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Question

Given, HF+H2OKaH3O++F
F+H2OKbHF+OH
Which of the following relation is correct?

A
Kb=Kw
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B
Kb=1Kw
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C
Ka×Kb=Kw
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D
KaKb=Kw
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Solution

The correct option is B Ka×Kb=Kw
The reaction for the dissociation of acid is as shown below.
HF+H2OKaH3O++F
The expression for the acid dissociation constant Ka is as shown below.
Ka=[H3O+][F][HF] ......(1)
The reaction of fluoride ion with water is as shown below
F+H2OKbHF+OH.
The expression for the constant Kb is as shown below.
Kb=[HF][OH][F] ......(2)
Multiply equation (1) with equation (2).
Ka×Kb=([H3O+][F][HF])×([HF][OH][F])=[H+][OH]=Kw.

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