A $0.100 m$ aqueous solution of a weak monobasic acid HA freezes at $- 0.2046^{\circ} C$ ( $K_{f} = 1.86 K kg mo l^{- 1}$ ). Treat molality as equal to molar concentration and use $HA H X^{+} + A X^{-}$ , $i = 1 + α$ , $K_{a} = \frac{c α ^{2}}{1 - α}$ . Find $K_{a} \times 1 0^{3}$ (a dimensionless number, two decimal places).

Numerical answer type, tolerance 0.01.

Answer: 1.11

i = 0.2046/ (1.86 \times 0.100) = 1.100

, so

α = 0.100

K_{a} = \frac{0.100 \times 0.10 0 ^{2}}{1 - 0.100} = 1.111 \times 1 0^{- 3}