      " b = -8.313270752246388e-06\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Linear Regression\n",
    "a, b, r, p, err = stats.linregress(c, v)\n",
    "print ('The predicted linear model is \"v = a x c + b\" whose characteristics are: \\n a = ' + str(a) + '\\n b = ' + str(b))\n",
    "\n",
    "# Figure plot of the speed and its linear predicted model \n",
    "# As a function of concentration\n",
    "plt.scatter(c, v, marker = '+', color = 'blue')\n",
    "plt.plot(c, a*c+b, color = 'red')\n",
    "\n",
    "plt.xlabel('Concentration in (mol/L)')\n",
    "plt.ylabel('Volumic speed of disapearence (mol/L/s)')\n",
    "plt.title('Speed evolution as a function of \\n the reactive concentration')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this we can infer that the reaction follows a first order rate law\n",
    "\n",
    "$$ v=k[H_2O_2] $$\n",
    "\n",
    "with \n",
    "- $k$ being the reaction rate coefficient in $s^{-1}$\n",
    "- $v$ the volumic speed of disapearance in $mol.L^{-1}.s^{-1}$\n",
    "- $[H_2O_2]$ the concentration of the reactant $H_2O_2(aq)$ in $mol.L^{-1}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We consider how to derive a rate law from this reaction.\n",
    "\n",
    "$$ \\dfrac{[H_2O_2]_t}{[H_2O_2]_0} = e^{-kt} $$\n",
    "\n",
    "## The Differential Representation\n",
    "\n",
    "Another way to calculate the reaction rate is to involve a differential equation:\n",
    "\n",
    "$$Rate = - \\dfrac{d[H_2O_2]}{dt} = k[H_2O_2]^1 = k[H_2O_2] \\label{1}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'H2O2 Concentration in mol/L')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Representation of the data collected \n",
    "t = C[\"Time (s)\"]\n",
    "t = np.array(t)\n",
    "\n",
    "plt.plot(t,x,marker= 'o', color='red')\n",
    "\n",
    "plt.xlabel(\"Time in seconds\")\n",
    "plt.ylabel(\"H2O2 Concentration in mol/L\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Perform an curve fit\n",
    "\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "def exp_func(t, a, b, c):\n",
    "    return a * np.exp(-b * t) + c\n",
    "\n",
    "time = t\n",
    "cdf = x\n",
    "popt, pcov = curve_fit(exp_func, t, x, bounds=(0, [10, 0.1, 1]))\n",
    "plt.plot(t, x,'b.')\n",
    "plt.plot(t, exp_func(t, *popt), 'r-', label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))\n",
    "plt.ylabel('Concentration in (mol/L)')\n",
    "plt.xlabel('Time in seconds')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that there is a need to Constrain the optimization to the region of  $$0 \\leq a \\leq 10$$  $$0 \\leq  b \\leq 0.1$$ $$0 \\leq c \\leq 1$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.004123383030417634\n",
      "-0.004620963839771338\n"
     ]
    }
   ],
   "source": [
    "# Compare the two methods to extract the constant k\n",
    "\n",
    "# Method 1: Getting the slope of the logarithm from the volumetric speed\n",
    "\n",
    "c = C1 # Fetch c from imported table\n",
    "v = np.diff(c)/50 # calculate the speed\n",
    "c = np.delete(c, len(c)-1, 0) # remove the last point of c\n",
    "\n",
    "a1, b, r, p, err = stats.linregress(c, v)\n",
    "print(a1)\n",
    "\n",
    "# Method 2: Fitting directly the exponential curve\n",
    "\n",
    "\n",
    "a,b2,c=tuple(popt)\n",
    "print(-b2) # Exponential factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question 2:\n",
    "\n",
    "Make the same analysis for the set of data that is in column 2\n",
    "\n",
    "Answer 2:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem\n",
    "\n",
    "On a bottle of oxygenated water $H_2O_2$, the label states: *\"Hydrogen peroxide stabilised at 110 volumes, it contains approximately 30% by weight of hydrogen peroxide and is capable of releasing approximately 110 times its volume of gaseous oxygen under standard conditions of temperature (273 K) and pressure (1.013 bar)\"*. Determine the concentration of $H_2O_2$ and the precise percentage by mass knowing that the density of the solution is $d=1.114$.\n",
    "\n",
    "One liter of $H_2O_2$ produces 110 liters of molecular oxygen folowing the dismutation relation:\n",
    "\n",
    "$$ H_2O_2{(aq)} \\longrightarrow H_2O_{(l)} \\,+\\,\\frac{1}{2} \\,O_2{(aq)} $$\n",
    "\n",
    "Calulate the number of moles of dioxygen obtained.\n",
    "\n",
    "$$n_{O_2} = PV/RT $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of moles of dioxygen is 0 mol\n"
     ]
    }
   ],
   "source": [
    "# Numerical application\n",
    "P=1.013E5#Pascal for one atmosphere\n",
    "V=110*1E-3#m3 of dioxygen gaz\n",
    "R=8.314#SI perfect gas constant\n",
    "T=273#Temperature in Kelvin\n",
    "\n",
    "#Write the literal expression of the \n",
    "#number of moles ?\n",
    "\n",
    "n_O2=0\n",
    "\n",
    "print(\"The number of moles of dioxygen is {} mol\".format(n_O2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Using the stochiometry of the reaction infer how many moles for H2O2\n",
    "n_H2O2=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Using the molar mass of H2O2 we infer the mass of the n_H2O2 moles\n",
    "# M_H2O2 = 34.0147 g/mol\n",
    "\n",
    "M_H2O2 = 34.0147#g/mol\n",
    "\n",
    "m_1_H2O2=M_H2O2*n_H2O2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Give the actual mass of H2O2 and divide by the total mass of one liter of such sample given the density\n",
    "# d_H2O is one kilogram per liter.\n",
    "\n",
    "d_H2O=1#kg per Liter\n",
    "d_H2O2=1.114*d_H2O#kg per Liter\n",
    "m_2_H2O2=d_H2O2/d_H2O*1#Mass in Kg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What is the massic in percentage ?\n",
    "m_1_H2O2/m_2_H2O2*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Questions 3:\n",
    "\n",
    "Commercial oxygenated water is **10 Vol** considering the same resolution give the percentage which is expected.\n",
    "\n",
    "**Answer:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "____"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "M=166.0028# g/mol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "V=0.1# L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1660.028"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M/V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.30119973879958645\n"
     ]
    }
   ],
   "source": [
    "m=5#g\n",
    "n=m/M\n",
    "c=n/V\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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