Question

A solution has 25% of water, 25% ethanol and 50% acetic acid by mass. Calculate the mole fraction of each component.

• A. 0.50, 0.3, 0.2
• B. 0.2, 0.3, 0.50
• C. 0.3, 0.2, 0.50
• D. 0.50, 0.2, 0.3

Answer 1

The correct option is D 0.50, 0.2, 0.3

25% of water by mass mean 25g of water.
Since 18 g of water =1 mol
Mole of 25 g of water $=\frac{25}{18}=1.38$ mol
Similarly, 25% ethanol and 50% acetic acid by mass mean 25g of ethanol and 50g of acetic acid.
46 g of ethanol = 1 mol
$\text{Mole of 25 g of ethanol}=\frac{25}{46}=0.55\text{mol}$
Again, 60 g of acetic acid = 1 mol
50 g of acetic acid $=\frac{50}{60}=0.83$ mol
$\therefore \text{Mole fraction of water}=\frac{\text{mole of water}}{\text{mole of acetic acid+mole of ethanol+mole of water}}$
$=\frac{1.38}{1.38+0.55+0.83}=0.50$
Similarly, mole fraction of ethanol
$=\frac{0.55}{1.38+0.55+0.83}=0.19=0.20$
Mole fraction of acetic acid $=\frac{0.83}{1.38+0.55+0.83}=0.3$ Hence option (d) is correct.