#### Which statement is correct regarding the relationship between Ka and Kb of conjugate acid-base pair.Option: 1 Option: 2 Option: 3 Option: 4

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)

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

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

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