Problem 115 - Chemistry: The Central Science

Question

Does the effect of intermolecular attraction on the properties of a gas become more significant or less significant if (a) the gas is compressed to a smaller volume at constant temperature; (b) the temperature of the gas is increased at constant volume?

Step-by-Step Solution

Answer

In conclusion, the effect of intermolecular attraction on the properties of a gas becomes: (a) more significant when the gas is compressed to a smaller volume at constant temperature, as the decrease in volume leads to an increase in intermolecular attractive forces; (b) less significant when the temperature of the gas is increased at constant volume, as the increase in kinetic energy of gas molecules opposes intermolecular forces of attraction.

Step 1: Understand intermolecular attraction in gases

Intermolecular attraction refers to the forces between molecules within a substance. In the case of gases, these forces can play a role in deviating the behavior of a gas from the ideal gas law. The Van der Waals equation introduces the constants 'a' and 'b' to account for the deviations caused by intermolecular attraction and the volume occupied by molecules: \( (P + \frac{an^2}{V^2})(V - nb) = nRT \), where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, T is temperature, a is a constant that represents intermolecular attraction, b is a constant that represents the volume occupied by gas molecules. Now let's analyze the scenarios presented in the exercise.

Step 2: Scenario (a): Gas compression at constant temperature

In this scenario, the gas is compressed to a smaller volume at a constant temperature. As the volume decreases, the term \(\frac{an^2}{V^2}\) will increase. This indicates that the intermolecular attraction will become more significant. This can be explained by understanding that as the volume decreases, the distance between gas molecules also decreases, leading to an increase in intermolecular attractive forces, which in turn deviate the gas behavior further from ideal gas law.

Step 3: Scenario (b): Increase in temperature at constant volume

In this scenario, the temperature of the gas is increased while the volume is held constant. As the temperature increases, the term \(\frac{an^2}{V^2}\) remains constant, as there is no change in volume. However, as the temperature increases, the gas molecules gain kinetic energy, which opposes intermolecular forces of attraction. This means that the effect of intermolecular attraction becomes less significant as the temperature increases. In conclusion, the effect of intermolecular attraction on the properties of a gas becomes: (a) more significant when the gas is compressed to a smaller volume at constant temperature; (b) less significant when the temperature of the gas is increased at constant volume.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry, which helps describe the behavior of gases. This law combines several simpler gas laws to form a comprehensive equation: \[ PV = nRT \] Here,

• \(P\) is the pressure exerted by the gas
• \(V\) is the volume the gas occupies
• \(n\) stands for the number of moles of the gas
• \(R\) is the ideal gas constant
• \(T\) is the temperature in Kelvin

The Ideal Gas Law assumes no attraction between gas molecules and that the volume of the molecules themselves is negligible compared to the volume the gas occupies. This makes it most applicable to ideal or hypothetical gases. However, real gases deviate from this law, especially at high pressures or low temperatures, due to intermolecular forces. Under such conditions, the simple \(PV = nRT\) equation may not accurately predict a gas's behavior. To account for these deviations, we look to corrections such as the Van der Waals equation.

Van der Waals Equation

The Van der Waals Equation adjusts the Ideal Gas Law to better represent real gases. It's presented as: \[(P + \frac{an^2}{V^2})(V - nb) = nRT \] In this equation, two constants, \(a\) and \(b\), are introduced:

• \(a\) represents the magnitude of intermolecular attractions
• \(b\) accounts for the volume occupied by the gas molecules

These corrections help describe how molecular size and attraction affect a gas's behavior. The term \(\frac{an^2}{V^2}\) increases sensitivity to intermolecular forces when a gas is compressed, as the molecules are closer together. Similarly, the term \(V - nb\) corrects for the finite volume of gas molecules. Both these terms help real gases, like Van der Waals gases, reveal their behavior more accurately under specific conditions. For example, at high pressure or when compressed at constant temperature, the influence of these deviations becomes significant. Van der Waals' equation effectively bridges the gap between ideal and real gas behaviors.

Molecular Kinetic Energy

Molecular Kinetic Energy is the energy associated with the motion of gas molecules. It is directly proportional to the temperature of the gas, which can be interpreted through the relation: \[ KE = \frac{3}{2}kT \] where

• \(KE\) is the kinetic energy of molecules
• \(k\) is the Boltzmann constant
• \(T\) is the temperature in Kelvin

The energy increases as temperature goes up, leading to faster-moving molecules. This change in speed impacts intermolecular forces, as faster molecules can overcome these forces more easily. Thus, when the temperature of a gas increases at constant volume, the effect of intermolecular attraction becomes less significant, since the increased kinetic energy counteracts these attractive forces. By comprehending molecular kinetic energy, one can observe why temperature adjustments lead to variations in gas behavior and interaction. This understanding is fundamental in explaining how gases behave differently under varying temperatures and pressures.