The ${\mathrm{pK}}_{\mathrm{b}}$ for fluoride ion at 25°C is 10.83, the ionisation constant of hydrofluoric acid at this temperature is

${\mathrm{F}}^{-}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons \mathrm{HF}+{\mathrm{OH}}^{-}$

${\mathrm{K}}_{\mathrm{b}}=\frac{\left[\mathrm{HF}\right]\left[{\mathrm{OH}}^{-}\right]}{\left[{\mathrm{F}}^{-}\right]}$

${\mathrm{K}}_{\mathrm{w}}=\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]\left[{\mathrm{OH}}^{-}\right]={10}^{-14}$

Dissociation of HF in water is represented by the equation,

$\mathrm{HF}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{F}}^{-}$

${\mathrm{K}}_{\mathrm{a}}= \frac{\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]\left[{\mathrm{F}}^{-}\right]}{\left[\mathrm{HF}\right]}$-----------(iii)

${\mathrm{K}}_{\mathrm{b}}·{\mathrm{K}}_{\mathrm{a}}=\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]\left[{\mathrm{OH}}^{-}\right]={\mathrm{K}}_{\mathrm{w}}$

or $\frac{{\mathrm{K}}_{\mathrm{w}}}{{\mathrm{K}}_{\mathrm{b}}}={\mathrm{K}}_{\mathrm{a}}$

Taking log on both sides

${\mathrm{logK}}_{\mathrm{a}}= {\mathrm{logK}}_{\mathrm{w}}-{\mathrm{logK}}_{\mathrm{b}}$

          $=-{\mathrm{pK}}_{\mathrm{w}}+{\mathrm{logK}}_{\mathrm{b}}$

          $=-14+10.83=-3.17$

     ${\mathrm{K}}_{\mathrm{a}}= 6.76\times {10}^{-4}$