Question

The mole fraction of ethanol in a solution of ethanol in water is $0.05$ and the density of solution is $0.997$ g/cc.
Which of the following statements is correct?

• A. Molarity of the solution is $2.57M$
• B. Molality of the solution is $2.92m$
• C. Both (a) and (b)
• D. Molality of the solution is $3.52m$

Answer 1

The correct option is C Both (a) and (b)

$\text{Mole fraction of}{C}_2{H}_{5}OH=\frac{\text{moles of}{C}_2{H}_{5}OH}{\text{moles of}{C}_2{H}_{5}OH+\text{moles of}{H}_{2}O}=0.05=\frac{5}{100}$
$\therefore 100\text{moles of solution contain}5\text{moles of}{C}_2{H}_{5}OH.$
$\text{Weight of}{C}_2{H}_{5}OH=\text{moles}\times \text{mol. wt.}$
$=5g\times 46gmo{l}^{-1}=230g.$
$\text{Weight of}{H}_{2}O=95\times 18=1710g$
$\therefore \text{Molality}=\frac{5}{1710}\times 1000=2.92m.$
$\therefore \text{Weight of solution}=230+1710=1940g$
$\text{Volume of solution}=\frac{1940}{0.997}cc=1945.8mL=1.9458L$
$\text{Molarity}=\frac{5}{1.9458}=2.57M$

Hence, the correct answer is option (c).