{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "6z8XXwDn3H8n" }, "source": [ "# **1. Résultats expérimentaux**" ] }, { "cell_type": "code", "metadata": { "id": "zs2qhYgjmLLm" }, "source": [ "#Importation des bibliothèques essentielles\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import numpy.random as rd" ], "execution_count": 1, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "vIp0cEsEXUgJ" }, "source": [ "#Données du problème (A compléter)\n", "\n", "M = 60 #g/mol (masse molaire de l'acide éthanoïque)\n", "rho = 1020 #g/L (masse volumique du vinaigre)\n", "t_Vbur = 0.03 #mL (tolérance de la burette)\n", "t_Va = 0.05 #mL (tolérance de la pipette jaugée)\n", "Cb = 0.100 #mol/L\n", "u_Cb = 0.00058 #mol/L\n", "Va = 10 #mL\n", "u_Va = 0.029 #mL\n", "u_Ve = 0.05 #mL (à adapter en fonction du déroulement réel du titrage)\n" ], "execution_count": 2, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "Q9o9O4n8XQv1" }, "source": [ "#Résultats expérimentaux\n", "\n", "V = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11.25, 11.5, 11.75, 12, 12.25, 12.4, 12.65, 12.9, 13.2, 13.4, 13.7, 13.9, 14.2, 14.9, 15.4, 16.4, 17.4, 18.4, 19.4, 20.4, 21.4])\n", "pH = np.array([2.83, 3.72, 4.05, 4.27, 4.45, 4.60, 4.74, 4.88, 5.03, 5.20, 5.41, 5.70, 5.80, 5.94, 6.12, 6.42, 7.66, 10.86, 11.27, 11.47, 11.61, 11.71, 11.79, 11.85, 11.91, 12.04, 12.11, 12.21, 12.29, 12.35, 12.40, 12.44, 12.48])\n" ], "execution_count": 3, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "1hMINeh43U_Z" }, "source": [ "#**2. Tracé de la courbe du pH en fonction du volume de solution titrante versé**" ] }, { "cell_type": "code", "metadata": { "id": "iFcc-ViS3RUZ", "colab": { "base_uri": "https://localhost:8080/", "height": 472 }, "outputId": "937c0824-3b53-48bc-a6b3-1e7a3b9fb3d8" }, "source": [ "#Tracé de la courbe pH = f(V)\n", "\n", "plt.plot(V, pH, 'b+')\n", "plt.xlabel('Volume de solution titrante versée / mL')\n", "plt.ylabel('pH')\n", "plt.title('Evolution du pH en fonction de V')\n", "plt.grid()\n", "plt.show()" ], "execution_count": 4, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "metadata": { "id": "6S8xExHPplB8" }, "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", "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." ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 489 }, "id": "k11fQxYxoHBv", "outputId": "386e3d78-6fac-44ea-eb16-7994afebbc41" }, "source": [ "def VolEq(V, pH):\n", " dpHdV = (pH[2:]-pH[0:-2])/(V[2:]-V[0:-2]) # [2:] de 2 jusqu'à la fin ; [0:-2] de 0 jusqu'à l'avant avant dernier (on retire à partir de l'avant dernier élément d'où le -2)\n", " V2 = V[1:-1] # [1:-1] de 1 jusqu'à l'avant dernier élément (on retire le dernier élèment d'où le -1)\n", " return V2[np.argmax(dpHdV)] # np.argmax renvoie l'indice pour lequel l'élément de l'array argument est le plus grand\n", "\n", "plt.plot(V[1:-1], (pH[2:]-pH[0:-2])/(V[2:]-V[0:-2]), 'b.')\n", "plt.xlabel('Volume de solution titrante versée / mL')\n", "plt.ylabel('$\\dfrac{pH}{dV}$')\n", "plt.title('Courbe dérivée du pH en fonction du volume')\n", "plt.grid()\n", "plt.show()\n", "\n", "print('Veq =', VolEq(V, pH), 'mL')\n" ], "execution_count": 5, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} }, { "output_type": "stream", "name": "stdout", "text": [ "Veq = 12.25 mL\n" ] } ] }, { "cell_type": "code", "source": [ "#Calcul et affichage de la concentration du vinaigre dilué\n", "Cdilué = Cb*VolEq(V,pH)/Va\n", "print('Cdilué =', Cdilué, 'mol/L')" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "prOdOCiprFSg", "outputId": "cfa4ab86-69c0-4084-8992-5eaf067bf590" }, "execution_count": 6, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Cdilué = 0.12250000000000001 mol/L\n" ] } ] }, { "cell_type": "markdown", "metadata": { "id": "gMpO87TVAILT" }, "source": [ "# **4- Principe de la méthode Monte-Carlo**\n", "\n", "---\n", "\n", "\n", "**Le résultat d'une mesure correspond à l'ensemble des valeurs raisonnablement attribuables à la grandeur mesurée.**\n", "\n", "L'écart-type de cet ensemble de valeurs est appelée l'incertitude-type.\n", "\n", "**Evaluation de type A :** Lorsque la mesure est répétée plusieurs fois, l'expérimentateur obtient plusieurs valeurs de la grandeur mesurée. L'incertitude-type est l'écart-type de cet ensemble de valeurs.\n", "\n", "**Evaluation de type B :** Lorsque l'expérience n'est pas répétée plusieurs fois, il faut mettre en oeuvre une autre méthode pour évaluer l'incertitude-type. Dans ce contexte, la méthode de Monte-Carlo consiste à simuler numériquement la répétition de l'expérience. L'écart-type de l'ensemble des valeurs obtenues lors de ces répétitions *in silico* fournit l'incertitude-type recherchée.\n", "\n", "La méthode de Monte-Carlo est très utile à mettre en oeuvre dans le cas d'une **propagation d'incertitudes**, c'est-à-dire lorsque l'on souhaite déterminer l'incertitude-type sur une grandeur calculée à partir de grandeurs expérimentales, mesurées ou fournies.\n", "\n", "## Sources d'incertitudes\n", "\n", "L'incertitude sur la concentration en acide est liée aux incertitudes sur les grandeurs $\\mathsf{ [CH_3COOH]_{titrée} \\text{ , } [HO^-]_{titrante} \\text{ et } V_{eq}}$. Celles-ci doivent être évaluées.\n", "\n", "Proposition à adapter en fonction de la situation :\n", "\n", "* **volume de solution titrée :** l'expérimentateur a utilisé une pipette jaugée de $\\mathsf{10 mL}$ pour prélever le volume $\\mathsf{V_{sol}}$. Selon l'habileté du manipulateur et la classe de la pipette, le volume effectivement prélevé a de grandes chances d'appartenir à l'intervalle $\\mathsf{[9,9 \\text{ , } 10,1] \\text{ mL}}$ *(valeurs à adapter selon le contexte et l'expérimentateur)*,\n", "\n", "* **concentration de la solution titrante :** selon la qualité des réactifs utilisés, la nature de la verrerie utilisée et l'habileté du préparateur, la solution titrante de concentration affichée $\\mathsf{[HO^-]_{titrante} = 0,100 \\text{ mol} \\cdot L^{-1}}$ a de grandes chances d'appartenir à l'intervalle $\\mathsf{[0.099 \\text{ , } 0.101] \\text{ mol} \\cdot L^{-1}}$ *(valeurs à adapter selon le contexte et l'expérimentateur)*,\n", "\n", "* **volume équivalent :** selon l'espacement entre les points de mesure sur la courbe de titrage, selon la méthode retenue pour évaluer le volume équivalent, selon la précision de la burette graduée utilisée et la capacité de l'expérimentateur à lire les volumes sur les graduations et à régler le zéro, on peut penser que si le volume équivalent $\\mathsf{V_{eq} = 9.7 \\text{ mL}}$ alors il a de grandes chances d'appartenir à l'intervalle $\\mathsf{[9.6 \\text{ , } 9.8] \\text{ mL}}$ *(valeurs à adapter selon le contexte et l'expérimentateur)*.\n", "\n" ] }, { "cell_type": "markdown", "source": [ "\n", "# **5- Etapes de la méthode**\n", "\n", "---\n", "\n", "1. Lister les grandeurs expérimentales utiles pour le calcul de $\\mathsf{ [CH_3COOH]_{titrée}}$ et associer à chacune, un intervalle au sein duquel on peut raisonnablement penser que celle-ci appartient,\n", "\n", "2. Faire procéder à un tirage au sort aléatoire d'un jeu de valeurs pour chaque grandeur expérimentale $\\mathsf{[HO^-]_{titrante} \\text{ et } V_{sol} \\text{ et } V_{eq}}$ et faire calculer la valeur de concentration $\\mathsf{ [CH_3COOH]_{titrée}}$ obtenue avec ce jeu de valeurs.\n", "\n", "3. Stocker la valeur dans une liste de résultats,\n", "\n", "4. Calculer la moyenne des valeurs de concentration $\\mathsf{ [CH_3COOH]_{titrée}}$ obtenues, meilleur estimateur de la concentration recherchée,\n", "\n", "5. Calculer l'écart-type de l'ensemble des valeurs de concentration, incertitude-type associée à $\\mathsf{ [CH_3COOH]_{titrée}}$.\n", "\n", "\n" ], "metadata": { "id": "dNWsrCu2vzTB" } }, { "cell_type": "markdown", "source": [ "\n", "# **6- Fonctions pour réaliser le tirage au sort**\n", "\n", "---\n", "\n", "La bibliothèque `numpy` est ici utilisée pour simuler un processus aléatoire (`numpy.random`).\n", "\n", "Pour réaliser le tirage au sort :\n", "\n", "* Si l'on suppose que la *valeur centrale* de l'intervalle **n'est pas plus probable** que les valeurs latérales de l'intervalle, on peut utiliser la commande `numpy.random.uniform(borne_inf , borne_sup)`.\n", "\n", "* Si l'on suppose que la *valeur centrale* de l'intervalle **est plus probable** que les valeurs latérales de l'intervalle, on peut utiliser la commande `numpy.random.triangular(borne_inf , centre , borne_sup)`.\n", "\n", "* Si **l'incertitude-type sur la grandeur est fournie/connue**, on peut utiliser la commande `numpy.random.normal(valeur centrale , incertitude-type)`." ], "metadata": { "id": "T91kPHD6v83O" } }, { "cell_type": "markdown", "source": [ "# **7- Exemple de code**" ], "metadata": { "id": "i_Ev-LjNu5bH" } }, { "cell_type": "code", "source": [ "# Simulation de N = 10000 titrages par la méthode de Monte Carlo\n", "N = 10000 # nombre de tirages à réaliser\n", "\n", "Va_sim = Va + rd.normal(0,u_Va, N) # simulation des valeurs de Va\n", "Cb_sim = Cb + rd.normal(0,u_Cb, N) # simulation des valeurs de Cb\n", "Ve_sim = 12.25 + rd.normal(0,u_Ve, N) # simulation des valeurs de Ve\n", "\n", "Ca_sim = Cb_sim*Ve_sim/Va_sim # simulation des valeurs de Ca\n", "\n", "# Représentation de l'histogramme\n", "plt.hist(Ca_sim, bins='rice')\n", "plt.show()\n" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 430 }, "id": "Vl2GIFJbu-l9", "outputId": "7d1ff4c6-c694-4a48-aebc-1bbbb8bcdf4b" }, "execution_count": 7, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ] }, { "cell_type": "code", "source": [ "# Analyse statistique des résultats de la simulation de Monte Carlo\n", "Ca_moy = np.average(Ca_sim) #Calcul de la valeur moyenne de Ca_sim\n", "uCa = np.std(Ca_sim,ddof=1) #Calcul de l'écart-type\n", "\n", "print(f'Concentration Ca : {Ca_moy} mol/L') #Affichage des résultats\n", "print(f'Incertitude-type u(Ca) : {uCa} mol/L')" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "pDqT4mYZxjq1", "outputId": "b39688e3-52ad-4a4d-9751-38edd0775030" }, "execution_count": 8, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Concentration Ca : 0.12248506555884883 mol/L\n", "Incertitude-type u(Ca) : 0.0009430697677779632 mol/L\n" ] } ] }, { "cell_type": "markdown", "source": [ "# **8- Conclusion**\n", "\n", "---\n", "\n", "\n", "Calculer le degré d'acidité du vinaigre et comparer à l'étiquette.\n" ], "metadata": { "id": "FcstWKVbvEie" } } ] }