Question

Phosphoric acid, H3PO4(aq), is a triprotic acid, meaning that one molecule of the acid has three acidic protons. Estimate the pH, and the concentrations of all species in a 0.400 M phosphoric acid solution.

pKa1	pKa2	pKa3
2.16	7.21	12.32

H3PO4=______M

H2PO4^-=______M

HPO4^2-=________M

PO4^3-=________M

H⁺=_______M

OH^-=_______M

pH=

Answer 1

ka1 = 6.91 * 10^-3
ka2 = 6.16 * 10^-8
ka3 = 4.78 * 10^-13
You can get these by formula: pka = - log (ka)
write 3 equilibria of dissociation of H3PO4
H3PO4 ⇌ [H+] + [H2PO4-]
[H2PO4-] ⇌ [H+] + [HPO4^2-]
[HPO4^3-] ⇌ [H+] + [PO4^3-]

Where ka1, ka2 and ka3 are the respective equilibrium constants.
In the first equilibrium, we cannot ignore the decreasing concentration of [H3PO4] and we have a quadratic for the value of concentration of [H+] and thus concentration of [H+] is 4.4 * 10^-2.
This implies that pH is 1.3566. [H2PO4-] is same as [H+] and [H3PO4] = 0.4 - 4.4 * 10^-2 = 0.356. [HPO4^2-] = ka2 = 6.16 * 10^-8. [PO4^3-] = 6.69 * 10^-19. All concentrations are expressed in M. Concentration of [OH-] = 2.27 * 10^-13.
Note that the addition of [H+] due to the second and third equilibrium is very low, and so we can neglect it.
These are simultaneous equilibria