醋酸解离常数的数据处理

HAc_pKa.py

import numpy as np
import xlrd
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d

path = 'Workbook1.xlsx'
workbook = xlrd.open_workbook(path)
sheet = workbook.sheet_by_index(0)

V_NaOH = []
pH = []

for row in range(1,68):
    V_NaOH.append(sheet.row(row)[0].value)
    pH.append(sheet.row(row)[1].value)

plt.plot(V_NaOH, pH)
# plt.show()

xvals = np.arange(0, V_NaOH[-1], 0.01)
f = interp1d(V_NaOH, pH, kind='cubic')
yinterp = f(xvals)
print('size of xvals', np.size(xvals))

plt.plot(xvals, yinterp)
V_wanted = []
pH_wanted = []
for i in range(1, np.size(xvals)):
    dx = xvals[i] - xvals[i-1]
    dy = yinterp[i] - yinterp[i-1]
    diff = dy/dx
    if diff <= 1.1 and diff >= 0.9 and i in range(500, 900):
        V_wanted.append(xvals[i])
        pH_wanted.append(yinterp[i])

print('V_wanted', V_wanted)
print('pH_wanted', pH_wanted)

# plt.plot(V_wanted, pH_wanted, 'o')

intersections = []
for i in range(np.size(V_wanted)):
    if i == 0 or i == np.size(V_wanted)-1:
        x = V_wanted[i]
        y = pH_wanted[i]
        intersection = y - x
        intersections.append(intersection)
        xp = np.arange(x-2, x+2, 0.01)
        yp = xp + intersection
        plt.plot(xp, yp, '--')
        plt.plot(x, y, 'o')

xp = np.arange(np.average(V_wanted)-2, np.average(V_wanted)+2, 0.01)
yp = xp + np.average(intersections)
plt.plot(xp, yp, '--')

# Solve intersection
mid = (np.average(xp)*100).astype(int)
print(mid)
yi = yinterp[mid-200:mid+200]
print(np.size(yi), np.size(yp))
# plt.plot(xp, yi, 'b--')

for i in range(np.size(yi)):
    if np.abs(yi[i] - yp[i]) <= 0.1:
        V_res = xp[i]
        pH_res = yp[i]
        print('@64 ', V_res, pH_res)
        plt.plot(V_res, pH_res, 'o')
        plt.plot(V_res*np.ones(100), np.linspace(1, pH_res, 100), '--')
        print(i)
        break

pKa = yinterp[(V_res/2*100).astype(int)]
print('The end point requires sodium hydroxide at volume of ', V_res/2, ' mL')
print('pKa = ', pKa, ', which means Ka = ', np.power(10, -pKa))
plt.plot(V_res/2*np.ones(100), np.linspace(0, pKa, 100), '--')
plt.plot(np.linspace(0, V_res/2, 100), pKa*np.ones(100), '--')
plt.grid(True)
# plt.rc('grid', linestyle='--', color='black')

# plt.show()
plt.ylabel('pH')
plt.xlabel('$V_{NaOH}$')
plt.savefig('fig.pdf', format='pdf')