{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"Fiche résolution système d'équations avec fsolve.ipynb","provenance":[],"authorship_tag":"ABX9TyM3DvUG7nJq4MrPQA2V2T12"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"code","source":["import numpy as np #Pour faire divers calculs\n","from scipy.optimize import fsolve #Importe la fonction pour faire la résolution d’équation\n","\n","## Constantes d’équilibre et concentration initiale\n","K1=10**(-4.8) # K° de la réaction 1 HA + H2O = A(-) + H3O(+)\n","K2=10**(-14) # K° de la réaction 2 H2O = HO(-) + H3O(+)\n","C=1e-7 # Concentration initiale de HA en mol/L\n","def f1(x): #définit la première équation x[0]=[A-], [H3O+]= x[0]+x[1]\n","\treturn\tx[0]*(x[0]+x[1])-K1*(C-x[0]) #Qr1-K1\n","def f2(x): #définit la seconde équation x[1]=[HO-], [H3O+]= x[0]+x[1]\n","\treturn\tx[1]*(x[0]+x[1]) - K2 #Qr2-K2\n","def func(x): #définit le système des deux équations\n","\treturn\tf1(x),f2(x) #système\n","root = fsolve(func, [C/2,C/2]) #résolution du système\n","print('les solutions sont :','[A-] = ',format(root[0], \"#.1e\"),'mol/L',' et [HO-] = ',format(root[1],\"#.1e\"), 'mol/L')\n","#affiche la solution\n","pH=-np.log10(root[0]+root[1]) #calcule le pH\n","print('[H3O+] = ',format(root[0]+root[1], \"#.1e\"),'mol/L',' et pH = ',format(pH,\"#.1f\")) #affiche le pH"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"FPkIrWQPcKDS","executionInfo":{"status":"ok","timestamp":1646817180164,"user_tz":-60,"elapsed":317,"user":{"displayName":"Lionnel Malara","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14Gg9uzWMkTid1qlQikWp7IMi29R7n5oSh3ECmY5O=s64","userId":"16342666118884215780"}},"outputId":"af161050-6da9-477c-aa4f-6854f2d48d57"},"execution_count":2,"outputs":[{"output_type":"stream","name":"stdout","text":["les solutions sont : [A-] =  9.9e-08 mol/L  et [HO-] =  6.2e-08 mol/L\n","[H3O+] =  1.6e-07 mol/L  et pH =  6.8\n"]}]}]}