Problem 117 - 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

The effect of intermolecular attraction on the properties of a gas becomes more significant when the gas is compressed to a smaller volume at constant temperature, as the term \(\frac{an^2}{V^2}\) increases. On the other hand, the effect becomes less significant when the temperature of the gas is increased at constant volume, as the increased kinetic energy overcomes the intermolecular forces.

Step 1: Recall the Ideal Gas Law

For an ideal gas, we have the equation: \(PV = nRT\), where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. In an ideal gas, there is no intermolecular attraction, and this equation holds true. However, real gases do have intermolecular forces, and therefore, we need to consider the Van der Waals equation to account for these forces.

Step 2: Recall the Van der Waals Equation

For a real gas, the Van der Waals equation is: \((P + \frac{an^2}{V^2})(V - nb) = nRT\), where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, T is the temperature, and "a" and "b" are Van der Waals constants specific to the gas. The term \(\frac{an^2}{V^2}\) accounts for the intermolecular attraction, while the term "nb" accounts for the volume occupied by the gas particles.

Step 3: Analyze Scenario (a) - Gas Compression at Constant Temperature

When a gas is compressed to a smaller volume at constant temperature (T), the term \(\frac{an^2}{V^2}\) would increase. The pressure (P) would also increase when the volume (V) is decreased according to the ideal gas law. Since the term \(\frac{an^2}{V^2}\) increases with the decrease in volume, we can conclude that the effect of intermolecular attraction on the gas properties becomes more significant when the gas is compressed to a smaller volume at constant temperature.

Step 4: Analyze Scenario (b) - Temperature Increase at Constant Volume

When the temperature (T) of a gas is increased at constant volume (V), the pressure (P) would also increase according to the ideal gas law. The term \(\frac{an^2}{V^2}\) remains unchanged since the volume and the number of moles are constant. However, due to increased temperature, the kinetic energy of the gas particles also increases. The increased kinetic energy overcomes the intermolecular forces, causing a lesser effect of intermolecular attraction on the gas properties. Thus, we can conclude that the effect of intermolecular attraction on the properties of a gas becomes less significant when the temperature of the gas is increased at constant volume.