Question

The [H⁺] for a weak acid of dissociation constant K_a and concentration C is nearly equal to :

(a) \(\sqrt{\frac{K_a}{C}}\)

(b) \(\sqrt{K_aC}\) 

(c) \(\frac{K_a}{\sqrt c}\) 

(d) \(\frac{c}{K_a}\)

Answer 1

(B) \(\sqrt{K_aC}\)

	\(AH\)	\(\rightleftharpoons\)	\(A^-\)	+	\(H^+\)
Initially	C		0		0
At Equilibrium	\(C(1-\alpha)\)		\(C\alpha\)		\(C\alpha\)

\(K_a=\frac{[A^-][H^+]}{[AH]}\)

= \(\frac{C\alpha \times C\alpha}{C(1-\alpha)}\)

= \(\frac{C^2\alpha^2}{C(1-\alpha)}\)

\(\because \) AH is weak acid.

\(\therefore \alpha<<1\)

\(K_a=C\alpha^2\)

\(\alpha =\sqrt{\frac{K_a}{C}}\)

\(\therefore [H^+]=C\alpha =C\sqrt{\frac{K_a}{C}}=\sqrt{K_a\times C}\)

Answer 2

Option : (b) \(\sqrt{K_aC}\)