2.1.4

# Free Energy (A2 Only)

Test yourself

## Free Energy

Free energy is a simple way to determine if a reaction is feasible. Free energy includes both entropy and enthalpy.

### Feasibility

• For a reaction to happen, the total entropy of everything involved must increase.
• This includes its molar entropies, but also the entropy change of the air when it is heated.
• Instead of calculating the entropies of everything, we can define the Gibbs free energy change as ΔG = ΔH - TΔS.
• There’s some complex maths, but it boils down to: If ΔG is negative, the overall entropy increases and a reaction will happen.
• The reaction is said to be feasible.

### Temperature dependance

• If a reaction has a negative ΔH and a positive ΔS it will always be feasible.
• But some reactions are endothermic, or lose entropy.
• These reactions show a temperature dependence of feasibility.
• We shall explore this on the next few slides.

### Endothermic reactions

• If a reaction has a positive ΔH, it will only be feasible if the ΔS term is positive and larger than it. You can see a graph above of ΔG vs T for positive ΔH, and positive ΔS.

### Reactions with a negative entropy change

• Entropy always increases. For a reaction to happen if the standard molar entropies of the reactants decreases, it must heat it's surroundings and cause the entropy of the surroundings to increase.
• So the reaction must be exothermic.
• Above is a graph of ΔG vs T for negative ΔH and ΔS.

## Free Energy Calculations

You can calculate the temperature at which a reaction becomes feasible.

### Feasibility

• For a reaction to happen, ΔG must be negative.
• We can calculate the temperature at which a reaction switches from unfeasible to feasible by setting ΔG equal to zero.
• To find this temperature, we must rearrange the equation for Gibbs free energy:
• ΔG = ΔH - TΔS becomes 0 = ΔH - TΔS
• So, T = $\frac{\Delta H}{\Delta S}$

### Example - bismuth extraction

• A step in the extraction of bismuth from it's ore is the reduction of bismuth hydroxide (Bi(OH)3) by hydrogen according to the equation:
• 2(Bi(OH)3) + 3H2 → 2Bi + 6H2O
• If the entropy change is: +400JK-1mol-1 and the enthalpy change is 50kJmol-1, what temperature does it become feasible at?
• See next slide for solution.

### Solution

• First, make sure your entropy change and enthalpy change both use Joules.
• 50kJmol-1 = 50,000Jmol-1
• Insert this value into the rearranged Gibbs free energy equation to find the temperature at which this reaction is feasible:
• T = 50,000 ÷ 400 = 125K
• So, the reaction is feasible at temperatures above 125K.