{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UVDFKcw0M4PR"
      },
      "source": [
        "#**1. Dosage pH - métrique des ions carbonate par l'acide chlorhydrique**\n",
        "\n",
        "## Description du protocole :\n",
        "- On procède à l'étalonnage du pH - mètre grâce aux solutions tampon de $pH = 4,0$ et $pH = 7,0$ ,\n",
        "- On remplit la burette d'une solution d'acide chlorhydrique ($\\mathrm {H_{3}O_{(aq)}^{+}, Cl_{(aq)}^{-})}$ à une concentration de $\\mathrm {0,1 \\ mol.L^{–1}}$\n",
        "- On prélève $20,0 \\ mL$ d'une solution de carbonate de solution $\\mathrm {( CO_{3(aq)}^{2-} , 2 Na_{(aq)} ^{+})}$ à l'aide d'une pipette jaugée deux traits de $20,0 \\ mL$ dont on cherche la concentration.\n",
        "\n",
        "## Mesures\n",
        "On relève le $pH$ en fonction du volume d'acide chlorhydrique versé en faisant très attention aux variations de $pH$. L'ajout s'arrête vers $\\mathrm {V_{acide} = 20, 0 \\ mL}$ quand on s'aperçoit que le second saut de pH est bien dépassé.\n",
        "\n",
        "La courbe est tracée au fur et à mesure de la prise des points."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "96fck9ucND4s"
      },
      "source": [
        "#Scripts Python\n",
        "On entre les valeurs de pH et de volumes relevées sous deux tableaux \"array\" disctincts.\n",
        "\n",
        "L'idée est de :\n",
        "  - Tracer la courbe pH - métrique,\n",
        "  - Ecrire une fonction dérivée pour déterminer le ou les volumes à l'équivalence,\n",
        "  - Calculer la concentration de la dibase,\n",
        "  - Tracer l'évolution des quantités de matière en fonction du volume de titrant versé, d'une façon générale :\n",
        "    - la dibase, ici les ions carbonate\n",
        "    - l'espèce amphotère, ici les ions hydrogénocarbonate\n",
        "    - le diacide, ici l'acide carbonique\n",
        "    - le titrant, ici l'acide chlorhydrique"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jk-8suNRNJrM"
      },
      "source": [
        "#Importation des bibliothèques\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# Entrée des valeurs expérimentales\n",
        "Va = np.array([## à compléter ##])\n",
        "pH = np.array([## à compléter ##])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#**2. Tracé de la courbe du pH en fonction du volume de solution titrante versé**"
      ],
      "metadata": {
        "id": "FRAhHQclWGOw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Tracé de la courbe pH = f(V)\n",
        "\n",
        "plt.plot(## à compléter ##)\n",
        "plt.xlabel('Volume de solution titrante versée / mL')\n",
        "plt.ylabel('pH')\n",
        "plt.title('Evolution du pH en fonction de Va versé')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "N2q5AmaHVg1s",
        "outputId": "ab2d8d3c-8dc3-48ce-ac40-d844a55aee90"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5i2d4fQjWvV0"
      },
      "source": [
        "# **3. Évaluation du volume équivalent**\n",
        "\n",
        "On estime numériquement les valeurs de $\\frac{\\mathrm{d}pH}{\\mathrm{d}V}$ pour divers volumes $V$ de solution titrante versée. Les valeurs de $\\frac{\\mathrm{d}pH}{\\mathrm{d}V}$ sont déterminées à l'aide de la dérivée centrée sur un point d'abscisse $V_i$, c'est à dire :\n",
        "\n",
        "$$ \\left( \\dfrac{dpH}{dV} \\right)_i =  \\dfrac {pH_{i+1}-pH_{i-1}}{V_{i+1}-V_{i-1}}. $$\n",
        "\n",
        "Ce schéma numérique limite en partie l'influence du bruit et n'induit pas de décalage. Il faut noter qu'on ne peut évaluer ainsi la dérivée sur les points extrèmes — on n'en a de toute façon pas besoin. On crée une fonction `VolEq` qui prend en argument les array `V` et `pH`, et qui retourne :\n",
        "* un array contenant les dérivées numériques ;\n",
        "* un array contenant les volumes, privés des deux points extrèmes.\n",
        "\n",
        "Pour évaluer le volume équivalent, on repère le volume qui maximise la dérivée précédemment calculée.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LOEc7svGNWQ6"
      },
      "source": [
        "#Calcul de la dérivée :\n",
        "- Calcul de la dérivée centrée via numpy qui fait tout le travail : élimination des deux points en amont et en aval pour permettre le calcul sur les vecteurs.\n",
        "- Numpy balaye automatiquement le tableau pour calculer les valeurs de cette dérivée centrée. Cela permet d'éviter de faire des boucles conditionnelles (type for ou while).\n",
        "\n",
        " - Exemple de premiers calculs : (10.45 - 10.83) / (1.0-0.0) = -0.38 et ainsi de suite : (10.27-10.63)/(1.5-0.5) = -0.36\n",
        "\n",
        "- En Python, avec Numpy, pour sélectionner un sous-ensemble de données dans un `array`, on utilise les crochets []. Par exemple :\n",
        "  * pour avoir un sous-ensemble des 10 _premiers_ éléments d'un `array` `x`, on fait : `x[:9]` ;\n",
        "  * pour avoir un sous-ensemble des 10 _derniers_ éléments d'un `array` `x`, on fait : `x[-9:]` ;\n",
        "  * pour avoir un sous ensemble avec les 2e, 3e et 4 éléments d'un `array` `x`, on fait : `x[1:4]` ;\n",
        "  * si on écrit `x[:-2]`; on enlève les deux *derniers* éléments d'un `array` `x` ;\n",
        "  * si on écrit `x[2:]`; on enlève les deux *premiers* éléments d'un `array` `x`.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def derivee1(x,y):\n",
        "    return (y[2:]-y[:-2])/(x[2:]-x[:-2])\n",
        "\n",
        "derpH = derivee1(Va, pH)\n",
        "\n",
        "Va_sub = Va[1:-1] # on redimensionne les valeurs de Va pour qu'elles soient de même taille que derpH\n",
        "\n",
        "\n",
        "plt.plot(## à compléter ##)\n",
        "plt.xlabel(\"Va (mL)\")\n",
        "plt.ylabel(\"$\\dfrac{pH}{dV}$'\")\n",
        "plt.grid(linestyle='-.')\n",
        "plt.title(\"détermination d'un volume à l'équivalence\")\n",
        "plt.xlim(0,20)\n",
        "plt.ylim(-10,0)\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "print('Vaeq 2 =', Va_sub[np.argmin(derpH)], 'mL')\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "-K1wBcClXOMB",
        "outputId": "d90e8bb3-d85a-4896-a76b-c1431336712e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Vaeq 2 = 10.0 mL\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sV614HkePS4r"
      },
      "source": [
        "# Détermination des deux volumes à l'équivalence"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k5ReGPYUZUuR"
      },
      "source": [
        "Pour l'instant, on a obtenu uniquement le second volume à l'équivalence.\n",
        "Pour obtenir également le premier, on peut également utiliser des opérateurs booléens pour sélectionner certaines valeurs. Par exemple :\n",
        "* `Va[Va<14]` sélectionne toutes les valeurs de `Va` qui sont plus petites que 14 ;\n",
        "* `Va[(Va<14) & (Va>1)]` sélectionne toutes les valeurs de `Va` qui sont plus petites que 14 et plus grandes que 1.\n",
        "\n",
        "On décide d'afficher les valeurs des volumes pour lesquels la dérivée du pH est inférieure à un seuil qu'on se donne en regardant le graphe précédent. Cela permet d'en déduire les deux volumes équivalents."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gu2CphsvPXQJ",
        "outputId": "d3ebdad8-c6ce-43c1-d544-07f45511140b"
      },
      "source": [
        "print( Va_sub[derpH<## à compléter ##], \"\\n\", derpH[derpH<## à compléter ##], sep='' )"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 4.6  4.8  5.   9.8 10.  10.2]\n",
            "[-2.    -2.85  -2.05  -3.025 -4.3   -2.725]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rNzpGU4KP534"
      },
      "source": [
        "#Calcul de l'évolution des quantités de matière au cours du dosage\n",
        "\n",
        "\n",
        "Méthode classique, valeur sûre, qui utilise des boucles conditionnelles et des listes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "5psMdomSQFlD",
        "outputId": "89de5876-129b-44a4-bfb5-aa5ef1afd4c6"
      },
      "source": [
        "#Calcul de la concentration de la dibase\n",
        "Ca = 0.1  # concentration de la solution titrante de l'acide chlorhydrique\n",
        "V_0=20.0\n",
        "Vae1=4.8\n",
        "Vae2=10\n",
        "\n",
        "C_b=(## à compléter ##)\n",
        "print (\"La concentration de la dibase est : \" , round(C_b,3),  \"en mol.L^-1\")\n",
        "\n",
        "#création des listes qui seront retransformées en tableaux numpy\"\n",
        "n_carb=[]\n",
        "n_amph=[]\n",
        "n_acide=[]\n",
        "n_acide_carb=[]\n",
        "\n",
        "def n_avant_eq1(i):\n",
        "                                            #La commande append permet de remplir une liste au fur et à mesure des itérations\n",
        "    n_carb.append((## à compléter ##))\n",
        "    n_amph.append(## à compléter ##)\n",
        "    n_acide.append(## à compléter ##)\n",
        "    n_acide_carb.append(## à compléter ##)\n",
        "\n",
        "def n_entre_Veq(i):\n",
        "    n_carb.append(## à compléter ##)\n",
        "    n_amph.append(## à compléter ##)\n",
        "    n_acide.append(## à compléter ##)\n",
        "    n_acide_carb.append(## à compléter ##)\n",
        "\n",
        "def n_apres_eq(i):\n",
        "                                         #La commande append permet de remplir une liste au fur et à mesure des itérations\n",
        "  n_carb.append(## à compléter ##)\n",
        "  n_amph.append(## à compléter ##)\n",
        "  n_acide_carb.append(## à compléter ##)\n",
        "  n_acide.append(## à compléter ##)\n",
        "\n",
        "\n",
        "for i in Va:\n",
        "    if i<=Vae1:\n",
        "     n_avant_eq1(i)\n",
        "\n",
        "    elif Vae1 < i < Vae2:\n",
        "\n",
        "     n_entre_Veq(i)\n",
        "\n",
        "    else:\n",
        "     n_apres_eq(i)\n",
        "\n",
        "#transformation des listes en array\n",
        "n_carb=np.array(n_carb)\n",
        "n_acide=np.array(n_acide)\n",
        "n_amph=np.array(n_amph)\n",
        "n_acide_carb=np.array(n_acide_carb)\n",
        "\n",
        "#Affichage graphique\n",
        "plt.plot(Va,n_carb,'+-', color= \"blue\", label=\"n(ions carbonate)\")\n",
        "plt.plot(Va,n_amph,'+-',color= \"purple\", label=\"n(ions hydrogénocarbonate)\")\n",
        "plt.plot(Va,n_acide_carb,'+-', color= \"green\", label=\"n(acide carbonique)\")\n",
        "plt.plot(Va,n_acide,'+-', color= \"red\", label=\"n(acide chlorhydrique)\")\n",
        "\n",
        "plt.xlabel('V en mL')\n",
        "plt.ylabel('n en mmol')\n",
        "plt.title('Évolution des quantités de matière au cours du titrage')\n",
        "plt.legend()\n",
        "plt.grid(linestyle='-.')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "La concentration de la dibase est :  0.025 en mol.L^-1\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}