Equilibrium Question 263

Question: The dissociation constant of a weak acid is $ 1.0\times {10^{-5}}, $ the equilibrium constant for the reaction with strong base is [MP PMT 1990]

Options:

A) $ 1.0\times {10^{-5}} $

B) $ 1.0\times {10^{-9}} $

C) $ 1.0\times 10^{9} $

D) $ 1.0\times 10^{14} $

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Answer:

Correct Answer: C

Solution:

HA ⇌ $ {H^{+}}+{A^{-}} $ ; $ K_{a}=\frac{[{H^{+}}][{A^{-}}]}{[HA]} $ –(i) neutralization of the weak acid with strong base is $ HA+O{H^{-}} $ ⇌ $ {A^{-}}+H_2O $

$ K=\frac{[{A^{-}}]}{[HA][O{H^{-}}]} $ –(ii) dividing (i) by (ii) $ \frac{K_{a}}{K}=[{H^{+}}][O{H^{-}}] $

$ =K_{w}={10^{-14}} $

$ K=\frac{K_{a}}{K_{w}}=\frac{{10^{-5}}}{{10^{-14}}}=10^{9} $ .



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