Question

The hydrogen ion concentration of a weak acid of dissociation constant K_a and concentration C is equal to

(A) \(\sqrt{\frac {K_a}C}\)

(B) \(\frac C {K_a}\)

(C) \(K_aC\)

(D) \(\sqrt{K_aC}\)

Answer 1

Correct option is (D) \(\sqrt{K_aC}\)

At equilibrium

\(\underset{C(1-\alpha)}{HA} \rightleftarrows \underset{C\alpha}{H_3O^+} + \underset{C\alpha}{A^-}\)

\([H_3O^+] = C\alpha\) and \(K_a = \frac {C\alpha \times C\alpha}{C(1 - \alpha)} = C\alpha^2 \Rightarrow \alpha = \sqrt{\frac{K_a}C}\)

So \([H_3O^+] = C\sqrt{\frac{K_a} C} = \sqrt{K_aC}\)