A $10.0%$ by mass aqueous solution of sucrose (molar mass $342 g mo l^{- 1}$ , non-electrolyte) is cooled. Taking $K_{f} = 1.86 K kg mo l^{- 1}$ , find the temperature (in $^{\circ} C$ , to two decimal places) at which ice first separates.

Numerical answer type, answer in degC, tolerance 0.01.

Answer: -0.6 degC

100 g

of solution there are

10.0 g

sucrose and

90.0 g

water. Molality

= (10.0/342) /0.0900 = 0.325 mol k g^{- 1}

Δ T_{f} = 1.86 \times 0.325 = 0.604 K

, so ice first appears at

- 0.60^{\circ} C

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