Question

Using Appendix IVB to compare the standard entropies at 25 °C for the following pairs of substances. In each case, explain the difference in the entropy values. (ΔS → degree of disorder/randomness)

(a) Sc(s) (34.6) and Sc(g) (174.7)
(b) NH₃(g) (192) and NH₃(aq) (111)
(c) 1 mol P₄(g) (280) and 2 mol P₂(g) (218)
(d) C (graphite) (5.69) and C (diamond) (2.43)

Answer 1

The standard entropies of substances vary based on their molecular complexity, physical state, and crystal structure. Gaseous scandium has higher entropy than solid due to greater freedom of movement. Gaseous ammonia has higher entropy than its aqueous form, tetraatomic phosphorus has a higher entropy than diatomic, and graphite has higher entropy than diamond due to structural differences.

Step-by-step explanation:

When comparing the standard entropies (S°) of different substances at 25 °C, we look at how the molecular structure and physical state affect the entropy:

• Scandium in the solid state (Sc(s), 34.6 J/mol·K) has a much lower entropy than in the gaseous state (Sc(g), 174.7 J/mol·K) because gases have much more disorder and freedom of movement compared to solids.
• Ammonia as a gas (NH₃(g), 192 J/mol·K) has higher entropy than when dissolved in water (NH₃(aq), 111 J/mol·K) due to loss of translational freedom upon solvation.
• For phosphorus, 1 mol of P₄(g) at 280 J/mol·K has higher entropy than 2 mol of P₂(g) at 218 J/mol·K each because the tetraatomic molecule P₄ has more complexity and thus more possible microstates than the diatomic P₂.
• Carbon as graphite (C (graphite), 5.69 J/mol·K) has a higher entropy than as diamond (C (diamond), 2.43 J/mol·K) due to the more disordered structure of graphite compared to the highly ordered structure of diamond.