Question

Condition to be satisfied for \( \alpha \) and \( \beta \) phases to be in equilibrium in a two-component (A and B) system at constant temperature and pressure is

• A. entropy of the system should be maximum
• B. Gibbs energy of the system should be minimum and \( \mu_A^{\alpha} = \mu_B^{\beta} \)
• C. Gibbs energy of the system should be minimum and \( \mu_A^{\alpha} = \mu_A^{\beta}, \mu_B^{\alpha} = \mu_B^{\beta} \)
• D. Helmholtz energy should be minimum

Hint:

In a two-phase system, equilibrium is achieved when the Gibbs energy is minimized and the chemical potentials of each component are equal in both phases.

Answer 1

The Correct Option is C

For two phases of a system to be in equilibrium at constant temperature and pressure, the Gibbs free energy of the system must be minimized. Additionally, the chemical potentials of each component (A and B) must be the same in both phases, meaning: \[ \mu_A^{\alpha} = \mu_A^{\beta}, \mu_B^{\alpha} = \mu_B^{\beta}. \] This condition ensures that there is no driving force for further phase transitions.

Step 1: Identify the condition for equilibrium.
The equilibrium condition in a multi-phase system is that the Gibbs free energy must be minimized, and the chemical potentials in both phases should be equal.

Step 2: Conclusion.
Thus, the correct condition is that the Gibbs energy should be minimized and the chemical potentials of the components are equal in both phases.

Final Answer: \text{(C) Gibbs energy of the system should be minimum and \( \mu_A^{\alpha} = \mu_A^{\beta}, \mu_B^{\alpha} = \mu_B^{\beta} \)}