Question

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

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

Solution

## The correct option is B $$5.0\times 10^{-15}$$$${ H }_{ 2 }A\longleftrightarrow { HA }^{ - }+{ H }^{ + }$$$${ K }_{ 1 }=\dfrac { \left[ { HA }^{ - } \right] \left[ { H }^{ + } \right] }{ \left[ { H }_{ 2 }A \right] }$$$${ HA }^{ - }\longleftrightarrow { H }^{ + }+{ A }^{ 2- }$$$${ K }_{ 2 }=\dfrac { \left[ { A }^{ 2- } \right] \left[ { H }^{ + } \right] }{ \left[ { HA }^{ - } \right] }$$for the reaction, $${ H }_{ 2 }A\longleftrightarrow { A }^{ 2- }+{ 2H }^{ + }$$$$K=\dfrac { \left[ { A }^{ 2- } \right] { \left[ { H }^{ + } \right] }^{ 2 } }{ \left[ { H }_{ 2 }A \right] }$$$$K=\left( { K }_{ 1 } \right) \left( { K }_{ 2 } \right)$$$$=1\times { 10 }^{ -5 }\times 5\times { 10 }^{ -10 }$$$$=5\times { 10 }^{ -15 }$$overall dissociation constant of acid will be $$5\times { 10 }^{ -15 }$$.Chemistry

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