A solution is 40.00% by volume benzene (C₆H₆) in carbon tetrachloride at 20°C. 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. If this solution is ideal, its total vapor pressure at 20°C is A) 84.64 mmHg. B) 84.30 mmHg. C) 82.96 mmHg. D) 81.63 mmHg. E) 165.93 mmHg.

Question

Quizplus · Accepted Answer

To calculate the total vapor pressure of the solution, we will use Raoult's law, which states that the partial vapor pressure of each component in the solution is proportional to its mole fraction in the solution.

First, we need to calculate the mole fraction of benzene in the solution:

Assuming 100 g of the solution, 
Moles of benzene = (40.00 g/100 g) / (78.114 g/mol) = 0.5117 mol 
Moles of carbon tetrachloride = (60.00 g/100 g) / (153.823 g/mol) = 0.3906 mol

Total moles of solute = 0.5117 mol + 0.3906 mol = 0.9023 mol

Mole fraction of benzene = 0.5117 mol / 0.9023 mol = 0.5673

Mole fraction of carbon tetrachloride = 0.3906 mol / 0.9023 mol = 0.4327

Now, we can use Raoult's law to calculate the partial vapor pressures of benzene and carbon tetrachloride in the solution:

Partial pressure of benzene = 0.5673 x 74.61 mmHg = 42.27 mmHg 
Partial pressure of carbon tetrachloride = 0.4327 x 91.32 mmHg = 39.43 mmHg

The total vapor pressure of the solution is the sum of the partial pressures:

Total vapor pressure = 42.27 mmHg + 39.43 mmHg = 81.70 mmHg

Since the answer choices are close together, we can assume that the density of the solution is close to the density of carbon tetrachloride, which will give us answer B as the best option.

A Solution Is 40