Free Energy and Equilibrium

Free energy, also known as Gibbs free energy (G), measures the maximum reversible work a thermodynamic system can perform at constant temperature and pressure.
It’s an important concept in thermodynamics and helps predict whether a chemical reaction will be spontaneous or not.
The change in free energy (ΔG) can be calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the absolute temperature, and ΔS is the change in entropy.
If the ΔG of a reaction is negative, the process is spontaneous and is said to occur exergonically. If ΔG is positive, it is non-spontaneous and referred to as endergonic.
A zero value of ΔG indicates the system is in equilibrium and no net change will occur.

Chemical equilibrium is the state in which the forward and reverse reactions take place at the same rate preventing the net amounts of reactants and products from changing.
At equilibrium, ΔG = 0, so ΔH = TΔS. When the system is at equilibrium, the free energy is at its minimum.
The concept of free energy helps to establish the position of the equilibrium, the point at which both the forward and reverse chemical reactions occur at the same rate.
The larger the negative value of ΔG, the further the position of the equilibrium lies to the right, favouring the products. Conversely, the larger the positive value of ΔG, the further the position of the equilibrium lies to the left, favouring the reactants.

The value of ΔG depends on the temperature of the system. Changes in temperature can therefore alter the spontaneity of reactions and the position of equilibrium.
A decrease in temperature favours exothermic reactions (ΔH < 0) and shifts the equilibrium position to the right (products side), whereas an increase in temperature favours endothermic reactions (ΔH > 0) and shifts the equilibrium position to the left (reactants side).
Thus, controlling the temperature can be a critical factor in managing the outcome of many industrial chemical processes.

While the ΔG of a reaction can tell us whether or not a reaction will occur spontaneously, it gives no information about the rate of the reaction.
It’s crucial to understand that having a negative ΔG (i.e., being spontaneous) does not necessarily mean a reaction will occur quickly. A reaction may be spontaneous but still proceed very slowly if there is a large activation energy barrier to overcome.
The reaction rate is determined by the energy barrier between reactants and products, known as the activation energy. This can be understood as the ‘hill’ a reaction must climb before it can proceed. The higher the hill, the slower the reaction, regardless of the overall change in free energy.