# If 20 ml of ethanol (density = 0.7893 gm/ml) is mixed with 40 ml of water (density = 0.9971 gm/ml) at $25^{\large\circ}$C, the final solution has density of 0.9571 gm / ml. Calculate the percentage change in total volume of mixing. Also calculate the molality of alcohol in the final solution.

Mass of ethanol = $v \times d$
W = $20 \times 0.7893 gm = 15.786 gm$
Mass of water = $v \times d$
$\Rightarrow 40\times 0.9971gm=39.884gm$
Total volume = 60 ml
Total mass = 15.786 + 39.884 = 55.67 gm
Let the volume of solution = x ml
X=mass/density=$\large\frac{55.67}{0.9571}$$=58.165ml Change in volume = 60 – 58.165 = 1.835 ml % change in volume=\large\frac{1.835}{60}$$\times 100=3.05\%$
Molality,$m=\large\frac{w}{M}\times \frac{1000}{W}=\frac{15.786}{46}\times \frac{1000}{39.884}$$=8.604m$
Hence (A) is the correct answer.