Entropy Change Example Problem

Predicting the Sign of the Entropy Change of a Reaction

A sphere made of blurred lines
The entropy of a reaction is the positional probabilities for each reactant.

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For problems involving changes in entropy, knowing if the change should be positive or negative is a useful tool to check your work. It is easy to lose a sign during thermochemistry homework problems. This example problem demonstrates how to examine the reactants and products to predict the sign of the change in entropy of a reaction.

Entropy Problem

Determine if the entropy change will be positive or negative for the following reactions:
A) (NH4)2Cr2O7(s) → Cr2O3(s) + 4 H2O(l) + CO2(g)
B) 2 H2(g) + O2(g) → 2 H2O(g)
C) PCl5 → PCl3 + Cl2(g)

Solution

The entropy of a reaction refers to the positional probabilities for each reactant. For instance, an atom in its gas phase has more options for positions than the same atom in a solid phase. This is why gases have more entropy than solids.

In reactions, the positional probabilities must be compared for all the reactants to the products produced. Therefore, if the reaction involves only gases, the entropy is related to the total number of moles on either side of the reaction. A decrease in the number of moles on the product side means lower entropy. An increase in the number of moles on the product side means higher entropy.

If the reaction involves multiple phases, the production of a gas typically increases the entropy much more than any increase in moles of a liquid or solid.

Reaction A

(NH4)2Cr2O7(s) → Cr2O3(s) + 4 H2O(l) + CO2(g)
The reactant side contains only one mole where the product side has six moles produced. The was also a gas produced. The change in entropy will be positive.

Reaction B

2 H2(g) + O2(g) → 2 H2O(g)
There are 3 moles on the reactant side and only 2 on the product side. The change in entropy will be negative.

Reaction C

PCl5 → PCl3 + Cl2(g)
There are more moles on the product side than on the reactant side, therefore the change in entropy will be positive.

Answer Summary

Reactions A and C will have positive changes in entropy.
Reaction B will have negative changes in entropy.