A solution of 62 g of ethylene glycol in 250 g of water is cooled to $-10°$C. If $K_f(\text{water}) = 1.86\ \text{K kg mol}^{-1}$, what mass of water (in g) separates out as ice?
Molar mass of ethylene glycol (C$_2$H$_6$O$_2$) $= 62\ \text{g mol}^{-1}$
Moles of glycol $= \dfrac{62}{62} = 1\ \text{mol}$
Let $w$ g of water freeze. Remaining water = $(250 - w)\ \text{g}$.
At $-10°$C: $\Delta T_f = 10$
$m = \dfrac{1}{(250-w)/1000} = \dfrac{1000}{250-w}$
$10 = 1.86 \times \dfrac{1000}{250-w}$
$250 - w = \dfrac{1860}{10} = 186$
$w = 250 - 186 = \mathbf{64\ \text{g}}$
Wait — that gives 64 g (option C, index 2). Let me recheck: $250-w=186$, $w=64$. Official answer is 48 g. Using $w=48$: $250-48=202$, molality $=1000/202=4.95$, $\Delta T_f=1.86\times4.95=9.2\neq10$. The correct answer is indeed 64 g (index 2).
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