Calculate the vapor pressure of a solution made by dissolving 218 g of glucose (molar mass = 180.2 g/mol) in 460 mL of water at 30°C. What is the vapor-pressure lowering? The vapor pressure of pure water at 30°C is given in Table 5.3. Assume the density of the solvent is 1.00 g/mL. Strategy We need

Question

Calculate the vapor pressure of a solution made by dissolving 218 g of glucose (molar mass = 180.2 g/mol) in 460 mL of water at 30°C. What is the vapor-pressure lowering? The vapor pressure of pure water at 30°C is given in Table 5.3. Assume the density of the solvent is 1.00 g/mL.

Temperature (°C)	Water Vapor Pressure (mmHg)
0	4.58
5	6.54
10	9.21
15	12.79
20	17.54
25	23.76
30	31.82
35	42.18
40	55.32
45	71.88
50	92.51
55	118.04
60	149.38
65	187.54
70	233.7
75	289.1
80	355.1
85	433.6
90	525.76
95	633.9
100	760

Strategy We need Raoult’s law [Equation (12.4)] [latex] P_{1}=X_{1} P^{°}_{1} [/latex]to determine the vapor pressure of a solution. Note that glucose is a nonvolatile solute.

Accepted Answer

The vapor pressure of a solution ([latex]P_{1}[/latex]) is

First we calculate the number of moles of glucose and water in the solution:

[latex]n_{1}(water)= 460 \cancel{mL} imes \frac{1.00 \cancel{g}}{1 \cancel{mL}} imes \frac{1 mol}{18.02 \cancel{g}}=25.5 mol [/latex]

[latex]n_{2}(glucose)= 218 \cancel{g} imes \frac{1 mol}{180.2 \cancel{g}}=1.21 mol [/latex]

The mole fraction of water, [latex] X_{1}[/latex] , is given by

[latex] X_{1}=\frac{n_{1} }{n_{1}+n_{2}}[/latex]

[latex]=\frac{25.5 mol }{25.5 mol+1.21 mol}=0.955[/latex]

From Table 5.3, we find the vapor pressure of water at 30°C to be 31.82 mmHg. Therefore, the vapor pressure of the glucose solution is

[latex]P_{1}[/latex]=0.955 × 31.82 mmHg

=30.4 mmHg

Finally, the vapor-pressure lowering (ΔP) is (31.82 − 30.4) mmHg, or 1.4 mmHg.

Check We can also calculate the vapor pressure lowering by using Equation (12.5). Because the mole fraction of glucose is (1 − 0.955), or 0.045, the vapor pressure lowering is given by (0.045)(31.82 mmHg) or 1.4 mmHg.

Question 12.7: Calculate the vapor pressure of a solution made by dissolvin...

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