‘x’ g of water is mixed with 69 g of ethanol. The mole fraction of ethanol in the resulting solution is 0.6. What is the value of ‘x’? (Molar masses: ethanol = 46 g mol−1, water = 18 g mol−1)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 18
The mole fraction of a component is its number of moles divided by the total number of moles in the solution:
\( \displaystyle x_{\text{ethanol}}=\frac{n_{\text{ethanol}}}{n_{\text{ethanol}}+n_{\text{water}}} \)
Moles of ethanol:
\( \displaystyle n_{\text{ethanol}}=\frac{69}{46}=1.5\,\mathrm{mol} \)
Moles of water from the given mole fraction:
\( \displaystyle 0.6=\frac{1.5}{1.5+n_{\text{water}}} \)
\( \displaystyle 1.5+n_{\text{water}}=\frac{1.5}{0.6}=2.5 \qquad n_{\text{water}}=1.0\,\mathrm{mol} \)
Mass of water:
\( \displaystyle x=1.0\times18=18\,\mathrm{g} \)