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 $ .



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