Question

Chemical potential is equal to:

• A. Enthalpy
• B. Gibbs free energy per mole
• C. Entropy
• D. Internal energy

Hint:

Always remember: Chemical potential $\mu$ is an intensive property.
For a pure substance, chemical potential is exactly equal to its molar Gibbs free energy.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the physical definition of chemical potential in thermodynamics.
Chemical potential determines the tendency of a substance to react, change phase, or diffuse.

Step 2: Key Formula or Approach:
The chemical potential $\mu_i$ of a species $i$ in a mixture is defined as the partial molar Gibbs free energy:
\[ \mu_i = \left(\frac{\partial G}{\partial n_i}\right)_{T, P, n_{j \neq i}} \]

Step 3: Detailed Explanation:

• For a pure, single-component system, the chemical potential is simply the Gibbs free energy divided by the number of moles:
\[ \mu = \frac{G}{n} = \bar{G} \]
where $\bar{G}$ is the molar Gibbs free energy.

• Thus, chemical potential represents the capacity of a system to do non-expansion work per mole of substance added or removed at constant temperature and pressure.

• While chemical potential can also be defined in terms of other thermodynamic potentials (like internal energy, enthalpy, or Helmholtz free energy), those definitions require keeping different variables constant (such as entropy, volume, etc.), making "Gibbs free energy per mole" the standard physical interpretation.

Step 4: Final Answer:
Chemical potential is equal to Gibbs free energy per mole.