Entropy of Reaction Example Problem

How to Calculate the Molar Entropy Change of a Reaction

Entropy is a measure of disorder in a system.
Entropy is a measure of disorder in a system. Mmdi, Getty Images

This example problem demonstrates how to find the entropy of reaction from standard molar entropy data on the reactants and products. Entropy is calculated as a change in the level of entropy before and after a chemical reaction. Essentially, it reflects whether the amount of disorder or randomness in the system increased or decreased as a consequence of the reaction.

Standard Molar Entropy Change Problem

What is the standard molar entropy change of the following reaction?



4 NH3(g) + 5 O2(g) → 4 NO(g) + 6 H2O(g)

Given:
NH3 = 193 J/K·mol
O2 = 205 J/K·mol
NO = 211 J/K·mol
H2O = 189 J/K·mol

(Note, in this type of problem you'll either be given the molar entropy values of the reactants and products or you'll need to look them up in a table.)

Solution

The change in the standard molar entropy of a reaction can be found by the difference between the sum of the molar entropies of the products and the sum of the molar entropies of the reactants.

ΔS°reaction = Σnpproducts - Σnrreactants

ΔS°reaction = (4 S°NO + 6 S°H2O) - (4 S°NH3 + 5 S°O2)

ΔS°reaction = (4(211 J/K·K) + 6(189 J/K·mol)) - (4(193 J/K·mol) + 5(205 J/K·mol))

ΔS°reaction = (844 J/K·K + 1134 J/K·mol) - (772 J/K·mol + 1025 J/K·mol)

ΔS°reaction = 1978 J/K·mol - 1797 J/K·mol)

ΔS°reaction = 181 J/K·mol

We can check our work using the techniques introduced in this example problem. The reaction involves all gasses and the number of moles of products is greater than the number of moles of reactants so the expected change in entropy should be positive.



Answer:

The standard molar entropy change of the reaction is 181 J/K·mol.