Under which of the following conditions is the law pV = RT obeyed most closely by a real gas?
a) Low temperature
b) High pressure
c) High temperature
d) Low pressure

The correct answers are C and D, which means that the law pV = RT is obeyed most closely by a real gas at high temperatures and low pressures. Let's understand why this is the case:

1. High Temperature:
- At high temperatures, the kinetic energy of gas particles increases, leading to greater motion and collisions between particles.
- The increased collisions result in more frequent and energetic collisions with the walls of the container, which increases the pressure.
- As the pressure increases, the volume occupied by the gas also increases to maintain equilibrium.
- Therefore, at high temperatures, the gas particles are more likely to behave ideally, obeying the ideal gas law more closely.

2. Low Pressure:
- At low pressures, the intermolecular forces between gas particles become less significant compared to the kinetic energy of the particles.
- The gas particles are more spread out and have more freedom to move around, reducing the impact of intermolecular forces.
- As a result, the gas particles tend to exhibit behavior that is closer to an ideal gas, following the ideal gas law more closely.

In summary, at high temperatures, the kinetic energy dominates, and at low pressures, the intermolecular forces become less significant. Both of these conditions favor the behavior of a real gas that is closer to an ideal gas, making the law pV = RT obeyed most closely.

To recap:
- High temperatures increase the kinetic energy of gas particles, leading to more energetic collisions and closer adherence to the ideal gas law.
- Low pressures reduce the influence of intermolecular forces, allowing gas particles to behave more ideally and follow the ideal gas law more closely.