Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.

Reaction Quotient (Q)

The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient, Q. For a reversible reaction described by

the reaction quotient is derived directly from the stoichiometry of the balanced equation as

where the subscript c denotes the use of molar concentrations in the expression. The concentration-based reaction quotient, Q_c, is used for condensed phase equilibria. If the reactants and products are gaseous, a reaction quotient may be similarly derived using partial pressures:

Under standard conditions, the reactant and product solution concentrations are 1 M, or the pressure of gases is 1 bar, and Q is equal to 1. Therefore, under standard conditions

Under nonstandard conditions, Q must be calculated.

The numerical value of Q varies as a reaction proceeds towards equilibrium; therefore, it can serve as a useful indicator of the reaction’s status. To illustrate this point, consider the oxidation of sulfur dioxide:

Consider two different experimental scenarios, one in which this reaction is initiated with a mixture of reactants only, SO₂ and O₂, and another that begins with only the product, SO₃. For the reaction that begins with a mixture of reactants only, Q is initially equal to zero:

As the reaction proceeds toward equilibrium in the forward direction, reactant concentrations decrease (as does the denominator of Q_c), product concentration increases (as does the numerator of Q_c), and the reaction quotient consequently increases. When equilibrium is achieved, the concentrations of reactants and products remain constant, as does the value of Q_c.

If the reaction begins with only the product present, the value of Qc is initially undefined (immeasurably large or infinite):

In this case, the reaction proceeds toward equilibrium in the reverse direction. The product concentration and the numerator of Q_c decrease with time, the reactant concentrations and the denominator of Q_c increase, and the reaction quotient consequently decreases until it becomes constant at equilibrium.

This text is adapted from Openstax, Chemistry 2e, Chapter 16.4: Free Energy and Openstax, Chemistry 2e, Chapter 13.2: Equilibrium Constants.