Polyprotic Acid Example Chemistry Problem

How to Work a Polyprotic Acid Problem

Sulfuric acid is an example of a common polyprotic acid.
Sulfuric acid is an example of a common polyprotic acid. LAGUNA DESIGN / Getty Images

A polyprotic acid is an acid that can donate more than one hydrogen atom (proton) in an aqueous solution. To find the pH of this type of acid, it's necessary to know the dissociation constants for each hydrogen atom. This is an example of how to work a polyprotic acid chemistry problem.

Polyprotic Acid Chemistry Problem

Determine the pH of a 0.10 M solution of H2SO4.

Given: Ka2 = 1.3 x 10-2


H2SO4 has two H+ (protons), so it is a diprotic acid that undergoes two sequential ionizations in water:

First ionization: H2SO4(aq) → H+(aq) + HSO4-(aq)

Second ionization: HSO4-(aq) ⇔ H+(aq) + SO42-(aq)

Note that sulfuric acid is a strong acid, so its first dissociation approaches 100%. This is why the reaction is written using → rather than ⇔. The HSO4-(aq) in the second ionization is a weak acid, so the H+ is in equilibrium with its conjugate base.

Ka2 = [H+][SO42-]/[HSO4-]

Ka2 = 1.3 x 10-2

Ka2 = (0.10 + x)(x)/(0.10 - x)

Since Ka2 is relatively large, it's necessary to use the quadratic formula to solve for x:

x2 + 0.11x - 0.0013 = 0

x = 1.1 x 10-2 M

The sum of the first and second ionizations gives the total [H+] at equilibrium.

0.10 + 0.011 = 0.11 M

pH = -log[H+] = 0.96

Learn More

Introduction to Polyprotic Acids

Strength of Acids and Bases

Concentration of Chemical Species

First IonizationH2SO4(aq)H+(aq)HSO4-(aq)
Initial0.10 M0.00 M0.00 M
Change-0.10 M+0.10 M+0.10 M
Final0.00 M0.10 M0.10 M
Second IonizationHSO42-(aq)H+(aq)SO42-(aq)
Initial0.10 M0.10 M0.00 M
Change-x M+x M+x M
At Equilibrium(0.10 - x) M(0.10 + x) Mx M
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Helmenstine, Anne Marie, Ph.D. "Polyprotic Acid Example Chemistry Problem." ThoughtCo, Feb. 12, 2018, thoughtco.com/polyprotic-acid-example-problem-603633. Helmenstine, Anne Marie, Ph.D. (2018, February 12). Polyprotic Acid Example Chemistry Problem. Retrieved from https://www.thoughtco.com/polyprotic-acid-example-problem-603633 Helmenstine, Anne Marie, Ph.D. "Polyprotic Acid Example Chemistry Problem." ThoughtCo. https://www.thoughtco.com/polyprotic-acid-example-problem-603633 (accessed February 22, 2018).