Question

Define the relation between $K_a$ and $K_b$.

Answer 1

Acid : $HA+H_{2}O\rightleftharpoons H_2{O}^{+}+A^{-}$

Base : $A^{-}+H_{2}O\rightleftharpoons HA+O{H}^{-}$

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$2H_{2}O\rightleftharpoons H_3{O}^{+}+O{H}^{-}$

$\Rightarrow \left[H_3{O}^{+}\right]\left[O{H}^{-}\right]=\frac{\left[H_3{O}^{+}\right]\left[A^{-}\right]}{\left[HA\right]}\times \frac{\left[HA\right]\left[O{H}^{-}\right]}{\left[A^{-}\right]}$

$\Rightarrow K_w=K_a\times K_b$