Statistical Mixing & Grand Review

Question 1

Define positional probability and relate it to entropy.

Answer 1

Positional probability is the likelihood of finding particles in a particular spatial arrangement; higher positional probabilities correspond to higher entropy.

Question 2

Why does spontaneous mixing of two ideal gases at equal pressure and temperature have ΔH≈0 but ΔS>0?

Answer 2

Because energy does not change appreciably, but the number of positional microstates increases enormously when the gases mix.

Question 3

How does confinement (e.g., compression) lower entropy from the positional-probability viewpoint?

Answer 3

Restricting volume decreases the spatial region available to each molecule, reducing microstate count and therefore entropy.

Question 4

Summarize how the First, Second, and Third Laws collectively determine reaction spontaneity and attainable states.

Answer 4

The First Law conserves energy; the Second Law directs processes toward maximum universal entropy; the Third Law provides the zero-entropy baseline, enabling quantitative assessment of all entropy changes. Spontaneity emerges when the combined enthalpic and entropic terms yield ΔG<0 under given conditions.

Question 5

Why must both enthalpy and entropy be considered when predicting phase stability at varied temperatures?

Answer 5

Because temperature scales the entropy term (TΔS), which can override enthalpic favorability as T changes, shifting the sign of ΔG.

Question 6

Explain how molecular-level interactions translate into macroscopic thermodynamic data used in engineering applications.

Answer 6

Statistical mechanics bridges atomic-scale forces and motions to ensemble averages, allowing derivation of state functions that engineers measure and manipulate in reactors, turbines, and refrigeration cycles.