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