**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.