Problem 105 - Chemistry: The Central Science

Question

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. \(\operatorname{In}\) an experiment, \(5.00 \mathrm{~L}\) of \(\mathrm{N}_{2}\) gas is passed through \(7.2146 \mathrm{~g}\) of liquid benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), at \(26.0^{\circ} \mathrm{C}\). The liquid remaining after the experiment weighs \(5.1493 \mathrm{~g}\). 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?

Step-by-Step Solution

Answer

The vapor pressure of the benzene in this experiment is approximately 99.8 torr.

Step 1: Calculate the mass of evaporated benzene

Subtract the final mass of the liquid benzene from the initial mass to find the mass of the benzene that evaporated: Evaporated benzene mass = Initial mass - Final mass Evaporated benzene mass = \(7.2146 \mathrm{~g}\) - \(5.1493 \mathrm{~g}\) Evaporated benzene mass = \(2.0653 \mathrm{~g}\)

Step 2: Calculate moles of evaporated benzene

Divide the mass of the evaporated benzene by its molar mass to find the moles of benzene: Moles of benzene = \(\frac{Evaporated~benzene~mass}{Molar~mass~of~benzene}\) The molar mass of benzene, C6H6, is: (6 × 12.01) + (6 × 1.01) = 78.12 g/mol. Moles of benzene = \(\frac{2.0653 \mathrm{~g}}{78.12 \mathrm{~g/mol}}\) Moles of benzene = \(0.02644 \mathrm{~mol}\)

Step 3: Calculate the partial pressure of benzene vapor

Use the ideal gas law equation, PV=nRT, to find the partial pressure of benzene vapor. In this case, the volume of the gas is given (5.00 L), and we have calculated the moles of benzene. The temperature is given in degrees Celsius, so we must first convert it to Kelvin by adding 273.15. The gas constant R is given as \(0.0821 \mathrm{~L*atm/mol*K}\). Temperature in Kelvin = \(26.0^{\circ} \mathrm{C}\) + 273.15 = 299.15 K Rearrange the ideal gas law equation to solve for the pressure (P): P = \(\frac{nRT}{V}\) Pressure = \(\frac{(0.02644 \mathrm{~mol}(0.0821 \mathrm{~L*atm/mol*K})(299.15 \mathrm{~K})}{5.00 \mathrm{~L}}\) Pressure = 0.1313 atm

Step 4: Convert pressure to torr

To convert a pressure in atm to torr, multiply by the conversion factor 760 torr/atm: Vapor pressure of benzene = Pressure × Conversion factor Vapor pressure of benzene = 0.1313 atm × 760 torr/atm Vapor pressure of benzene = 99.8 torr The vapor pressure of the benzene in this experiment is approximately 99.8 torr.

Key Concepts

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry that describes the relationship between four properties of a gas: pressure (P), volume (V), temperature (T), and the amount in moles (n). This relationship is expressed in the formula \( PV = nRT \). Here, \( R \) stands for the ideal gas constant, which is usually provided as \( 0.0821 \, \text{L*atm/mol*K} \). To use this law, it is essential to ensure all variables are in the correct units:

• Pressure (P) in atmospheres (atm)
• Volume (V) in liters (L)
• Temperature (T) in Kelvin (K), converted from Celsius by adding 273.15
• Moles (n) which represent the quantity of the gas

The versatility of the ideal gas law allows it to solve problems involving gases. By rearranging the equation, you can find any one of the variables if the others are known. For instance, you could calculate pressure if you have the number of moles, temperature, and volume. In our case, the formula helped find the vapor pressure of benzene when the volume remained constant, and the moles and temperature were known.

Evaporation

Evaporation is a type of vaporization that occurs when a liquid turns into a gas at a temperature below its boiling point. This process is crucial in many natural and industrial settings, including the behavior of volatile substances like benzene. Evaporation happens at the surface of a liquid as molecules gain enough energy to break away into the gas phase:

• It increases with temperature since heat provides energy for molecules to escape.
• Surface area also affects evaporation; larger areas mean more molecules can vaporize.
• The process is part of dynamic equilibrium in closed systems, with molecules constantly moving between liquid and vapor phases.

In our experiment, the evaporation of benzene was evident when the mass decreased after nitrogen gas bubbled through it. This lost mass represented the amount of benzene that had vaporized and filled the space with its vapor, ultimately allowing us to calculate its vapor pressure.

Benzene

Benzene is a simple aromatic hydrocarbon with the molecular formula \( C_6H_6 \). It is composed of six carbon atoms joined in a ring, with each carbon atom also bonded to a single hydrogen atom. Known for its stability and unique structure, benzene is used extensively in the chemical industry for manufacturing various chemicals.Important properties of benzene include:

• It's a volatile liquid with a characteristic sweet odor.
• Benzene is a nonpolar solvent, often used in organic chemistry experiments.
• Its volatility makes it significant in studies of vapor pressure, such as the one detailed in our experiment.

Though widely used, benzene must be handled carefully due to its toxic nature. Exposure can cause harmful effects, hence proper safety measures are critical in a laboratory setting. In the context of our experiment, understanding benzene's properties helped us to predict how it would behave under given conditions, allowing us to calculate its vapor pressure accurately.