Question

Part A Calculate [ H 3 O + ] and pH of the following polyprotic acid solution: 0.120 M H 2 CO 3 .

Part B Calculate [H3O+] and pH of the following polyprotic acid solution: 0.125 M H3C6H5O7 .

Answer 1

As K_a or pK_a values are not provided in the question these data has been taken from standard reference. So final answers may differ slightly. But the calculation theory and methods should be the same.
From my reference:
Ka1 H2CO3 = 4.3*10^-7, pKa = 6.37
Ka2 H2CO3 = 5.6*10^-11, pKa = 10.25

Because H2CO3 is a diprotic weak acid, we will make some assumptions that will not affect the end result, but will allow much easier calculation:
H2CO3 dissociates in two steps:
H2CO3 ↔ H+ + HCO3-
HCO3- ↔ H+ + CO3 2-

We will assume:
1) [H+] = [HCO3-]= [CO3 2-]
[H2CO3] = [HCO3-]

For first dissociation:
Ka = [H+]*[HCO3-] / [H2CO3]
Ka = [H+]²/[H2CO3]
4.3*10^-7 = [H+]²/ 0.120
[H+]² = 5.16*10^-8
[H+] = 2.27*10^-4

For second dissociation:
Ka = [H+]*[CO3 2-]/[HCO3-]
5.6*10^-11 = [H+]²/[HCO3-]
5.6*10^-11 * 0.120 = [H+]²
[H+]² = 6.72*10^-12
[H+] = 2.59*10^-6

Total [H+] ( or [H3O+] = (2.27*10^-4) + 2.59*10^-6) = 2.29*10^-4M

pH=3.64