Equilibrium Constant, Reaction Quotient, and Gibbs Free Energy

A state of equilibrium is defined as a state of balance between two opposing factions. Consider a hot cup of tea left on a table; we know the temperature inside the cup is significantly greater than the surrounding temperature. As time passes, we observe that the cup releases heat into the atmosphere. It keeps on releasing the heat until the temperature inside the cup equals the surrounding temperature. This is called the condition of equilibrium.

This article explores the relationship between equilibrium constant, reaction quotient, and Gibbs free energy and provides equilibrium constant examples.

Chemical Equilibrium 

A chemical reaction is said to have attained a state of chemical equilibrium when no further changes in the concentration of the reactants and products are possible. When a chemical reaction reaches a state of chemical equilibrium, the rate of forward reaction at the reactant’s side is always equal to the rate of backward reaction at the product side. Equilibrium mixture in the chemical equilibrium state is defined as the mixtures of the reactants and the product components of the reaction.

The chemical equilibrium is further classified into the following three groups,

1. When only a small amount of the concentration of the reactant has remained, the reaction achieves a state of equilibrium.
2. When a very small amount of product is obtained, the chemical reaction achieves a state of equilibrium.
3. When the mixture of the contents of the reaction is incomparable, the reaction achieves a state of equilibrium.

Equilibrium Constant

The law of chemical equilibrium gives the equilibrium constant. For the chemical equilibrium state, at a fixed constant temperature, the ratio of the multiplication of product of the reaction to the multiplication of concentration of reactants of the equation, and each is raised to the power to the corresponding coefficients of the elements in the reaction.

For a general chemical reaction, the chemical equilibrium is given by,

a.A + b.B ⇌ c.C + d.D,

Kc = [C]c [D]d / [A]a [B]b (Kc = Equilibrium Constant)

Features of Equilibrium Constant

Some of the important features of equilibrium constants are as follows, 

• The equilibrium constant can only be expressed when the concentration of the elements in reactants and elements in products have achieved a constant value at the chemical equilibrium state. 
• The value of the equilibrium constant does not depend on the initial concentrations of the elements in reactants and elements in products. 
• Equilibrium constant depends on the temperature at which the reaction occurs; it has one fixed value for a chemical reaction, and a balanced equation represents this value at a given temperature. 
• The Kc for the reverse reaction is equal to the inverse equilibrium constant (Kc) value for the forward reaction and visa-versa.

Solved Example

Question: At equilibrium, the concentrations of N2 = 2.0 × 10 –3M, O2 = 6 × 10–3M and NO= 5 × 10–3M in a sealed vessel at a temperature 800K. What will be Kc for the reaction

N2 + O2 ⇌ 2NO

Solution:

For the reaction equilibrium constant, Kc can be written as, 

Kc = [NO]2 / [N]1.[O]1

Kc = [5 x 10-3]2 / [2 x 10-3].[6 x 10-3]

Kc = 2.08.

Reaction Quotient

The reaction quotient (Q) is similar to the chemical equilibrium constant Kc; the only difference between the two is that the concentrations in the calculation of the reaction quotient are not chemical equilibrium values. 

For a general chemical reaction: 

aA + bB ⇌ cC + dD 

Qc = [C]c [D]d / [A]a [B]b 

Then, 

If Qc > Kc, the reaction will be a reverse reaction, 

If Qc < Kc, the reaction will be a forward reaction,

If Qc = Kc, the reaction is at equilibrium.

Gibbs Free Energy

When a chemical reaction occurs at a constant temperature and constant pressure, the second law of thermodynamics can be arranged in such a way that it gives a new expression,

∆G = H – T.S

This is the expression for Gibbs free energy (∆G),

Here, H = enthalpy

T = temperature

S = entropy

Relationship Between Equilibrium Constant, Reaction Quotient and Gibbs Free Energy

The rate of a chemical reaction doesn’t affect the value of the chemical equilibrium of the reaction. However, the value of Kc is dependent on the thermodynamics of the reaction, and thus of Gibbs free energy (∆G).

For ∆G, we get the following conditions,

• When ∆G has a -ve value, the reaction is forward
• When ∆G has a +ve value, the reaction is reversed
• When ∆G = 0, the reaction is at equilibrium.

The following expression gives the relationship between the equilibrium constant, reaction quotient, and Gibbs free energy,