Equilibrium: Minimizing Free Energy

When is a chemical system in equilibrium?

When the equilibrium condition is met. For the reaction

aA + bB <-> cC + dD

the proper quotient of concentrations is defined for any circumstance by the concentrations of all the species present:

Q is called the reaction quotient. When the system is at equilibrium, the proper quotient of equilibrium concentrations is equal to the equilibrium constant


The system is at equilibrium when the concentrations are in their equilibrium values, i.e., [A] = [A]e, [B] = [B]e, etc. and thus

Q = Keq

Which way will the reaction progress if the reaction mixture is NOT at equilibrium?

If the proper quotient of concentrations at any given instant, the so-called reaction quotient, Q, is less that the equilibrium constant at that temperature, than the reaction will proceed forward in the direction the reaction is written. More products and fewer reactants will increase the size of the reaction quotient and thus get the system closer to equilibrium. If the concentrations of species in the reactor is such that the reaction quotient that is bigger than the equilibrium constant the reaction will proceed spontaneously in the reverse direction.

What is the chemical 'driving force' for the achievment of equilibrium?

Reactions that proceed in the direction of the chemical driving 'force' are called spontaneous reactions. Reactions that proceed in the opposite direction are impossible. The chemical driving force is affected by two things about the reaction: the tendency to release energy and the tendency to produce disorder. The energy (or enthalpy) released upon reaction is called exothermicity, but reactions themselves can be endothermic or exothermic.

The combustion of coal is used to generate electricity. A similar exothermic reaction is the combustion of pure graphite:

Not all combustions are exothermic. The combustion of nitrogen molecule is endothermic.

The science of measuring the exothermicity of a reaction is Thermochemistry.

The spontaneity of a reaction is favored if it is exothermic, but endothermic reactions are possible too. Why? The other factor that affects the direction of spontaneous change may dominate.

Order - Disorder transitions, regardless of their energetics appear to be favored in the world around us. They point the arrow of time. Humpty Dumpty couldn't be put back together because of the disorder his fall created. A measure of the disorder of a system is called its Entropy, S.

Reactions that split molecules up increase the disorder in the universe and have a positive change in entropy.

A condensation reaction creates order (a liquid is more ordered than a gas)

The calculation and measurement of the entropy of a system is the realm of Thermodynamics.

A reaction that has a positive change in entropy and a negative change in enthalpy will be strongly favored to proceed in the forward direction, i.e the reaction will have a very large equilibrium constant. But if both entropy and enthalpy increase or decrease together upon reaction, the effects of energy release and creating disorder will tend to oppose each other.

How can one tell whether a reaction is spontaneous, if both entropy and enthalpy affect spontaneity?

We can combine entropy and enthalpy together to make a new quantity, the Free Energy which, under conditions of constant temperature and pressure, will determine the direction of spontaneous change

How is free energy related to enthalpy and entropy?

What does the 0 mean in the expressions above?

The 0 means "standard". The standard enthalpy change for a reaction is the heat released when one mole of reaction proceeds in the forward direction and all the reactants and products are held at standard concentration (1 molar concentration, one atm pressure, etc)

How is the free energy related to the direction a chemical reaction will proceed?

A reaction will proceed to decrease the free energy of the system. In other words, all spontaneous processes have a negative change in free energy.

How is free energy change for a given reaction related to the standard free energy change for the reaction?

How is the free energy change related to the equilibrium constant?

If a system is in equilibrium, there is no driving force for spontaneous reaction in either direction. therefore: