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  • Which statement is correct regarding the relationship between Ka and Kb of conjugate acid-base pair.Option: 1 <img alt="K_{w}=

Which statement is correct regarding the relationship between Ka and Kb of conjugate acid-base pair.

Option: 1

K_{w}= \frac{K_{b}}{K_{a}}


Option: 2

K_{w}= \frac{K_{a}}{K_{b}}


Option: 3

K_{w}=K_{a} + K_{b}


Option: 4

K_{w}=K_{a} \times K_{b}


Answers (1)

best_answer

Let's consider a conjugate acid-base pair HA and A-. 

The acid reacts with water as :

\text { HA }(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+A^{-}(a q)...............(A)

K_{a}=\frac{\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[A^{-}\right]}{[\mathrm{H} A]}...............................(1)

Conjugate base reacts with water as :

A^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H} A+\mathrm{OH}^{-}..............................(B)

K_{b}=\frac{[\mathrm{H} A]\left[\mathrm{OH}^{-}\right]}{\left[A^{-}\right]}........................(2)

Adding equations (A) and (B)

\begin{array}{c}{2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q)} \\ {K_{w}=\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right]}\end{array}.................(3)

By equations (1), (2), and (3)

K_{w}=K_{a} \times K_{b}

Posted by

jitender.kumar

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