C03-EX24-professeur-explications.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Titre](C03.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <span style='color:#AC1620'> Explication du programme en langage Python</span>\n",
    "\n",
    "### <span style='color:#163538'> Exercice 24 p 68  : Traitement d'un effluent </span>\n",
    "\n",
    "**Pour faire fonctionner le programme à l'aide de Jupyter Notebook, il faut exécuter les cellules contenant du code les unes après les autres** \n",
    "\n",
    "La première étape consiste à importer :\n",
    "* le logarithme décimal *log10* de la bibliothèque <span style='color:red' > math </span> ;\n",
    "* la bibliothèque <span style='color:red' > matplotlib.pyplot </span> avec l'alias *plt*. Elle sert à réaliser le graphique ;\n",
    "* la bibliothèque <span style='color:red' > numpy </span> avec l'alias *np* . Elle est utile pour de nombreux outils mathématiques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import log10\n",
    "### Bibliothèques importées\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On définit l'ensemble des constantes et variables utilisées dans ce programme :\n",
    "* *VE* est le volume versé à l'équivalence, exprimé en L. Il vaut $13 \\times 10^{-3}~ \\mathrm{L}$ ;\n",
    "* *Veff* est le volume d'effluent à traiter, exprimé en L. Il vaut $200~ \\mathrm{L}$ ; \n",
    "* *compteur* est un compter initialisé à 0, utilisé plus loin dans le programme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Définition des variables\n",
    "VE=13*0.001\n",
    "Veff=200    \n",
    "compteur=0    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On calcule la quantité de matière initiale en ion hydroxyde présente dans l'effluent. D'après la réaction support du titrage : \n",
    "$$ n(\\mathrm{HO^-})=n(\\mathrm{H_3O^+})_E = Veff \\times \\frac{[\\mathrm{H_3O^+}] \\times VE}{V_0} $$\n",
    "où $V_0$ est le volume d'effluent pour le titrage conductimétrique en B. Ainsi : \n",
    "$$n(\\mathrm{HO^-})_{\\mathrm{initial}}= Veff \\times \\frac{5,0 \\times 10^{-2} \\times VE}{1,0 \\times 10^{-3}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "nHOinitial=Veff*(0.05*VE/0.001)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On définit ensuite le volume maximal _Vmax_ à introduire. Il correspond à une quantité de matière en ion oxonium deux fois plus importante que la quantité de matière en ion hydroxyde. C'est une valeur entière qui est retenue. Ainsi : \n",
    "$$n(\\mathrm{H_3O^+})= 2 \\times n(\\mathrm{HO^-})_{\\mathrm{initial}} = [\\mathrm{H_3O^+}] \\times Vmax \\Rightarrow Vmax= \\frac{\\displaystyle 2 \\times n(\\mathrm{HO^-})_{\\mathrm{initial}}}{\\displaystyle [\\mathrm{H_3O^+}]}= \\frac{\\displaystyle 2 \\times n(\\mathrm{HO^-})_{\\mathrm{initial}}}{\\displaystyle 10}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vmax=int(2*(nHOinitial/10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On initialise les listes qui seront utiles :\n",
    "* _nOH_ correspond à la quantité de matière en ions hydroxyde ;\n",
    "* _nH_ correspond à la quantité de matière en ions oxonium ; \n",
    "* _pH_ est la liste qui rassemble les valeurs du pH ; \n",
    "* _V_ est la liste qui rassemble les volumes versés en solution d'acide chlorhydrique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "nHO, nH, pH, V = [nHOinitial], [0], [-log10(1E-14/(nHOinitial/Veff))], [0] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remplit alors les listes à l'aide du compteur _compteur_ qui correspond au volume versé en solution d'acide. Pour cela en rentre dans une boucle ``while`` qui tournera tant que le compteur est inférieur ou égal à _Vmax_.\n",
    "\n",
    "On initialise une variable _aux_ qui correspond à la quantité de matière en ions hydroxyde qu'il reste dans la solution d'effluent : \n",
    "$$aux = n(\\mathrm{HO^-})_{\\mathrm{initial}} - [\\mathrm{H_3O^+}] \\times V = nOHinitial - 10 \\times compteur$$.\n",
    "\n",
    "On rentre alors dans un boucle conditionnelle : \n",
    "* Si _aux_ est supérieure à 0, cela signifie que l'on est avant l'équivalence : \n",
    "    * La quantité de matière en ions hydroxyde est égale à _aux_. On complète la liste.\n",
    "    * La quantité de matière en ion oxonium est nulle.\n",
    "    * Le pH se déduit de la concentration en ion hydroxyde : \n",
    "    $$pH = - \\log \\left( \\frac{\\displaystyle \\mathrm{Ke}}{\\displaystyle [\\mathrm{HO^-}]} \\right) = - \\log \\left( \\frac{\\displaystyle \\mathrm{Ke}\\times (Veff+ V)}{\\displaystyle n(\\mathrm{HO^-})} \\right)= - \\log \\left( \\frac{\\displaystyle 1,0 \\times 10^{-14}\\times (Veff+ V)}{\\displaystyle aux} \\right) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Si la quantité d'ions oxonium versée est supérieur à la quantité initiale en ion hydroxyde _nOHinitial_, cela signifie que l'équivalence est dépassée : \n",
    "    * La quantité de matière en ions hydroxyde est nulle.\n",
    "    * La quantité de matière en ion oxonium vaut : \n",
    "    $$n(\\mathrm{H_3O^+}) = [\\mathrm{H_3O^+}] \\times V - n(\\mathrm{HO^-})_{\\mathrm{initial}} = 10 \\times compteur -  nOHinitial$$\n",
    "    * Le pH se déduit de la concentration en ions oxonium : \n",
    "    $$pH = - \\log \\left( [\\mathrm{H_3O^+}] \\right)=- \\log \\left( \\frac{\\displaystyle n(\\mathrm{H_3O^+}) }{\\displaystyle Veff + V} \\right)=- \\log \\left( \\frac{\\displaystyle n(\\mathrm{H_3O^+}) }{\\displaystyle Veff + compteur} \\right)  $$\n",
    "\n",
    "* Sinon, cela signifie que le volume correspond au volume équivalent le pH est alors égal à 7.\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Remplissage des listes\n",
    "while compteur <= Vmax :\n",
    "    compteur=compteur+1\n",
    "    aux=nHOinitial-10*compteur\n",
    "    if aux > 0 :\n",
    "        nHO.append(aux)\n",
    "        nH.append(0)\n",
    "        V.append(compteur)\n",
    "        pH.append(- log10(1E-14/(aux/(Veff+compteur))))   #expression du pH si on connaît [HO-]\n",
    "    elif 10*compteur-nHOinitial > 0 :\n",
    "        nHO.append(0)\n",
    "        nH.append(10*compteur-nHOinitial)\n",
    "        V.append(compteur)\n",
    "        pH.append(- log10(nH[compteur]/(Veff+compteur)))\n",
    "    else :\n",
    "        nHO.append(0)\n",
    "        nH.append(0)\n",
    "        V.append(compteur)\n",
    "        pH.append(7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On trace le graphique à l'aide des fonctions de la bibliothèque <span style='color:red' > matplotlib.pyplot </span>.\n",
    "\n",
    "On crée une figure de 1600 pixels de large sur 800 pixels de haut à l'aide de la commande (``plt.figure(figsize=(16,8))``)\n",
    "On crée deux sous-figures à l'aide de la commande ``plt.subplot()``.\n",
    "\n",
    "Pour chaque sous-figure : \n",
    "* ``plt.plot(x,y,args)`` permet de tracer la courbe souhaitée;\n",
    "* ``plt.legend()`` permet d'insérer sur le graphique une légende pour chacune des courbes ;\n",
    "* ``plt.ylim()`` permet de fixer les limites de l'axe des ordonnées ;\n",
    "* ``plt.xlabel()`` permet d'ajouter un titre à l'axe des abscisses ;\n",
    "* ``plt.ylabel()`` permet d'ajouter un titre à l'axe des ordonnées.\n",
    "\n",
    "Enfin,  ``plt.show()`` permet d'afficher le graphique ainsi obtenu."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Affichage des graphiques\n",
    "plt.figure(figsize=(16,8))\n",
    "plt.subplot(121)\n",
    "plt.plot(V, nHO, 'bx-', label=\"$n(\\mathrm{HO^-})$ en mol\")\n",
    "plt.plot(V, nH, 'rx-', label=\"$n(\\mathrm{H_3O^+}) en mol\")\n",
    "plt.xlabel(\"volume en L\")\n",
    "plt.ylabel('$n$ (mol)')\n",
    "plt.legend()\n",
    "plt.subplot(122)\n",
    "plt.ylim(0,14) #définition des valeurs max et min des ordonnées\n",
    "plt.plot(V, pH, 'rx-', label=\"pH\")\n",
    "plt.xlabel(\"volume en L\")\n",
    "plt.ylabel('$pH$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
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