# Understanding entropy / spontaneity

I have issues understanding the spontaneity for these processes:

Which of the following processes are spontaneous:

(c) alignment of iron filings in a magnetic field;

(d) the reaction of sodium metal with chlorine gas to form sodium chloride;

The answer given for both (c) and (d) is that the entropy of the system decreases.

This has me puzzled because I don't think that even answers the question. Clearly I would think both (c) and (d) are spontaneous processes. For (c), the iron will naturally align itself in the magnetic field. For (d), I know the reverse reaction is non-spontaneous (table salt does not normally disassociate), so the forward reaction must be spontaneous.

Assuming I am correct, how do I reconcile this with the book answer?

The entropy of the universe increases for any spontaneous process. If we assume the entropy of the system is negative (like the book does) then the entropy of the surroundings must be positive and greater. I don't know what that would mean in this context.

I agree that it makes sense that the entropy of the system is negative. The iron filings are moving to a more ordered state in (c). For (d) there are more micro-states originally since there were more moles of reactants.

## 1 Answer

Based on your provided context, your book's "answers" are indeed misleading and non-answers.

Clearly I would think both (c) and (d) are spontaneous processes. For (c), the iron will naturally align itself in the magnetic field. For (d), I know the reverse reaction is non-spontaneous (table salt does not normally disassociate), so the forward reaction must be spontaneous.

The entropy of the universe increases for any spontaneous process. If we assume the entropy of the system is negative (like the book does) then the entropy of the surroundings must be positive and greater.

I agree that it makes sense that the entropy of the system is negative. The iron filings are moving to a more ordered state in (c). For (d) there are more micro-states originally since there were more moles of reactants.

These statements are correct. As you've argued, the change in entropy of the surroundings must be positive for these reactions to be spontaneous. The surroundings constitute a thermal reservoir, so the change in entropy is simply proportional to the heat evolved during the process, which implies that heat must be transferred from the system to the surroundings.

For the formation of sodium chloride, this is quite intuitive: sodium chloride is very stable and has a large, negative enthalpy of formation. The case of magnetization is less obvious, but it can be shown (see Ex 17.4 in Blundell and Blundell's Concepts in Thermal Physics) that an isothermal increase in the magnetic field leads to evolution of heat into the surroundings, and the same reasoning as above applies.