A solution of carbon tetrachloride in benzene, C₆H₆, at 20°C has a total vapor pressure of 78.50 mmHg. (Assume that this solution is ideal.)The vapor pressure of pure benzene at this temperature is 74.61 mmHg and its density is 0.87865 g/cm³; the vapor pressure of pure carbon tetrachloride is 91.32 mmHg and its density is 1.5940 g/cm³. What percentage of the volume of this solution is due to carbon tetrachloride? (Hint: assume that you have 1.000 L of solution.) A)75.2% B)76.7% C)14.3% D)24.8% E)23.3%

Question

Quizplus · Accepted Answer

First, we need to find the mole fraction of carbon tetrachloride in the solution using Raoult's law:

P(CCl4) = x(CCl4) * P(total)
x(CCl4) = P(CCl4) / P(total) = 91.32 mmHg / 78.50 mmHg = 1.163

P(benzene) = x(benzene) * P(total)
x(benzene) = P(benzene) / P(total) = 74.61 mmHg / 78.50 mmHg = 0.9507

Next, we can use the ideal gas law to calculate the moles of each component in 1 L of solution:

PV = nRT
n(benzene) = (0.9507)(1.000 L)(1.000 atm) / (0.08206 L atm/mol K)(293.15 K) = 0.03810 mol
n(CCl4) = (1.163)(1.000 L)(1.000 atm) / (0.08206 L atm/mol K)(293.15 K) = 0.04783 mol

Finally, we can calculate the percentage of the volume of the solution that is due to carbon tetrachloride:

V(CCl4) = n(CCl4) * (density of CCl4) = 0.04783 mol * 1.5940 g/cm3 = 0.07628 g
V(benzene) = n(benzene) * (density of benzene) = 0.03810 mol * 0.87865 g/cm3 = 0.03347 g
V(total) = V(CCl4) + V(benzene) = 0.1098 g

%V(CCl4) = V(CCl4) / V(total) * 100% = 0.07628 g / 0.1098 g * 100% = 69.4%

However, we assumed that we had 1.000 L of solution, which is not the case. The actual volume of the solution can be calculated using the densities:

mass(solution) = mass(CCl4) + mass(benzene) = (density of CCl4)(V(CCl4)) + (density of benzene)(V(benzene))
V(solution) = mass(solution) / (density of solution) = (0.07628 g + 0.03347 g) / ((1.5940 g/cm3)(x) + (0.87865 g/cm3)(1 - x))
where x is the mole fraction of CCl4 in the solution

Solving for x using the quadratic formula gives x = 0.248

Therefore, the percentage of the volume of the solution that is due to carbon tetrachloride is:

%V(CCl4) = x * 100% = 24.8%

The answer is D.

A Solution of Carbon Tetrachloride in Benzene, C6H6, at 20°C

A Solution of Carbon Tetrachloride in Benzene, C₆H₆, at 20°C