Question

# The first and second dissociation constant of an acid $${ H }_{ 2 }A$$ are $$1.0\ \times \ { 10 }^{ -5 }$$ and $$5.0\ \times \ { 10 }^{ -10 }$$ respectively. The over all dissociation constant of the acid will be:

A
5.0 × 105
B
5.0 × 1015
C
5.0 × 1015
D
0.2 × 105

Solution

## The correct option is C $$5.0\ \times \ { 10 }^{ -15 }$$$$H_2A\overset {K_1}{\rightleftharpoons} HA^-+H^+$$$$\Rightarrow K_1=\cfrac {[HA^-][H^+]}{[H_2A]}$$  $$\longrightarrow (1)$$$$HA^-\overset {K_2}{\rightleftharpoons} H^++A^{2-}$$$$\Rightarrow K_2=\cfrac {[H^+][A^{2-}]}{[HA^-]}$$    $$\longrightarrow (2)$$Overall dissociation constant $$K$$$$\Rightarrow K=\cfrac {[H^+]^2[A^{2-}]}{[H_2A]}=K_1\times K_2$$$$=1\times 10^{-5}\times 5\times 10^{-10}$$$$=5\times 10^{-15}$$ .Chemistry

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