Question

calculate the mole fractio of ethanol and water 8in the sample of rectified spirit which contains 95% ethanol by weight . (95% means 95g ethanol in 100g solution)

Answer 1

Let us take the weight of the solution = 100 g
Since it is given that it is 95% mass/ mass by solution, thus
weight of ethanol in solution = 95g
weight of water = 5g

Molar mass of ethanol (C₂H₅OH) = 12$\times$2 +5$\times$1 + 16 + 1 = 46 g / mol
​Now moles of ethanol in solution = $\frac{\mathrm{weight}\mathrm{of}\mathrm{ethanol}\mathrm{in}\mathrm{solution}}{\mathrm{molar}\mathrm{mass}\mathrm{of}\mathrm{ethanol}}$
= $\frac{95}{46}$
= 2.065
Molar mass of water (H₂O) = 18 g / mol
​Now moles of water in solution = $\frac{\mathrm{weight}\mathrm{of}\mathrm{water}\mathrm{in}\mathrm{solution}}{\mathrm{molar}\mathrm{mass}\mathrm{of}\mathrm{water}}$
= $\frac{5}{18}$
= 0.278
Mole fraction of ethanol = $\frac{\mathrm{Number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{ethanol}}{\mathrm{Number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{ethanol}+\mathrm{Number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{water}}$
= $\frac{2.065}{2.065+0.278}$
= 0.88
Mole fraction of water = 1- mole fraction of ethanol
= 1 - 0.88
= 0.12