Problem 107 - 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 summary, the effect of intermolecular attraction on the properties of a gas becomes more significant as the gas is compressed to a smaller volume at constant temperature, and less significant when the temperature of the gas is increased at constant volume. This is because the impact of intermolecular forces becomes more noticeable at smaller volumes, while the increase in kinetic energy at higher temperatures reduces the influence of attractive forces on the gas molecules.

Step 1: Part (a): Gas compressed to a smaller volume at constant temperature

The ideal gas law states that the pressure P, volume V, and temperature T of an ideal gas are related by: \(PV = nRT\) Where \(n\) represents moles of the gas and \(R\) is the ideal gas constant. However, real gases do not always follow this law due to intermolecular attractions and repulsions. The van der Waals equation is a more accurate description of the behavior of real gases, which takes into account both intermolecular attraction (represented by \(a\)) and repulsion (represented by \(b\)): \(\left( P + a \left(\frac{n}{V}\right)^2 \right) (V - nb) = nRT\) In this equation, if the effects of intermolecular attraction and repulsion are negligible, the equation will converge to the ideal gas law. When the gas is compressed to a smaller volume at constant temperature, the volume term \(V\) decreases. Consequently, the factors representing intermolecular attraction \(\left( a \left( \frac{n}{V} \right)^2 \right)\) and repulsion \(\left( nb \right)\) will have a more significant impact on the gas's behavior since they have an inverse relationship to the volume. Therefore, the effect of intermolecular attraction on the properties of a gas becomes more significant as the gas is compressed to a smaller volume at constant temperature.

Step 2: Part (b): Temperature of the gas is increased at constant volume

When the temperature of the gas is increased at constant volume, the kinetic energy of the gas molecules will also increase. Due to the increase in kinetic energy, gas molecules will move faster, and the overall effect of intermolecular attractions will be reduced because the molecules are less likely to be influenced by attractive forces and are more likely to overcome them. At high temperatures, the gas molecules have sufficient energy to break away from the attractive forces, making the gas behave more like an ideal gas, where intermolecular attractions are considered negligible. So, in this case, the effect of intermolecular attraction on the properties of the gas becomes less significant when the temperature of the gas is increased at constant volume.