Entropy (4) Using ΔG Gibbs free energy to predict reaction feasibility

Edexcel A level Chemistry (2017)

Topic 13B: Entropy:

Here are the learning objectives to do with free energy change ΔG:

13B/18. To know that the balance between the entropy change and the enthalpy change determines the feasibility of a reaction and is represented by the equation

ΔG = ΔH – TΔSsystem

13B/19.  To be able to use the equation ΔG = ΔH − TΔSsystem to:

i) predict whether a reaction is feasible 


ii) determine the temperature at which a reaction is feasible

Using the Gibbs Free energy to predict reaction feasibility

If we want to predict the feasibility of a chemical change we can look at the entropy changes in the system and in the surroundings.

And if the sum of these two entropy changes is positive then we can conclude that the chemical change is feasible. 

We saw here in the analysis of the combustion of magnesium in oxygen that the sum of the entropy change in the system and surrounding was positive.

Defining ΔG, the Gibbs Free Energy change.

If we look at the Gibbs Free Energy change the problem is simplified because in the 19^th century J.W.Gibbs showed that we can combine the two entropy calculations into one.

We have seen that

ΔS_total =  ΔS_system   +    ΔS_surroundings

And if we want to use this equation we have to do two calculations to find both ΔS_system and ΔS_surroundings  

And if we find that    ΔS_total  > 0   then the chemical change is spontaneous and feasible.  

We can also say that

and if we insert this expression into the expression for ΔS_total  we obtain

Here the total entropy change is determined in terms of the properties   of the system alone i.e. ΔS_system ,  ΔH and T.

All we need to remember is that this relationship only holds true if the temperature and pressure of the process are constant. 

Now if we multiply through by —T we obtain:

—TΔS_total  = —TΔS_system  +  ΔH

and this leads to a definition of the Gibbs Free Energy change since

ΔG  =   ΔH —TΔS_system

And also that

ΔG  =  —TΔS_total

Implications of ΔG

From this it is possible to conclude that the Free Energy Change is proportional to the total change in entropy in both system and surroundings.

But there is a difference in sign between ΔG and ΔS_total

Whereas a spontaneous change meant that  ΔS_total   >   0 now , providing temperature and pressure remain constant in the process, ΔG <  0  for a spontaneous chemical change. 

So in a spontaneous chemical change at constant temperature and pressure the Gibbs Free Energy falls.        

But again this is only significant because the total entropy is increasing!!

The other thing we get from the Gibbs Free Energy change is that its value is a measure of the total non-expansion work that we can obtain from any chemical change.  More about that under redox equilibria.

Reaction Feasibility and ΔG

So the equation above:

                                          ΔG  =   ΔH —TΔS_system

shows us that the feasibility of a reaction depends upon the values of ΔH and ΔS for the system.   

Here’s how we can see if a reaction is feasible using ΔG:

ΔH (enthalpy change of the system)	ΔSsystem	ΔG (free energy change of the system)	Feasibility of the reaction
Negative	positive	Always negative	Reaction is feasible
Positive	negative	Always positive	Reaction is never feasible
Negative	negative	Negative at low temps	Feasible at low temps
Positive	positive	Negative at high temps	Feasible at high temps.

So most exothermic reactions are, as we suspected, feasible and spontaneous.

And even if the system becomes more ordered the positive entropy change in the surroundings more than compensates for the negative value in the system and ensures that the reaction is spontaneous.

We can see also that enthalpy (ΔH) more than entropy (ΔS_system) contributes to ΔG.

And we can also use

ΔG  =   ΔH —TΔS_system

to find out the temperature at which a reaction becomes spontaneous.

Question:

At what temperature does the decomposition of magnesium carbonate become spontaneous and feasible?

Equation:                             MgCO₃     ⟶  MgO    +   CO₂

First find out the enthalpy change in the system:

ΔH_reaction    =     (—601.7  +   —393.5 )—  —1095.8

ΔH_reaction    =     +100.6 kJmol^—1

The enthalpy change is endothermic.

Second find out what is the entropy change in the system?

ΔS_system   =     (+26.9  +   +213.6 )— +65.7

ΔS_system   =     +174.8  J.mol^—1. K^—1

The entropy change in the system suggests that the reaction is feasible.

If

ΔG  =   ΔH —TΔS_system

Then rearrange this equation to find out the temperature  T when ΔG is zero i.e. when the reaction becomes spontaneous

So if now 

0  =   ΔH —TΔS_system

Then adding TΔS_system to each side gives

TΔS_system =   ΔH

And therefore

T =   ΔH/ΔS_system

So

T =   100.6  × 1000/174.8  =  576K

So this confirms what we already know from experience that heating magnesium carbonate decomposes it and in fact if the temperature rises to 576 K or above (302^oC) the substance decomposes spontaneously.