Solutions: Common Mistakes and Fixes (7)

easy 2 min read

Question

The vapour pressure of pure water at 25°C25°\text{C} is 23.8 mm Hg23.8\text{ mm Hg}. When 18 g18\text{ g} of glucose (M=180M = 180) is dissolved in 180 g180\text{ g} of water, find (a) the mole fraction of glucose, (b) the relative lowering of vapour pressure, (c) the new vapour pressure.

Solution — Step by Step

Moles of glucose =18/180=0.1= 18/180 = 0.1. Moles of water =180/18=10= 180/18 = 10. Total moles =10.1= 10.1.

xglucose=0.110.10.0099x_{\text{glucose}} = \frac{0.1}{10.1} \approx 0.0099

Raoult’s law for non-volatile solute:

P0PP0=xsolute0.0099\frac{P^0 - P}{P^0} = x_{\text{solute}} \approx 0.0099
P=P0(1xsolute)=23.8×(10.0099)=23.8×0.9901P = P^0(1 - x_{\text{solute}}) = 23.8 \times (1 - 0.0099) = 23.8 \times 0.9901 P23.56 mm HgP \approx 23.56\text{ mm Hg}

xglucose0.0099x_{\text{glucose}} \approx 0.0099, relative lowering 0.0099\approx 0.0099, P23.56 mm HgP \approx 23.56\text{ mm Hg}.

Why This Works

Raoult’s law states that the partial pressure of a volatile component in a solution is its mole fraction times its pure vapour pressure. For a non-volatile solute, only the solvent contributes to the vapour, so the relative lowering equals the solute’s mole fraction.

This is a colligative property — it depends on the number of solute particles, not on what they are. A non-electrolyte gives one particle per formula unit; ionic solutes give more (Van’t Hoff factor).

Alternative Method

For dilute solutions, mole fraction can be approximated by nsolute/nsolventn_{\text{solute}}/n_{\text{solvent}} (ignoring the solute in the denominator): 0.1/10=0.010.1/10 = 0.01. Close to 0.00990.0099 — useful for quick MCQ checks.

Common Mistake

Using mass fraction instead of mole fraction in Raoult’s law. The mole fraction is what matters because the law is about particles, not mass. 18 g18\text{ g} glucose has the same particle count as 0.10.1 mol — using 18/19818/198 as a “fraction” is a frequent error.

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