Entropy and Reaction Spontaneity Example Problem

This example problem demonstrates how to use changes in entropy of a system and its surroundings to determine a reaction's spontaneity and whether or not the reaction will be exothermic or endothermic.

Problem:

Using the following values for entropy
a) determine if a reaction would be spontaneous.
b) determine if the reaction is exothermic or endothermic with respect to the system

I) ΔS_sys = 30 J/K , ΔS_surr = 50 J/K
II) ΔS_sys = 60 J/K, ΔS_surr = -85 J/K
III) ΔS_sys = 140 J/K, ΔS_surr = -85 J/K

Solution

Part 1 - Determine if a reaction will be spontaneous.

A reaction will be spontaneous if the total entropy change is positive. It will not be spontaneous if the total entropy change is negative.

ΔS_total = ΔS_sys + ΔS_surr

where
ΔS_total is the total entropy change
ΔS_sys is the entropy change of the system
ΔS_surr is the entropy change of the surroundings

System I

ΔS_total = ΔS_sys + ΔS_surr
ΔS_total = 30 J/K + 50 J/K
ΔS_total = 80 J/K

The total entropy change is positive, therefore the reaction will be spontaneous.

System II

ΔS_total = ΔS_sys + ΔS_surr
ΔS_total = 60 J/K + -85 J/K
ΔS_total = -25 J/K

The total entropy change is negative, therefore the reaction will not be spontaneous.

System III

ΔS_total = ΔS_sys + ΔS_surr
ΔS_total = 140 J/K + -85 J/K
ΔS_total = 55 J/K

The total entropy change is positive, therefore the reaction will be spontaneous.

Part 2 - Determine if the reaction is exothermic or endothermic

A reaction would be exothermic with respect to the system if it adds entropy to the surroundings and endothermic if it reduces entropy of the surroundings. This means

ΔS_surr > 0 - exothermic
ΔS_surr < 0 - endothermic

System I

ΔS_surr = 50 : Positive - exothermic

System II

ΔS_surr = -85 : negative - endothermic

System III

ΔS_surr = -85 : negative - endothermic

Answer:

A reaction in system I is spontaneous and exothermic.
A reaction in system II is not spontaneous and endothermic.
A reaction in system III is spontaneous and endothermic.