Question

Calculate pH of 10 mM weak acid (HA) dissociated in water. Assume $\alpha$ to be negligible. Given $\text{pK}_a = 4$

• A. 2
• B. 4
• C. 3
• D. 5

Hint:

For weak acids, $\text{pH} = \frac{1}{2}\text{pK}_a - \frac{1}{2}\log C$.

Answer 1

The Correct Option is C

Concentration $C = 10 \text{ mM} = 10 \times 10^{-3} \text{ M} = 10^{-2} \text{ M}$.
Given $\text{pK}_a = 4$.
Using the weak acid approximation formula ($\alpha \ll 1$):
$\text{pH} = \frac{1}{2} (\text{pK}_a - \log C)$.
Substitute values:
$\text{pH} = \frac{1}{2} (4 - \log(10^{-2}))$.
$\text{pH} = \frac{1}{2} (4 - (-2))$.
$\text{pH} = \frac{1}{2} (6) = 3$.