Question

I have a problem with the definition of the standard Gibbs energy and its connection to the equilibrium constants.

I think, that I've basically understood what the different equation mean but there is one thing, I'm unable to understand:

On the one hand:

One may describe a chemical reaction with ΔG=ΔG∘+RTlnQ. In equilibrium ΔG=0 and the equation reads ΔG∘=−RTlnK.

On the other hand:

The definition of standard state is very clear: pressure = 1 bar and all reactants and products must have activity = 1.

If I consider these two aspects separately, everything seems to be fine. But these two concepts have to be valid at the same time, what leads to ΔG∘=0 (always), since K=1 (all activities are per definition = 1).

Therefore, ΔG∘ would be always zero. I know that this isn't true, but I don't understand why.

Can anyone explain this to me?

Thanks!

Answer 1

The standard Gibbs energy (ΔG°) is not always zero; it indicates the spontaneity of a reaction under standard conditions. The standard state is a reference point and activities in this state are defined to be 1, but actual reactant and product concentrations at equilibrium are not necessarily 1. Therefore, the standard Gibbs energy is related to the equilibrium constant, which is derived from actual equilibrium concentrations or pressures, not the standard state values.

Step-by-step explanation:

The apparent contradiction in the standard Gibbs energy arises from a misunderstanding of the definition of the standard state. The standard state is a reference point, not the actual condition of reactants and products at equilibrium.

At the standard state, activities of all species are defined to be 1, but this does not mean that their actual concentrations are 1 when the reaction is at equilibrium. The important equation ΔG° = -RT ln K relates the standard Gibbs free energy change to the equilibrium constant (K), and applies when the reaction equation as written corresponds to the formation of 1 mole of product from the standard states of the reactants.

The standard Gibbs free energy change (ΔG°) is not zero by definition; it depends on the intrinsic properties of the substances involved and indicates whether the reaction is spontaneous under standard conditions. If a reaction has a ΔG° < 0, it means that the reaction is spontaneous in the forward direction under standard conditions, whereas a ΔG° > 0 suggests non-spontaneity.

When the reaction is at equilibrium (ΔG = 0), it is the actual concentrations or partial pressures of the reactants and products that yield the equilibrium constant K, which generally is not equal to 1, and thus the standard Gibbs energy change is not necessarily zero.

The relationship ΔG = ΔG° + RT ln Q indicates that ΔG (the actual Gibbs free energy change) varies with the reaction quotient Q, and only at equilibrium does ΔG equal to 0, leading to the expression ΔG° = -RT ln K, where K is the equilibrium constant reflective of the actual ratio of product and reactant activities at equilibrium.