# CHEM C5: Gibbs Free Energy Change

Today we’re covering:

• What is Gibbs Free Energy?
• Predicting the effect of temperature on the spontaneity of a reaction

Let’s go!

From the previous post, we know that:
For a reaction to be spontaneous/feasible, the TOTAL entropy of the system +  surroundings MUST increase.

Generally*, you can know if a reaction has a positive ΔStotal if:

• The entropy of the system increases
ΔSsystem > 0
• The reaction releases heat to the surroundings (exothermic)
ΔHr < 0

*However, there are exceptions.
The most accurate way to tell if a reaction is spontaneous is to look at its
Gibbs Free Energy Change.

What is Gibbs Free Energy?
The amount of available energy in a reaction that can be used to do work.

It is denoted by ‘G’.

A change in G is defined as:
ΔG = -TΔStotal
or
ΔG = ΔH – TΔSsystem

 Proof ΔStotal = ΔSsystem + ΔSsurroundings -TΔStotal = -TΔSsystem – TΔSsurroundings   Since ΔSsurroundings = –ΔHreaction/T, TΔSsurroundings = –ΔHreaction   -TΔStotal = -TΔSsystem – ΔHreaction ΔG = ΔH – TΔSsystem

How do you use ΔG to tell if a reaction is spontaneous?
Look at the value of ΔG, if:

 ΔG < 0 (negative) Reaction IS spontaneous. Since the reaction increases the total entropy of system + surroundings, it disperses energy. When entropy increases, useful energy is dispersed as wasteful energy. Thus, available (free) energy DECREASES. ΔG > 0 (positive) Reaction IS NOT spontaneous. However, the reaction CAN occur if energy is constantly supplied by an external source. The reaction CAN also occur in REVERSE (i.e. the products form the reactants) since the ΔG of the reverse reaction is negative. ΔG = 0 Reaction is in equilibrium. Reaction can occur both forwards & backwards, but has no net change in amounts of reactants & products.

Calculating ΔG manually:

 STEP 1: Calculate ΔHr can be calculated from other given info; using either: Calorimetry Hess’ Law Bond Enthalpies remember: convert kJmol-1 to Jmol-1 STEP 2: Calculate ΔSsystem can be calculated from given standard enthalpies STEP 3: Identifying T must be given by the question must be in Kelvin at standard conditions, T = 298 K STEP 4: Using the Formula ΔG = ΔH – TΔSsystem STEP 5: Is the reaction spontaneous? ΔG < 0: spontaneous ΔG > 0: non-spontaneous ΔG = 0: equilibrium

Calculating ΔG using Hess’ Law
Just like ΔH, ΔG can be calculated by using alternate pathways.

Just as how certain reactions have Standard Enthalpies,
they also have Standard Gibbs Free Energy Changes:

The Steps in calculating ΔG using Hess’ Law are the same as calculating ΔH
(see here)

From Cambridge International A Level Chemistry

What increases the spontaneity of a reaction?
Based on the equation ΔG = ΔH – TΔSsystem,
to make ΔG more NEGATIVE, you need:

1. A LOWER (more negative) ΔH
2. A HIGHER Temperature
3. A HIGHER ΔSsystem

What can you do to make a non-spontaneous reaction spontaneous?
Since you can’t change ΔSsystem or ΔH directly,
you have to INCREASE the temperature.

Q: Doesn’t increasing T affect ΔSsystem or ΔH?
A: Yes, but very slightly, such that the difference is negligible.