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Entropy and Reaction Spontaneity Example Problem

Using Entropy Change to Determine if a Reaction is Spontaneous

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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) ΔSsys = 30 J/K , ΔSsurr = 50 J/K
II) ΔSsys = 60 J/K, ΔSsurr = -85 J/K
III) ΔSsys = 140 J/K, ΔSsurr = -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.

ΔStotal = ΔSsys + ΔSsurr

where
ΔStotal is the total entropy change
ΔSsys is the entropy change of the system
ΔSsurr is the entropy change of the surroundings

System I

ΔStotal = ΔSsys + ΔSsurr
ΔStotal = 30 J/K + 50 J/K
ΔStotal = 80 J/K

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

System II

ΔStotal = ΔSsys + ΔSsurr
ΔStotal = 60 J/K + -85 J/K
ΔStotal = -25 J/K

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

System III

ΔStotal = ΔSsys + ΔSsurr
ΔStotal = 140 J/K + -85 J/K
ΔStotal = 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

ΔSsurr > 0 - exothermic
ΔSsurr < 0 - endothermic

System I

ΔSsurr = 50 : Positive - exothermic

System II

ΔSsurr = -85 : negative - endothermic

System III

ΔSsurr = -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.
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