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, \(8.00 \mathrm{~L}\) of argon gas is passed through \(11.7872 \mathrm{~g}\) of liquid hexane \(\mathrm{C}_{6} \mathrm{H}_{14}\) at \(30.0^{\circ} \mathrm{C}\). The mass of the remaining liquid after the experiment is \(4.875 \mathrm{~g}\). Assuming that the gas becomes saturated with hexane vapor and that the total gas volume and temperature remain constant, what is the vapor pressure of hexane in atm?

Short answer

The vapor pressure of hexane at 30.0°C is 0.1964 atm.

Step-by-step solution

Calculate the mass of hexane vapor

Subtract the mass of the remaining liquid from the initial mass of the liquid hexane to find the mass of the hexane vapor. Mass of hexane vapor = Initial mass - Remaining mass = 11.7872 g - 4.875 g = 6.9122 g

Calculate the moles of hexane vapor

To find the moles of hexane vapor, divide the mass of hexane vapor by its molar mass (86.18 g/mol, since hexane is \(\mathrm{C}_6\mathrm{H}_{14}\)). Moles of hexane vapor = Mass of hexane vapor / Molar mass of hexane = 6.9122 g / 86.18 g/mol = 0.0802 mol

Calculate the mole fractions of argon and hexane

First, calculate the moles of argon gas using the ideal gas law: PV = nRT Where P is pressure (in atm), V is volume (in L), n is the moles of gas, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature (in K). We're given that the volume of argon gas is 8.00 L and the temperature is 30°C, which is equal to 303.15 K. Assume the atmospheric pressure is 1 atm. 1 atm * 8.00 L = n * 0.0821 L·atm/mol·K * 303.15 K n (moles of argon) = 0.3283 mol Now, calculate the mole fractions of argon and hexane: Mole fraction of argon (X_Ar) = moles of argon / (moles of argon + moles of hexane) = 0.3283 mol / (0.3283 mol + 0.0802 mol) = 0.8036 Mole fraction of hexane (X_C6H14) = moles of hexane / (moles of argon + moles of hexane) = 0.0802 mol / (0.3283 mol + 0.0802 mol) = 0.1964

Use Dalton's Law of Partial Pressures to calculate vapor pressure

According to Dalton's Law of Partial Pressures, the partial pressure of each gas in a mixture is equal to its mole fraction times the total pressure. Partial pressure of hexane (P_C6H14) = Mole fraction of hexane (X_C6H14) * Total pressure = 0.1964 * 1 atm = 0.1964 atm Thus, the vapor pressure of hexane at 30.0°C is 0.1964 atm.

Key concepts

Volatile Liquid

A volatile liquid is a substance that easily evaporates at room temperature due to its relatively high vapor pressure.

These liquids have molecules that are not held together very strongly, allowing them to transition into vapor easily. For example, the hexane in the exercise is a volatile liquid. Its molecules break free from the liquid phase and mix with the argon gas.

• The extent to which a liquid is volatile is characterized by its vapor pressure—the higher the vapor pressure, the more volatile the liquid.
• In practical experiments, understanding the volatility of liquids helps predict how much of the liquid will evaporate under given conditions.

Volatile liquids are significant in various applications, such as in the preparation of chemical formulations and in culinary techniques, where evaporation affects taste and preservation.

Ideal Gas Law

The ideal gas law is a fundamental equation connecting the physical properties of a gas: its pressure, volume, temperature, and amount of substance. This relationship is expressed as: \[PV = nRT\]

Where

• \(P\): Pressure in atm
• \(V\): Volume in liters
• \(n\): Number of moles of the gas
• \(R\): Ideal gas constant, 0.0821 L·atm/mol·K
• \(T\): Temperature in Kelvin

This equation assumes that gas molecules do not attract or repel each other and occupy negligible space. It's crucial for calculating one property if others are known, as in this exercise where it's used to find the moles of argon.

It's essential to convert all your measurements to appropriate units: pressure in atmospheres, volume in liters, and temperature in Kelvin, to use the ideal gas law effectively.

Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases.

This principle is useful in determining the vapor pressure of a volatile substance in a gas mixture. According to Dalton’s Law: \[P_{total} = P_1 + P_2 + ext{...} + P_n\]

For any specific gas, like hexane, the partial pressure can be calculated by: \[P_{hexane} = X_{hexane} imes P_{total}\]

• Where \(X_{hexane}\) represents the mole fraction of hexane, and \(P_{total}\) is the atmospheric pressure.

Understanding Dalton's Law helps in analyzing gas mixtures, particularly in predicting the behavior of each gas component. It explains how gases in a liquid's vapor state contribute to the total pressure in a system, as seen in this exercise to determine the vapor pressure of hexane.