Question

A solution is prepared by dissolving ethanol in water. The mole fraction of ethanol in this solution is 0.04. What is the molarity (in $\text{mol L}^{-1}$) of the solution? (density of water is $1\text{ g mL}^{-1}$. Neglect the volume of ethanol)

• A. 0.96
• B. 2.31
• C. 1.96
• D. 3.31

Hint:

When mole fraction is small, you can relate molarity directly to molality because the volume of solute is negligible.
Formula: $M \approx m = \frac{x_2 \times 1000}{x_1 \times M_1}$.
Here, $M \approx \frac{0.04 \times 1000}{0.96 \times 18} \approx 2.31\text{ M}$.

Answer 1

The Correct Option is B

Step 1: Pick a friendlier basis.
Mole fractions with decimals get messy, so scale up. Take a batch of 25 mol total solution. Since $x_{ethanol}=0.04$, that gives exactly $n_{ethanol}=1$ mol and $n_{water}=24$ mol, same ratio, cleaner numbers.
Step 2: Convert the water's moles into a volume.
Mass of water $= 24 \times 18 = 432$ g. With density $1\text{ g mL}^{-1}$ and ethanol's volume ignored, the solution volume is just this water volume: $V = 432\text{ mL} = 0.432\text{ L}$.
Step 3: Compute molarity from moles of solute over volume.
\[ M = \frac{n_{ethanol}}{V} = \frac{1}{0.432} \]
\[ \boxed{M \approx 2.31\text{ mol L}^{-1}} \]