Topic 9.1 Introduction to Entropy: describe entropy as a measure of the dispersal of energy and matter, and predict the sign of the entropy change for physical and chemical processes.

What this topic is asking

The College Board (Topic 9.1) wants you to describe entropy as a measure of the dispersal of energy and matter, and to predict the sign of the entropy change for physical and chemical processes. Entropy is the new state function that, together with enthalpy, decides whether a process is thermodynamically favorable.

What entropy is

The more spread out and disordered the energy and matter, the higher the entropy. A gas, with its particles free to move throughout a container, has far more accessible arrangements than the same substance as an orderly solid, so it has much higher entropy. Entropy is a state function, like enthalpy.

What increases entropy

The single most useful clue for a chemical reaction is the change in the number of moles of gas: more gas moles on the product side means a positive entropy change, fewer means negative. Phase changes and dissolving are the next most common cues. Temperature increases always raise entropy because more energy states become accessible.

Predicting the sign of the entropy change

To predict the sign of $\Delta S$, compare the dispersal of the products with that of the reactants. If the products are more disordered (a gas is produced, gas moles increase, a solid dissolves), $\Delta S > 0$. If the products are more ordered (a gas condenses or freezes, gas moles decrease), $\Delta S < 0$. When the change is not obvious from phase, fall back on the change in moles of gas. This qualitative prediction is enough for most exam questions and feeds directly into the free-energy calculation of Topic 9.3.

Try this

Q1. Predict the sign of $\Delta S$ for $2\text{NO}_2(g) \rightarrow \text{N}_2\text{O}_4(g)$. [2 points]

• Cue. Two gas moles become one, so the gas moles decrease and $\Delta S < 0$ (negative).

Q2. State whether the entropy of a substance increases or decreases when it is heated, and explain. [2 points]

• Cue. Increases; raising the temperature increases thermal motion and the number of accessible energy states, dispersing the energy more.