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

1. To calculate the pH of a weak acid solution, we use the formula for the dissociation of a weak acid, which is represented as: \(HA \rightleftharpoons H^+ + A^−\)
2. The acid dissociation constant \(K_a\) is given by: \(K_a = \frac{[H^+][A^-]}{[HA]}\)
3. Assuming the degree of dissociation \(\alpha\) is negligible for weak acids, the concentration of undissociated acid remains approximately the same as the initial concentration. Thus, the concentration of \([H^+]\) can be approximated as: \([H^+] = \sqrt{K_a \times [HA]}\)
4. We know that \(\text{pK}_a = 4\), hence: \(K_a = 10^{-4}\)
5. Given \([HA] = 10 \, \text{mM} = 0.01 \, \text{mol/L}\), the concentration of hydrogen ions can be calculated as: \([H^+] = \sqrt{10^{-4} \times 0.01}\) 
   Calculating further: \([H^+] = \sqrt{10^{-6}} = 10^{-3} \, \text{mol/L}\)
6. The pH is given by the negative logarithm (base 10) of the hydrogen ion concentration: \(\text{pH} = -\log_{10}[H^+]\)
7. Substitute the hydrogen ion concentration: \(\text{pH} = -\log_{10}(10^{-3}) = 3\)
8. Therefore, the correct answer is 3.
9. To rule out other options:
   • If the pH were 2, it would imply a much higher concentration of \([H^+]\) inconsistent with the given \(\text{pK}_a\).
   • A pH of 4 or 5 would imply a lower degree of dissociation or incorrectly assume full ionization, which isn't applicable for a weak acid.