Indicate whether each statement is true or false. (a) Unlike enthalpy, where we can only ever know changes in H, we can know absolute values of S. (b) If you heat a gas such as CO₂, you will increase its degrees of translational, rotational and vibrational motions. (c) CO₂(g) and Ar(g) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.

Verified step by step guidance

1. (a) Consider the nature of entropy (S) and enthalpy (H). Entropy is a measure of disorder or randomness in a system, and unlike enthalpy, which is a state function where we typically measure changes (ΔH), entropy can be measured in absolute terms because it is based on the third law of thermodynamics, which states that the entropy of a perfect crystal at absolute zero is zero. Therefore, we can determine absolute values of S.
2. (b) When a gas such as CO₂ is heated, its kinetic energy increases. This increase in energy affects the gas's degrees of freedom: translational (movement of the entire molecule through space), rotational (rotation of the molecule around its center of mass), and vibrational (periodic motion of atoms within the molecule). Heating the gas increases all these types of motion.
3. (c) To compare CO₂(g) and Ar(g), consider their molar masses and the concept of microstates. CO₂ has a molar mass of about 44 g/mol, while Ar has a molar mass of about 40 g/mol. Although their molar masses are similar, the number of microstates (possible configurations of a system) depends on the complexity of the molecules. CO₂ is a triatomic molecule with more vibrational modes compared to the monoatomic Ar, which affects the number of microstates.

Key Concepts

Enthalpy and Absolute Values of Entropy

Enthalpy (H) is a state function that measures the total heat content of a system, but we can only determine changes in enthalpy (ΔH) between states, not absolute values. In contrast, entropy (S) is also a state function, but it can be assigned absolute values based on the third law of thermodynamics, which states that the entropy of a perfect crystal at absolute zero is zero.

Degrees of Freedom in Gases

The degrees of freedom of a gas refer to the number of independent ways in which the molecules can move. For a gas like CO₂, heating increases its kinetic energy, which enhances translational (movement through space), rotational (spinning), and vibrational (oscillating) motions, thereby increasing the gas's temperature and energy.

Microstates and Statistical Mechanics

Microstates are specific configurations of a system that correspond to a particular macrostate, defined by macroscopic properties like temperature and pressure. While CO₂ and Ar have similar molar masses, their molecular structures differ, affecting their microstates. At the same temperature, the number of microstates can vary, leading to different entropy values despite similar molar masses.