Question

Chemical potential is

• A. Work done by system
• B. Total enthalpy
• C. Partial molar Gibbs free energy
• D. Heat absorbed

Hint:

Chemical potential (\(\mu\)) controls chemical mass transfer in the same way electrical potential controls electrical current or temperature controls heat flow. Its thermodynamic baseline definition is always the Partial Molar Gibbs Free Energy under constant temperature and pressure conditions.

Answer 1

The Correct Option is C

Concept: In open systems or multi-component mixtures where the quantities of chemical species can vary due to mass transfer or phase changes, classical thermodynamic state functions must account for changes in composition. The chemical potential (\(\mu_i\)) of a given constituent species \(i\) represents the rate of change of the system's free energy relative to a change in the molar amount of that species, while all other state properties remain constant. Mathematical Definition:
For a multi-component system, the total Gibbs free energy function can be written as a function of temperature, pressure, and the molar amounts of each individual chemical component: \(G = G(T, P, n_1, n_2, \ldots, n_k)\). Taking the total differential yields: \[ dG = \left(\frac{\partial G}{\partial T}\right)_{P, n_i} dT + \left(\frac{\partial G}{\partial P}\right)_{T, n_i} dP + \sum_{i=1}^k \left(\frac{\partial G}{\partial n_i}\right)_{T, P, n_{j \neq i}} dn_i \] The partial derivative term evaluated at constant temperature and pressure is the definition of the chemical potential (\(\mu_i\)): \[ \mu_i = \left(\frac{\partial G}{\partial n_i}\right)_{T, P, n_{j \neq i}} \] Because this partial differentiation measures the variation in Gibbs free energy per mole of component \(i\) added to an extensive mixture at fixed \(T\) and \(P\), it is called the partial molar Gibbs free energy (\(\bar{G}_i\)): \[ \mu_i = \bar{G}_i \] Let us review the alternative options:
• Option (1) is incorrect because work done is a path-dependent energy transfer process defined by mechanical displacement (\(\int P\,dV\)).
• Option (2) is incorrect because total enthalpy (\(H\)) is an extensive properties representing overall heat content, not a partial molar derivative.
• Option (4) is incorrect because heat absorbed is a transient thermal path energy transfer quantity (\(Q\)). Thus, Chemical Potential is identical to the partial molar Gibbs free energy, which is Option (3).