Quick Notes Free Energy (Gibbs)

• The feasibility of a reaction refers to how likely it is to happen.
• High feasibility means a reaction is likely to happen.
• Low feasibility means a reaction is unlikely to happen.
• For a reaction to be feasible, energy must be released overall.
• The overall energy change of a reaction is determined by both the change in enthalpy and the change in entropy that would occur.
• Gibbs free energy (ΔG) is a value calculated to shows how energy changes overall during a reaction.
• The equation is: ΔG = ΔH - TΔS
where ΔH = enthalpy change, T = temperature (in Kelvin) and ΔS = entropy change.
• If Gibbs free energy is negative, the reaction is feasible.
• If Gibbs free energy is positive, the reaction is not feasible.
• If for a reaction:
• -ΔH and +ΔS, the reaction is always feasible.
• -ΔH and -ΔS, the reaction may be feasible at low temperatures.
• +ΔH and +ΔS, the reaction may be feasible at high temperatures.
• +ΔH and -ΔS, the reaction is never feasible.

Full Notes Free Energy (Gibbs)

A reaction that can theoretically occur is called feasible. A reaction that happens by itself (needs no ‘input’ of energy to start) is called spontaneous.

The changes in enthalpy and entropy in a reaction influence how likely it is to happen – both need to be considered.

Reactions are favoured if they lead to an increase in stability of ‘the universe’ or, for chemists, ‘a system’.

In an exothermic reaction, the enthalpy change is negative as heat energy is released during the reaction. It is easy to see how exothermic reactions can proceed because the products are at a lower energy (more stable) than the reactants, meaning the overall stability has increased.

It seems strange that endothermic reactions can occur at all; a positive enthalpy change shows the products have gained heat energy and are less stable than the reactants. However, if the entropy change is also considered when determining how feasible a reaction is, endothermic reactions can (sometimes) be feasible. Remember entropy is also a unit of energy!

If the products of a reaction have a higher entropy than the reactants, there is an increase in stability of the universe. This suggests that all solids should spontaneously react to form gases (gases have a higher entropy value than solids). The fact they don’t is because the enthalpy change of a reaction also determines its feasibility. If the enthalpy change of a reaction is positive (endothermic), the change in entropy would have to be very large to make up for the heat energy gained by the products.

When determining the feasibility (how to likely it is to happen) of a reaction, we must consider the balance between the enthalpy change and entropy change that would occur.

To do this, we also consider the temperature the reaction is occurring at, as entropy changes with temperature. This is why some reactions are more likely to happen at higher temperatures, as the entropy change would be greater.

The result of balancing these factors is called free energy (sometimes referred to as Gibbs free energy, named after Willard Gibbs who pioneered early calculations using entropy).

Change in free energy, ΔG, can be calculated using:

ΔG = ΔH - TΔS

where ΔH = enthalpy change, T = temperature (in Kelvin) and ΔS = entropy change.

For a reaction to be feasible there must be an overall release of energy by the reaction and the free energy must be less than zero. A negative free energy (-ΔG) shows us that the reactants have more ‘free energy’ than the products.

## Rules

If a reaction has a negative enthalpy change (exothermic, -ΔH) and a positive entropy change (+ΔS), the reaction will always be feasible, as the free energy value will always be negative (-ΔG).

If a reaction has a negative enthalpy change (exothermic, -ΔH) and a negative entropy change (-ΔS), the reaction can be feasible, but only at low temperatures.

If a reaction has a positive enthalpy change (endothermic, +ΔH) and a positive entropy change (+ΔS), the reaction can be feasible, but only at high temperatures.

If a reaction has a positive enthalpy change (endothermic, +ΔH) and a negative entropy change (-ΔS), the reaction is never feasible, as the free energy value will always be greater than zero (+ΔG).

When calculating free energy, it is important to remember the units. Entropy is given in J K-1 mol-1 and enthalpy in kJ mol-1. For calculations, convert entropy into kJ before finding the free energy change.