Question

Variation in equilibrium pressure with temperature for any two phases of a given substance is given by the

• A. Gibbs - Duhem
• B. Maxwell's
• C. Clapeyron
• D. Margules

Hint:

Associate "phase boundary", "P-T diagram", "coexistence curve", or "equilibrium between two phases" with the Clapeyron equation. A simplified version for liquid-vapor and solid-vapor equilibrium is the Clausius-Clapeyron equation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The question asks for the equation that describes the relationship between pressure and temperature along a phase boundary (e.g., solid-liquid, liquid-vapor, or solid-vapor) for a pure substance at equilibrium.

Step 2: Key Formula or Approach:
The relevant equation is the Clapeyron equation, which gives the slope of the coexistence curve on a pressure-temperature diagram: \[ \frac{dP}{dT} = \frac{\Delta H}{T \Delta V} \] where \(\frac{dP}{dT}\) is the slope of the phase boundary, \(\Delta H\) is the latent heat of the phase transition, \(T\) is the absolute temperature, and \(\Delta V\) is the change in volume during the phase transition.

Step 3: Detailed Explanation:
Let's analyze the given options in the context of the problem:

Gibbs-Duhem Equation: This equation relates the changes in chemical potential for the components in a mixture. It is used for solutions and mixtures, not for describing the P-T relationship of a phase transition in a pure substance.

Maxwell's Relations: These are a set of equations derived from the definitions of thermodynamic potentials. While fundamental to thermodynamics, they do not directly provide the simple P-T relationship for a phase boundary like the Clapeyron equation does.

Clapeyron Equation: This is the correct answer. As shown in Step 2, it directly relates the change in pressure with respect to temperature (\(dP/dT\)) along a line of equilibrium between two phases.

Margules Equation: This is a model for the activity coefficients of components in a liquid mixture. It is irrelevant to the phase equilibrium of a single-component system.

Step 4: Final Answer:
The Clapeyron equation gives the relationship between the equilibrium pressure and temperature for two phases of a pure substance.