First slide

Ionization constants of weak acids, PH of weak acids

Question

The ionization constant of HF is $3.2 \times 10^{- 4} .$ Which of the following is the correct value of degree of dissociation if concentration is 0.02 M?

Moderate

A

0.12
B

0.012
C

0.024
D

0.24

Solution

$\frac{{Cα}^{2}}{1 - α} = K_{a} (The solution is not very dilute)$
$\frac{0.02 \times α^{2}}{1 - α} = 3.2 \times 10^{- 4} (given)$
$\frac{α^{2}}{1 - α} = 1.6 \times 10^{- 2}$
$α^{2} + (1.6 \times 10^{- 2}) α - 1.6 \times 10^{- 2} = 0$
$α = \frac{- (1.6 \times 10^{- 2}) \pm \sqrt{{(1.6 \times 10^{- 2})}^{2} + 4 \times 1.6 \times 10^{- 2}}}{2}$
$= \frac{- 1.6 \times 10^{- 2} + \sqrt{6.4 \times 10^{- 2}}}{2}$ $[{(1.6 \times 10^{- 2})}^{2} neglected]$
$= \frac{- 0.016 + 0.253}{2} 0.12$
Alternatively,
For dilute weak acid, $α = \sqrt{\frac{K}{C}}$
$α = \sqrt{\frac{3.2 \times 10^{- 4}}{0.02}} = \sqrt{1.6 \times 10^{- 2}} = 0.126$

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