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. In an experiment, \(5.00 \mathrm{~L}\) of \(\mathrm{N}_{2}\) gas is passed through \(7.2146 \mathrm{~g}\) of liquid benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) 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?

Short answer

The vapor pressure of the benzene is approximately \(104.4\text{ torr}\).

Step-by-step solution

Calculate the mass of vaporized benzene

Since we know the initial weight of the liquid benzene and its remaining weight after the experiment, we can find the mass of the vaporized benzene: Mass of vaporized benzene = Initial weight - Remaining weight Mass of vaporized benzene = \(7.2146\text{g} - 5.1493\text{g} = 2.0653\text{g}\).

Determine the molar mass of benzene

Benzene has a chemical formula of \(\mathrm{C_6H_6}\), so to calculate the molar mass, we need to add up the molar masses of all the atoms in the molecule. The molar mass for carbon (C) is \(12.01\text{g/mol}\) and hydrogen (H) is \(1.008\text{g/mol}\). Molar mass of benzene = (6 × Molar mass of carbon) + (6 × Molar mass of hydrogen) Molar mass of benzene = (6 × \(12.01\text{g/mol}\)) + (6 × \(1.008\text{g/mol}\)) = \(74.12\text{g/mol}\).

Calculate the moles of vaporized benzene

To find the moles of vaporized benzene, we will use the following formula: Moles of vaporized benzene = \(\frac{\text{Mass of vaporized benzene}}{\text{Molar mass of benzene}}\) Moles of vaporized benzene = \(\frac{2.0653\text{g}}{74.12\text{g/mol}} = 0.02786\text{mol}\).

Use the Ideal Gas Law to find the vapor pressure

The Ideal Gas Law can be expressed as: \(PV=nRT\), where P = Pressure (atm), V = Volume (L), n = Moles of gas, R = Gas constant (\(0.0821\frac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}}\)), T = Temperature (K). First, we need to convert the temperature from Celsius to Kelvin: T = \(26.0^{\circ}\text{C} + 273.15 = 299.15\text{K}\). Now, we can calculate the vapor pressure (P) using the Ideal Gas Law: \(P = \frac{nRT}{V} = \frac{0.02786\text{mol} \times 0.0821\frac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}} \times 299.15\text{K}}{5.00\text{L}} = 0.1374\text{ atm}\).

Convert the vapor pressure to torr

Pressure can be converted to different units using their respective conversion factors. To convert the vapor pressure from atm to torr, we need to use the following conversion factor: \(1\text{ atm} = 760\text{ torr}\). Vapor pressure in torr = \(0.1374\text{ atm} \times \frac{760\text{ torr}}{1\text{ atm}} = 104.4\text{ torr}\). The vapor pressure of the benzene is approximately \(104.4\text{ torr}\).

Key concepts

Vapor Pressure Determination

Vapor pressure is a critical property of liquids that reflects their tendency to evaporate. It depends on the temperature and the identity of the liquid. To determine the vapor pressure of a substance like benzene, one can perform an experiment where a known volume of inert gas, such as nitrogen (N₂), is bubbled through it at a constant temperature. When the gas becomes saturated with the vapor of the liquid, we can assess the quantity of liquid that has evaporated and hence the amount of vapor in the gas phase.

Calculating Vapor Pressure: Here's how the process looks step by step:

• We initially measure the mass of the volatile substance (benzene in our case) before the experiment.
• After bubbling nitrogen through the liquid, we measure the mass again. The difference in mass gives us the mass of benzene that has vaporized.
• From this, the moles of benzene vapor are calculated using its molar mass.
• Using the Ideal Gas Law, which relates pressure, volume, temperature, and number of moles of a gas, we can find the vapor pressure of the benzene vapor in the nitrogen gas mixture.
• Finally, if needed, we convert the pressure calculation to the desired units, such as torr, to report our findings.

This method is an application of basic principles of chemistry in a practical setting, bridging laboratory measurements to theoretical calculations.

Molar Mass of Benzene

The molar mass of a compound like benzene is fundamental in chemistry because it allows chemists to convert between the mass of a substance and the amount of substance in moles. For benzene, with the chemical formula C₆H₆, the calculation is straightforward but requires attention to the molar masses of carbon (C) and hydrogen (H).

Calculating Molar Mass:

• Carbon has a molar mass of approximately 12.01 g/mol and hydrogen is about 1.008 g/mol.
• Since benzene is composed of six carbon atoms and six hydrogen atoms, we sum six times the molar mass of carbon and six times the molar mass of hydrogen to calculate its molar mass.
• The total gives us the molar mass of benzene, which is crucial for further calculations, such as finding out the moles of benzene that vaporized in the described experiment.

Understanding the concept of molar mass and its calculation is vital since it lays the groundwork for stoichiometry and is used in various calculations across chemistry, including this exercise.

Ideal Gas Law

The Ideal Gas Law is an equation that serves as a powerful tool in the determination of various properties of gases. It provides a relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas through the formula PV=nRT, where R is the Universal Gas Constant.

Application of the Ideal Gas Law: In the context of our problem, we use the Ideal Gas Law to find the vapor pressure of benzene by performing the following steps:

• Calculate the number of moles of benzene that vaporized in the experiment.
• Convert the temperature from Celsius to Kelvin for use in the formula.
• With the volume of gas known, and R being a constant value (0.0821 L·atm/mol·K), we can solve for the pressure (P).

However, the law assumes ideal conditions that real gases do not perfectly adhere to, such as no intermolecular forces and gas particles having no volume. While these assumptions aren't true in reality, the Ideal Gas Law can still provide a close approximation under many conditions and is essential for basic understanding and calculations in gas behavior.