The vapor pressure of a volatile liquid can be determined by slowly bubbling a known volume of gas through it at a known temperature and pressure. In an experiment, 5.00 L of N2 gas is passed through 7.2146 g of liquid benzene (C6H6) at 26.0 °C. The liquid remaining after the experiment weighs 5.1493 g. Assuming that the gas becomes saturated with benzene vapor and that the total gas volume and temperature remain constant, what is the vapor pressure of the benzene in torr?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

Verified step by step guidance

Calculate the mass of benzene that has evaporated by subtracting the final mass of the liquid from the initial mass: \( \text{mass evaporated} = 7.2146 \text{ g} - 5.1493 \text{ g} \).

Convert the mass of evaporated benzene to moles using its molar mass: \( \text{moles of C}_6\text{H}_6 = \frac{\text{mass evaporated}}{\text{molar mass of C}_6\text{H}_6} \).

Use the ideal gas law to find the partial pressure of benzene vapor. First, calculate the total moles of gas (N2 + benzene vapor) using the ideal gas law: \( PV = nRT \).

Determine the moles of N2 gas using the ideal gas law, assuming the initial conditions (before benzene evaporation) and subtract the moles of benzene vapor to find the moles of N2.

Calculate the vapor pressure of benzene by using the ratio of moles of benzene vapor to total moles of gas and multiplying by the total pressure: \( P_{\text{benzene}} = \left( \frac{\text{moles of C}_6\text{H}_6}{\text{total moles}} \right) \times P_{\text{total}} \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It reflects the tendency of molecules to escape from the liquid phase into the vapor phase. The higher the vapor pressure, the more volatile the substance, indicating that it evaporates easily. Understanding vapor pressure is crucial for determining how much of a liquid will evaporate under specific conditions.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the behavior of gases under varying conditions. In this experiment, it helps to understand how the volume of nitrogen gas and the temperature affect the saturation of benzene vapor in the gas phase, allowing for the determination of vapor pressure.

Mass Loss and Molar Mass

In this experiment, the mass loss of benzene is critical for calculating the amount of benzene that evaporated. By knowing the initial and final masses of the liquid, one can determine the mass of benzene that transitioned to vapor. Additionally, the molar mass of benzene (approximately 78.11 g/mol) is necessary to convert the mass of evaporated benzene into moles, which can then be used to find the vapor pressure using the Ideal Gas Law.

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