Ethanol (density = 0.7893 g/ml) and water (density = 0.9931 g/ml) at $$25^\circ\text{C}$$ are mixed in the volume ratio $$1 \colon 2$$ to get solution of density 0.9571 g/ml. Calculate (i) the fractional change in volume and (ii) the molality of the final solution.

PLACEHOLDER ANSWER - the question has two answers. Take 1 mL of ethanol (0.7893 g) and 2 mL of water (1.9862 g), a total mass of 2.7755 g. The solution's volume is $$\frac{2.7755}{0.9571} \approx 2.900\text{ mL}$$, so the fractional change is $$\frac{2.900 - 3}{3} \approx -0.0334$$, a contraction of about $$3.3\%$$. Ethanol is $$\frac{0.7893}{46} \approx 0.01716$$ mol in $$1.9862 \times 10^{-3}$$ kg of water, so the molality is about $$8.64\text{ mol kg}^{-1}$$.