Question

A sample of carbonic acid (0.125 L, 0.109 M, pK_a1 = 6.35, pK_a2 = 10.33) was titrated with 1.79 M NaOH. Calculate the pH at the following points:

a) Before the titration.

b) At the 1st midpoint.

c) At the 1st stoichiometric point.

d) At the 2nd midpoint.

e)

Answer 1

a)

before titration,

H2CO3 --> H+ + HCO3- main acid

Ka = [H+][HCO3-]/[H2CO3]

(10^-6.35) = x*x/(0.109 -x)

x = 2.20*10^-4

[H+] = 2.20*10^-4

pH = -log(2.20*10^-4) = 3.66

b)

in 1st midpoint --> this is a buffer

pH = pKa1 + log(HCO3- / H2CO3)

pKa1 = 6.35

pH = 6.35+ log(1/1)

pH = 6.35

c)

1st stocihometric point;

this point is between pKA1 and pKA2 so:

pH = 1/2*(pKa1 + pKA2)

pH = 1/2*(6.35+10.33) = 8.34

d)

2nd mid point --> 2nd ionization, CO3-2 and HCO3-

pH = pKa2 + log(CO3-2/HCO3-)

pH = 10.33