Q. Approximate relationship between dissociation constant of water ($K$) and ionic product of water ($K_{w}$) is
A) $K_{w} = K$
B) $K_{w} = 55.6 \times K$
C) $K_{w} = 18 \times K$
D) $K_{w} = 14 \times K$
Explanation
(b)
Dissociation constant
$H_{2}O \rightleftharpoons H^{+} + {OH}^{-}:\left\lbrack H^{+} \right\rbrack = {OH}^{-} = 1 \times 10^{- 7}\ M$
And [$H_{2}O$]=1 g/mL = $1000\ gL^{- 1}$
$= \frac{1000}{18}\ mol\ L^{- 1} = 55.56\ M$
$K = \frac{\left\lbrack H^{+} \right\rbrack\left\lbrack {OH}^{-} \right\rbrack}{H_{2}O} = \frac{10^{- 14}}{55.6}$
$K_{w} = 1 \times 10^{- 14}$
So, $K_{w} = 55.6 \times K$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.