{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"Fiche Réactions acide-base et de précipitation.ipynb","provenance":[{"file_id":"1o8aw74np1uWX0D72Zp4WwRcUwKPOAPLu","timestamp":1655448074968}],"collapsed_sections":[],"authorship_tag":"ABX9TyOIf/EI1Nfl4HK8VV1uMw6X"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["**Tracer, à l’aide d’un langage de programmation, le diagramme de distribution des espèces d’un ou plusieurs couples acide-base, ou d’espèces impliquées dans une réaction de précipitation.**"],"metadata":{"id":"s_hLhivUZX4N"}},{"cell_type":"markdown","source":["Diagramme de distribution du couple $HNO_2/NO_2^-$ de pKa = 3.2"],"metadata":{"id":"Rl1GkkTsZg-S"}},{"cell_type":"code","source":["import numpy as np #Pour faire divers calculs\n","import matplotlib.pyplot as plt #Pour tracer des graphiques\n","\n","## Données pour la réaction étudiée\n","K=10**(-3.2) \t\t#valeur de K\n","\n","## Définition des fonctions\n","def HA(x):\t\t# % de HA (h/(Ka+h))\n","\treturn (x)/(K+x)*100\n","def A(x): \t\t# % de A- (Ka/(Ka+h))\n","\t return K/(K+x)*100\n","\n","## Graphe\n","n=100\t\t#nombre de points de l'intervalle pH = [0;14]\n","x_min= 0\t#pH_min\n","x_max=14\t #pH_max\n","x = np.linspace(x_min,x_max,n) \t#liste des pH\n","h=10**(-x) \t#liste des [H3O+]\n","acide = []\t\t\t#initialisation du np.array des %HA\n","base = []\t\t\t#initialisation du np.array des %A-\n","for h in h: \t\t#boucle de calcul des concentrations sur l'intervale\n","\tacide.append(HA(h))\t#calcul et stockage des %HA\n","\tbase.append(A(h))\t#calcul et stockage des %A-\n","plt.figure(1)\n","plt.xlabel('pH') \t#légende de l’axe des abscisses\n","plt.ylabel('%') \t#légende de l’axe des ordonnées\n","plt.plot(x,acide,'b-',label='%HNO_2')\n","#représente %HA en fonction du pH en bleu de manière continue avec une étiquette pour la courbe\n","plt.plot(x,base,'r-',label='%NO_2-')\n","#représente %A- en fonction du pH en rouge de manière continue avec une étiquette pour la courbe\n","plt.legend() #affiche l’étiquette de la courbe\n","plt.grid() #affiche le quadrillage\n","plt.show() #affiche le graphique\n","print('pKa = 3.2')\n"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":297},"id":"XhzsgJxqZix1","executionInfo":{"status":"ok","timestamp":1655735991025,"user_tz":-120,"elapsed":309,"user":{"displayName":"Lionnel Malara","userId":"16342666118884215780"}},"outputId":"2026a9d1-7744-4fe9-8457-1d0dbeb29cdb"},"execution_count":2,"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":["pKa = 3.2\n"]}]},{"cell_type":"markdown","source":["Diagramme de distribution du l'acide phosphorique $H_3PO_4$ de pKa = 2.1 ; 7.2 et 12.4"],"metadata":{"id":"gGXtT4bzNYQQ"}},{"cell_type":"code","source":["import numpy as np #Pour faire divers calculs\n","import matplotlib.pyplot as plt #Pour tracer des graphiques\n","\n","## Données pour la réaction étudiée\n","K1=10**(-2.1) \t\t#valeur de K1\n","K2=10**(-7.2) \t\t#valeur de K2\n","K3=10**(-12.4) \t\t#valeur de K3\n","\n","## Définition des fonctions\n","def H3A(x):\t\t# % de H3A (h^3/(Ka1*Ka2*Ka3+h*Ka1*Ka2+h^2*Ka1+h^3))\n","\treturn (x**3)/(K1*K2*K3+x*K1*K2+x**2*K1+x**3)*100\n","def H2A(x): \t\t# % de H2A-(h^2*Ka1/(Ka1*Ka2*Ka3+h*Ka1*Ka2+h^2*Ka1+h^3))\n","  return x**2*K1/(K1*K2*K3+x*K1*K2+x**2*K1+x**3)*100\n","def HA(x): \t\t# % de HA-2 (h*Ka1*Ka2/(Ka1*Ka2*Ka3+h*Ka1*Ka2+h^2*Ka1+h^3))\n","\treturn x*K1*K2/(K1*K2*K3+x*K1*K2+x**2*K1+x**3)*100\n","def A(x): \t\t# % de A-3 (Ka1*Ka2*Ka3/(Ka1*Ka2*Ka3+h*Ka1*Ka2+h^2*Ka1+h^3))\n","\treturn K1*K2*K3/(K1*K2*K3+x*K1*K2+x**2*K1+x**3)*100  \n","\n","## Graphe\n","n=100\t\t#nombre de points de l'intervalle pH = [0;14]\n","x_min= 0\t#pH_min\n","x_max=14\t #pH_max\n","x = np.linspace(x_min,x_max,n) \t#liste des pH\n","h=10**(-x) \t#liste des [H3O+]\n","diacide = []\t\t\t#initialisation du np.array des %H3A\n","amph1 = []\t\t\t#initialisation du np.array des %H2A-\n","amph2 = []\t\t\t#initialisation du np.array des %HA-2\n","dibase = []\t\t\t#initialisation du np.array des %A-3\n","\n","for h in h: \t\t#boucle de calcul des concentrations sur l'intervale\n","  diacide.append(H3A(h))\t#calcul et stockage des %H3A\n","  amph1.append(H2A(h))\t#calcul et stockage des %H2A-\n","  amph2.append(HA(h))\t#calcul et stockage des %HA-2\n","  dibase.append(A(h))\t#calcul et stockage des %A-3\n","\n","plt.figure(1)\n","plt.xlabel('pH') \t#légende de l’axe des abscisses\n","plt.ylabel('%') \t#légende de l’axe des ordonnées\n","plt.plot(x,diacide,'b-',label='%H3A')\n","#représente %H3A en fonction du pH en bleu de manière continue avec une étiquette pour la courbe\n","plt.plot(x,amph1,'g-',label='%H2A-')\n","#représente %H2A- en fonction du pH en vert de manière continue avec une étiquette pour la courbe\n","plt.plot(x,amph2,'y-',label='%HA-2')\n","#représente %HA-2 en fonction du pH en jaune de manière continue avec une étiquette pour la courbe\n","plt.plot(x,dibase,'r-',label='%A-3')\n","#représente %A- en fonction du pH en rouge de manière continue avec une étiquette pour la courbe\n","plt.legend() #affiche l’étiquette de la courbe\n","plt.grid() #affiche le quadrillage\n","plt.show() #affiche le graphique\n","print('pKa_1 = 2.1 ; pKa_2 = 7.2 ; pKa_3 = 12.4')"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":297},"id":"6-nLhqSIhl48","executionInfo":{"status":"ok","timestamp":1642409788565,"user_tz":-60,"elapsed":419,"user":{"displayName":"Lionnel 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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}},{"output_type":"stream","name":"stdout","text":["pKa_1 = 2.1 ; pKa_2 = 7.2 ; pKa_3 = 12.4\n"]}]},{"cell_type":"markdown","source":["Diagramme de distribution d'un précipité $AgCl$ de pKs = 9.8"],"metadata":{"id":"2A0hz9KWZ5gP"}},{"cell_type":"code","source":["import numpy as np #Pour faire divers calculs\n","import matplotlib.pyplot as plt #Pour tracer des graphiques\n","\n","## Données pour la réaction étudiée\n","pKs=9.8 \t\t#valeur de pKs\n","C_0=0.01\t\t#concentration initiale de Ag(+) en mol/L\n","\n","## Définition des fonctions\n","def Ag(C):\t\t# % de Ag(+)\n","\treturn 100*(10**(-pKs))/C/C_0\n","\n","## Graphe\n","n=10000\t\t#nombre de points de l'intervalle pCl\n","x_min= 5\t#pCl_min\n","x_max=10\t #pCl_max\n","x = np.linspace(x_min,x_max,n) \t#liste des pCl\n","ion_Ag =[]\t\t\t#initialisation du np.array des %Ag(+)\n","Cl=10**(-x)\t\t\t#concentration de Cl(-)\n","for Cl in Cl: \t\t#boucle de calcul des pourcentages de Ag(+) sur l'intervale\n","\tif Cl*C_0<10**(-pKs):\t#test de condition de précipitation\n","\t\tion_Ag.append(100)\t#pourcentages de Ag(+) si aucun précipité\n","\telse:\n","\t\tion_Ag.append(Ag(Cl))\t#pourcentages de Ag(+) si AgCl existe\n","\n","plt.figure(1)\n","plt.xlabel('pCl') \t#légende de l’axe des abscisses\n","plt.ylabel('%Ag(+)') \t#légende de l’axe des ordonnées\n","plt.plot(x,ion_Ag,'b-',label='%Ag(+)')\n","#représente %Ag(+) en fonction du pCl en bleu de manière continue avec une étiquette pour la courbe\n","plt.legend() #affiche l’étiquette de la courbe\n","plt.grid() #affiche le quadrillage\n","plt.show() #affiche le graphique\n"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"jiKoTzG4Z6LN","executionInfo":{"status":"ok","timestamp":1655448312878,"user_tz":-120,"elapsed":590,"user":{"displayName":"Lionnel Malara","userId":"16342666118884215780"}},"outputId":"76e0c19e-4974-43f3-8d6c-4dbea283687e"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 432x288 with 1 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\n"},"metadata":{"needs_background":"light"}}]}]}