A solution is 40.0% by mass benzene (C₆H₆) in carbon tetrachloride (CCl₄) at 20^$\circ$C. The vapor pressure of pure benzene and pure carbon tetrachloride at this temperature is 74.61 mmHg and 91.32 mmHg, respectively. Calculate the vapor pressure of the solution at 20^$\circ$C: A) 66.4 mmHg B) 73.8 mmHg C) 81.8 mmHg D) 83.0 mmHg E) 84.6 mmHg

Question

Quizplus · Accepted Answer

To calculate the vapor pressure of the solution, we use Raoult's Law, which states that the vapor pressure of a solution is equal to the sum of the mole fraction of each component multiplied by its pure component vapor pressure. First, we need to calculate the mole fractions of benzene and carbon tetrachloride in the solution.Given that the solution is 40.0% by mass benzene, the mass of benzene is 40.0 g and the mass of carbon tetrachloride is 60.0 g (since it makes up the remaining 60% of the solution).Molar mass of benzene (C6H6) = 78.11 g/molMolar mass of carbon tetrachloride (CCl4) = 153.82 g/molMoles of benzene = 40.0 g / 78.11 g/mol = 0.512 molesMoles of carbon tetrachloride = 60.0 g / 153.82 g/mol = 0.390 molesTotal moles = 0.512 + 0.390 = 0.902 molesMole fraction of benzene = 0.512 / 0.902 = 0.568Mole fraction of carbon tetrachloride = 0.390 / 0.902 = 0.432Using Raoult's Law:Vapor pressure of solution = (mole fraction of benzene * vapor pressure of pure benzene) + (mole fraction of carbon tetrachloride * vapor pressure of pure carbon tetrachloride)= (0.568 * 74.61 mmHg) + (0.432 * 91.32 mmHg)= 42.38 mmHg + 39.45 mmHg= 81.83 mmHgTherefore, the vapor pressure of the solution is approximately 81.8 mmHg.

A Solution Is 40 ∘\circ∘ C the Vapor Pressure of Pure Benzene and Pure Carbon

A Solution Is 40 $\circ$ C the Vapor Pressure of Pure Benzene and Pure Carbon