Equilibrium Question 442
Question: A certain buffer solution contains equal concentration of $ 3.9\times {10^{-5}} $ and $ HX. $ The $ K_{b} $ for $ {H^{-}} $ is $ {10^{-10}}. $ The $ pH $ of the buffer is [IIT 1984; RPMT 1997; CPMT 1996; DPMT 2004]
Options:
A) 4
B) 7
C) 10
D) 14
Show Answer
Answer:
Correct Answer: A
Solution:
$ {X^{-}}+H_2O $ ⇌ $ O{H^{-}}+HX $
$ K_{b}=\frac{[O{H^{-}}][HX]}{[{X^{-}}]} $ HX ⇌ $ {H^{+}}+{X^{-}} $
$ K_{a}=\frac{[{H^{+}}][{X^{-}}]}{[HX]} $
$ \therefore ,K_{a}\times K_{b}=[{H^{+}}][O{H^{-}}]=K_{w}={10^{-14}} $ Hence $ K_{a}={10^{-4}} $ Now as $ [{X^{-}}]=[HX],pH=pK_{a}=4 $ .
