Dry nitrogen gas is bubbled through liquid benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) at \(20.0^{\circ} \mathrm{C} .\) From \(100.0 \mathrm{L}\) of the gaseous mixture of nitrogen and benzene, \(24.7 \mathrm{g}\) benzene is condensed by passing the mixture through a trap at a temperature where nitrogen is gaseous and the vapor pressure of benzene is negligible. What is the vapor pressure of benzene at \(20.0^{\circ} \mathrm{C} ?\)

We are given the following information: 1. Initial volume of the gaseous mixture of nitrogen and benzene: 100.0 L 2. Mass of benzene condensed: 24.7 g 3. Temperature of the system: 20.0°C = 293.15 K (converting to Kelvin) We need to determine the vapor pressure of benzene at this temperature.

First, we need to calculate the moles of condensed benzene using the given mass and the molar mass of benzene (C6H6): Molar mass of benzene = (6 × 12.01 g/mol C) + (6 × 1.01 g/mol H) = 78.12 g/mol Moles of condensed benzene = mass / molar mass = 24.7 g (C6H6) / 78.12 g/mol = 0.3161 mol (C6H6)

Since benzene is condensed, the remaining gaseous mixture in the 100 L container must only be nitrogen gas. Using the Ideal Gas Law, we can determine the initial moles of benzene vapor: PV = nRT Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (8.314 J/mol K), and T is the temperature. Rearranging the formula to solve for the number of moles (n): n = PV / RT We know that the volume (V) is 100 L, the temperature (T) is 293.15 K, and R is 8.314 J / (mol K). However, we don't have the pressure yet, but we can find the partial pressure of benzene in the mixture using the condensed moles: Partial pressure of benzene (P_benzene) = Moles of condensed benzene × R × T / V = 0.3161 mol × 8.314 J / (mol K) × 293.15 K / 100 L = 0.9785 atm

Now that we have the partial pressure of benzene, we can calculate the vapor pressure of benzene at 20.0°C. The partial pressure of benzene is equal to its vapor pressure at this temperature: Vapor pressure of benzene = Partial pressure of benzene = 0.9785 atm The vapor pressure of benzene at 20.0°C is 0.9785 atm.