Which state in each of the following pairs has the higher entropy per mole of substance? (a) H₂ at 25 °C in a volume of 10 L or H₂ at 25 °C in a volume of 50 L

Verified step by step guidance

1. Entropy is a measure of the disorder or randomness in a system. In general, the greater the volume a gas occupies, the greater the number of possible positions and arrangements for the gas molecules, leading to higher entropy.
2. Consider the two states of H₂ gas: one at 10 L and the other at 50 L, both at the same temperature of 25 °C.
3. Since both samples are at the same temperature, the kinetic energy of the molecules is the same in both cases. Therefore, temperature does not affect the comparison of entropy in this scenario.
4. The key difference between the two states is the volume. A larger volume allows for more possible microstates (ways to arrange the molecules), which increases the entropy.
5. Therefore, H₂ at 25 °C in a volume of 50 L has higher entropy per mole of substance compared to H₂ at 25 °C in a volume of 10 L.

Key Concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. Higher entropy indicates greater disorder and more available microstates, which is crucial for understanding the spontaneity of processes.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of an ideal gas through the equation PV = nRT. This law helps predict how gases behave under different conditions and is essential for understanding how changes in volume affect the entropy of a gas, as it influences the number of accessible microstates.

Volume and Entropy Relationship

For gases, an increase in volume generally leads to an increase in entropy. This is because a larger volume allows gas molecules to occupy more positions and configurations, resulting in greater disorder. Therefore, when comparing two states of the same substance at the same temperature, the state with the larger volume will typically have higher entropy.