# What is chemical potential? Write its physical significance.

## Chemical Potential

Chemical potential (μ) is a thermodynamic quantity that represents the change in the Gibbs free energy of a system when some amount of substance is added or removed at constant temperature and pressure.

chemical potential (μ) of a component in a system is defined mathematically as the partial derivative of the Gibbs free energy (G) with respect to the number of particles (N) at constant temperature (T) and pressure (P).

μ = (δG/δN)_{T,P}

We know that, Free energy function-

F = H − TS

or, F = E + PV − TS (As H = E + PV)

or, dF = dE + PdV + VdP − TdS − SdT

or, dF = VdP − SdT (As dq = dE + PdV = TdS)

At constant T-

(dF)_{T} = VdP = RT(dP/P) (As PV = RT for one mole)

On integrating the above equation we get-

∫dF = RT∫dP/P

or, F = F^{o} + RT lnP ----- Equation:1

From Raoult's law-

∆P/P^{o} = X

and X ∝ C ∝ a
Hence, Equation:1 becomes-

F = F^{o} + RT lna

μ = μ^{o} + RT lna

μ is called free energy per mole or chemical potential. μ^{o} is called standard free energy per mole. Th μ^{o} is constant at a constant temperature.

## Significance of Chemical Potential

At equilibrium, the chemical potential of each component in a system must be equal, otherwise the system will not be in a stable state.

A process will occur spontaneously if it decreases the Gibbs free energy of the system, which corresponds to a decrease in the chemical potential of the reacting species.

Chemical potential of a substance is different in different phases (solid, liquid, gas). At the phase transition point, the chemical potentials of the two phases must be equal.

In electrochemical systems, the chemical potential is combined with the electrical potential to give the electrochemical potential, which determines the driving force for ion transport and redox reactions.

Chemical equilibrium constants can be expressed in terms of the standard state chemical potentials of the reactants and products, allowing the prediction of the composition at equilibrium.

Clausius-Clapeyron Relation can be derived using the concept of chemical potential.