{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[],"authorship_tag":"ABX9TyPNdVXfiGOmlKMEFAeMyy8m"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["#TP Titrage du vinaigre \n","L'objectif est ici de reprendre l'analyse faite avec open office calc\n"],"metadata":{"id":"gukBAfovxnn7"}},{"cell_type":"markdown","source":["Pour travailler avec Python il faut d'abord installer des bibliothèques dans lesquelles nous irons chercher des outils. "],"metadata":{"id":"Y8BRzonuyaLC"}},{"cell_type":"code","execution_count":2,"metadata":{"id":"1lgUjNIoxaZf","executionInfo":{"status":"ok","timestamp":1666023074276,"user_tz":-120,"elapsed":8,"user":{"displayName":"Physique Chimie Val d'Argens","userId":"11438166584008528880"}}},"outputs":[],"source":["#bibliothèques\n","import numpy as np\n","import matplotlib.pyplot as plt"]},{"cell_type":"markdown","source":["On va rentrer les mesures manuellement dans des tableaux numpy et afficher le graphique donnant le $p\\mathrm{H}$ en fonction du volume de solution titrante versé : $V$\n","1. Remplacer les valeurs par celles obtenues lors du TP\n","\n"],"metadata":{"id":"7DvBe0Nsyps3"}},{"cell_type":"code","source":["V=np.array([0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]) \n","pH= np.array([2.29,2.86,3.25,3.55,3.78,3.97,4.13,4.29,4.48,4.59,4.77,4.97,5.2,5.69,9.2,11.02,11.32,11.48,11.59,11.65,11.71,11.75,11.79,11.87,11.91,11.95]) # A remplir\n","\n","\n","#graphique\n","plt.figure(dpi=100) #permet d'afficher le graphique avec une meilleure résolution\n","plt.plot(V,pH,'b.',label='Expérience')\n","plt.xlabel('$V$ en mL')\n","plt.ylabel(r'$p$H')\n","plt.title('Titrage du vinaigre dilué 20 fois')\n","plt.legend()\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":405},"id":"oZJBNKZPyvXr","executionInfo":{"status":"ok","timestamp":1666023540762,"user_tz":-120,"elapsed":319,"user":{"displayName":"Physique Chimie Val d'Argens","userId":"11438166584008528880"}},"outputId":"8148ff7d-3760-428d-8854-d0365dd9e459"},"execution_count":8,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 600x400 with 1 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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["## Calcul de la dérivée : $\\dfrac{\\mathrm{d}p\\mathrm{H}}{\\mathrm{d}V}$\n","\n","On utilise ici la méthode du point milieu dans un premier temps, on rappelle qu'on ne peut pas calculer la dérivée au dernier point ainsi qu'au premier. \n","\n","$$\\dfrac{\\mathrm{d}p\\mathrm{H}}{\\mathrm{d}V}=\\dfrac{p\\mathrm{H}[i+1]-p\\mathrm{H}[i-1]}{V[i+1]-V[i-1]}\n","$$\n"],"metadata":{"id":"oXtrZJERuAUC"}},{"cell_type":"code","source":["#dérivée\n","dpH=np.array([]) #on crée un tableau vide\n","V1=np.array([])# on est obligé de créer un deuxième tableau qui ait la même dimension que dpH\n","\n","for i in range (1,len(V)-1): \n","  dpH=np.append(dpH,(pH[i+1]-pH[i-1])/(V[i+1]-V[i-1]))\n","  V1=np.append(V1,V[i])\n","\n","#graphique\n","plt.figure(dpi=100) #permet d'afficher le graphique avec une meilleure résolution\n","plt.plot(V,pH,'b.',label='Expérience')\n","plt.plot(V1,dpH,'r-', label='Dérivée')\n","plt.xlabel('$V$ en mL')\n","plt.ylabel(r'$p$H')\n","plt.title('Titrage du vinaigre dilué 20 fois')\n","plt.grid()\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":405},"id":"_8YgffGFuXZD","executionInfo":{"status":"ok","timestamp":1666024528692,"user_tz":-120,"elapsed":365,"user":{"displayName":"Physique Chimie Val d'Argens","userId":"11438166584008528880"}},"outputId":"ae36f3c5-40a9-4b88-8030-2a78cc515dd6"},"execution_count":17,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 600x400 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["## Recherche de la valeur de $V=V_{eq}$ où la dérivée est maximale "],"metadata":{"id":"c0o-KExTv0iu"}},{"cell_type":"code","source":["N=np.where(dpH==max(dpH))[0][0]# cherche l'indice du tableau dpH où la valeur est égale au maximun de dpH\n","Veq=V[N]#permet de calculer le volume à l'équivalence\n","print(N)\n","print('veq=',Veq,'mL')"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"01Et_DCBv8ce","executionInfo":{"status":"ok","timestamp":1666024537447,"user_tz":-120,"elapsed":498,"user":{"displayName":"Physique Chimie Val d'Argens","userId":"11438166584008528880"}},"outputId":"ebb7de67-e1df-4e07-9653-50b2f4c69554"},"execution_count":18,"outputs":[{"output_type":"stream","name":"stdout","text":["13\n","veq= 13 mL\n"]}]},{"cell_type":"markdown","source":["##A vous de jouer\n","A l'aide de ce qui précède essayer de calculer la dérivée avec la méthode dite à droite : \n","$$\\dfrac{\\mathrm{d}p\\mathrm{H}}{\\mathrm{d}V}=\\dfrac{p\\mathrm{H}[i+1]-p\\mathrm{H}[i]}{V[i+1]-V[i]}\n","$$"],"metadata":{"id":"Mgg7dwbXydY9"}},{"cell_type":"code","source":[],"metadata":{"id":"d5Yy7T34z4oq"},"execution_count":null,"outputs":[]}]}