Chemical Equilibrium

Chemical equilibrium is an important part of chemical thermodynamics and deals with the conditions under which a reversible chemical reaction reaches a state of equilibrium. At equilibrium, the forward and reverse reactions continue simultaneously, but their rates become equal. As a result, the macroscopic properties of the system, such as concentration, pressure and other measurable properties, remain constant with time.

The position of chemical equilibrium is described quantitatively by the equilibrium constant. Thermodynamics provides a deeper interpretation of equilibrium through Gibbs free energy and chemical potential. The relationship between the equilibrium constant and standard Gibbs free energy allows us to determine the thermodynamic tendency of a chemical reaction.

The effect of changes in concentration, pressure and temperature on an equilibrium system is explained by Le-Chatelier’s principle. The dependence of equilibrium on temperature is further studied using the van’t Hoff equation, while the variation of equilibrium pressure with temperature during phase changes is described by the Clapeyron and Clausius-Clapeyron equations.

Topics Covered in This Unit

1. Equilibrium Constant and Free Energy
2. Thermodynamic Derivation of the Law of Mass Action
3. Le-Chatelier’s Principle
4. Reaction Isotherm
5. Reaction Isochore
6. Clapeyron Equation
7. Clausius-Clapeyron Equation
8. Applications of the Clapeyron-Clausius Equation

Learning Objectives

After studying this unit, the student should be able to explain the concept of chemical equilibrium and equilibrium constants, establish the thermodynamic relationship between equilibrium constant and Gibbs free energy, derive the law of mass action from thermodynamic principles, and explain the effect of concentration, pressure and temperature on equilibrium using Le-Chatelier’s principle.

The student should also be able to understand reaction isotherm and reaction isochore, derive the van’t Hoff equation, derive the Clapeyron equation and obtain the Clausius-Clapeyron equation for liquid-vapour equilibrium. The equations can be applied to calculate equilibrium constants, vapour pressures, enthalpy of vaporisation and the temperature dependence of equilibrium.

Important Thermodynamic Relations

The following relations are central to the topics discussed in this unit:

$$\Delta G = \Delta G^\circ + RT\ln Q$$

At equilibrium,

$$\Delta G=0,\qquad Q=K$$

Therefore,

$$\Delta G^\circ=-RT\ln K$$

The temperature dependence of the equilibrium constant is given by the van’t Hoff equation:

$$\frac{d\ln K}{dT}=\frac{\Delta H^\circ}{RT^2}$$

For a phase equilibrium, the Clapeyron equation is:

$$\frac{dP}{dT}=\frac{\Delta H}{T\Delta V}$$

For liquid-vapour equilibrium, under the usual ideal-gas approximation, it becomes the Clausius-Clapeyron equation:

$$\frac{d\ln P}{dT}=\frac{\Delta H_{\mathrm{vap}}}{RT^2}$$