pH Practice Problems with Answers

1. Phosphoric acid (H₃PO₄) has three dissociable protons, with the pK_a’s shown below. Which form of phosphoric acid predominates in a solution at pH 4?

Acid pK_a

H₃PO₄ 2.14

H₂PO₄^– 6.86

HPO₄^2– 12.4

Ans: At pH 4, the first dissociable proton (pK_a = 2.14) has been titrated completely, and the second (pK_a = 6.86) has just started to be titrated. The dominant form at pH 4 is therefore H₂PO₄^–, the form with one dissociated proton.

2. What is the pH of a solution containing 0.2 M acetic acid (pK_a = 4.7) and 0.1 M sodium acetate?

Ans:

pH = pK_a + log (conjugate base/ acid)

pH = 4.7 + log (0.1/0.2)

= 4.7 – 0.3

pH = 4.4

3. For a weak acid with a pK_a of 6.0, show how you would calculate the ratio of acid to salt at pH 5.
Ans:

4. Suppose you have just added 100 mL of a solution containing 0.5 mol of acetic acid per liter to 400 mL of 0.5 M NaOH. What is the final pH?
(The pK_a of acetic acid is 4.7.)

Ans: Addition of 200 mmol of NaOH (400 mL ´X 0.5 M) to 50 mmol of acetic acid (100 mL X 0.5 mM) completely titrates the acid so that it can no longer act as a buffer and leaves 150 mmol of NaOH dissolved in 500 mL, an [OH^–] of 0.3 M.
Given [OH^–], [H⁺] can be calculated from the water constant:

[H⁺][OH^–] = 10^–14

[H⁺] = 10^–14 M² / 0.3 M

pH is, by definition, log (1/[H⁺])

pH = log (0.3 M /10^–14 M²) = 12.48.

5. A weak acid HA, has a pK_a of 5.0. If 1.0 mol of this acid and 0.1 mol of NaOH were dissolved in one liter of water, what would the final pH be?

Ans: Combining 1 mol of weak acid with 0.1 mol of NaOH yields 0.9 mol of weak acid and 0.1 mol of salt.

pH = pK_a + log