First slide

Ionization constants of weak acids, PH of weak acids

Question

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

Difficult

A

$2.72 \times 10^{- 5}$
B

$3.52 \times 10^{- 3}$
C

$6.76 \times 10^{- 4}$
D

$5.38 \times 10^{- 2}$

Solution

$F^{-} + H_{2} O ⇌ HF + {OH}^{-}$
$K_{b} = \frac{[HF] [{OH}^{-}]}{[F^{-}]}$
$K_{w} = [H_{3} O^{+}] [{OH}^{-}] = 10^{- 14}$
Dissociation of HF in water is represented by the equation,
$HF + H_{2} O ⇌ H_{3} O^{+} + F^{-}$
$K_{a} = \frac{[H_{3} O^{+}] [F^{-}]}{[HF]}$ -----------(iii)
$K_{b} \cdot K_{a} = [H_{3} O^{+}] [{OH}^{-}] = K_{w}$
or $\frac{K_{w}}{K_{b}} = K_{a}$
Taking log on both sides
${logK}_{a} = {logK}_{w} - {logK}_{b}$
$= - {pK}_{w} + {logK}_{b}$
$= - 14 + 10.83 = - 3.17$
$K_{a} = 6.76 \times 10^{- 4}$

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