Chemical potential

Chemical Potential

Diagram illustrating chemical potential in a system.

The chemical potential is a concept in thermodynamics and physical chemistry that refers to the change in the Gibbs free energy of a system when an additional amount of substance is added, keeping temperature and pressure constant. It is a measure of the potential energy stored in a substance that can be released during a chemical reaction or phase transition.

In mathematical terms, the chemical potential \( \mu \) of a component in a system is defined as the partial derivative of the Gibbs free energy \( G \) with respect to the number of moles \( n_i \) of the component, at constant temperature \( T \) and pressure \( P \):

\[ \mu_i = \left( \frac{\partial G}{\partial n_i} \right)_{T,P,n_{j \neq i}} \]

Importance in Thermodynamics

The concept of chemical potential is crucial in understanding how substances interact in a system. It helps predict the direction of chemical reactions and the conditions under which phase equilibrium is achieved. In a system at equilibrium, the chemical potential of a substance is the same in all phases.

Chemical potential is also used to describe the behavior of mixtures and solutions. In a mixture, each component has its own chemical potential, and the total Gibbs free energy of the system is the sum of the chemical potentials of all components.

Applications

Chemical potential is applied in various fields such as:

• Electrochemistry: It helps in understanding the movement of ions in an electrochemical cell.
• Biochemistry: It is used to describe the energy changes in metabolic pathways.
• Materials science: It aids in predicting the stability of different phases in a material.

Mathematical Formulation

In a system with multiple components, the chemical potential can be expressed in terms of the molar Gibbs free energy and the activity of the components. For an ideal solution, the chemical potential \( \mu_i \) of component \( i \) is given by:

\[ \mu_i = \mu_i^0 + RT \ln a_i \]

where \( \mu_i^0 \) is the standard chemical potential, \( R \) is the universal gas constant, \( T \) is the temperature, and \( a_i \) is the activity of the component.

Related Concepts

• Fugacity
• Activity coefficient
• Phase rule
• Chemical equilibrium

Related Pages

• Gibbs free energy
• Thermodynamic equilibrium
• Phase diagram
• Entropy