CALCULATING VAPOR-PRESSURE LOWERING How many grams of sucrose must be added to 320 g of water to lower the vapor pressure by 1.5 mm Hg at 25°C? The vapor pressure of water at 25 °C is 23.8 mm Hg, and the molar mass of sucrose is 342.3 g/mol. STRATEGY According to Raoult’s law, Psoln = Psolv × Xsolv

Question

CALCULATING VAPOR-PRESSURE LOWERING

How many grams of sucrose must be added to 320 g of water to lower the vapor pressure by 1.5 mm Hg at 25 °C? The vapor pressure of water at 25 °C is 23.8 mm Hg, and the molar mass of sucrose is 342.3 g/mol.

STRATEGY
According to Raoult’s law, [latex]P_{soln} = P_{solv} × X_{solv}[/latex], which can be rearranged to the form [latex]X_{solv} = P_{soln}/P_{solv}[/latex]. This equation can then be solved to find the number of moles of sucrose and hence the number of grams.

Accepted Answer

First, calculate the vapor pressure of the solution, [latex]P_{soln}[/latex], by subtracting the amount of vapor-pressure lowering from the vapor pressure of the pure solvent, [latex]P_{solv}[/latex]:

[latex]P_{soln}[/latex] = 23.8 mm Hg - 1.5 mm Hg = 22.3 mm Hg

Now calculate the mole fraction of water, [latex]X_{solv}[/latex].

Since [latex]P_{soln} = P_{solv} × X_{solv}[/latex]

then [latex]X_{solv} = \frac{P_{soln}}{P_{solv}} = \frac{22.3 mm Hg}{23.8 mm Hg}[/latex] = 0.937

This mole fraction of water is the number of moles of water divided by the total number of moles of sucrose plus water:

[latex]X_{solv} = \frac{Moles of water}{Total moles}[/latex]

Since the number of moles of water is

Moles of water = 320 g × [latex]\frac{1 mol}{18.0 g}[/latex] = 17.8 mol

then the total number of moles of sucrose plus water is

Total moles = [latex]\frac{moles of water}{X_{solv}} = \frac{17.8 mol}{0.937}[/latex] = 19.0 mol

Subtracting the number of moles of water from the total number of moles gives the number of moles of sucrose needed:

Moles of sucrose = 19.0 mol - 17.8 mol = 1.2 mol

Converting moles into grams then gives the mass of sucrose needed:

Grams of sucrose = 1.2 mol × 342.3 [latex]\frac{g}{mol}[/latex] = 4.1 × 10² g

Question 11.9: CALCULATING VAPOR-PRESSURE LOWERING How many grams of sucros...

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