Question

Excess properties in thermodynamics are defined as:

• A. Difference between actual and residual property
• B. Difference between actual and ideal solution property
• C. Sum of pure component properties
• D. Property at infinite dilution

Hint:

Excess Gibbs free energy (\( G^E \)) is directly related to the activity coefficients (\( \gamma_i \)) of the species in a solution by:
\[ G^E = R \cdot T \cdot \sum x_i \cdot \ln \gamma_i \]
This relationship is highly important for VLE modeling.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the thermodynamic definition of "excess properties" (\( M^E \)) in solution thermodynamics.
Excess properties are used to quantify deviations from ideal solution behaviour.

Step 2: Key Formula or Approach:
Let \( M \) represent any thermodynamic property (such as volume, enthalpy, entropy, or Gibbs free energy) of a real solution.
Let \( M^{id} \) represent the same property calculated for an ideal solution at the exact same temperature, pressure, and composition.
The excess property is defined as:
\[ M^E = M - M^{id} \]

Step 3: Detailed Explanation:

• Concept of Excess Properties: An ideal solution is a model where molecular interactions between different species are identical to those between like molecules.
Real solutions deviate from this behaviour.
Excess properties quantify this difference.
For example, the excess volume \( V^E = V - V^{id} \) is the change in volume upon mixing of real components compared to the volume of ideal mixing (which is zero).

• Comparison with Residual Properties: Residual properties (\( M^R \)) are defined as the difference between a real gas property and an ideal gas property at the same temperature and pressure:
\[ M^R = M - M^{ig} \]
This should not be confused with excess properties, which compare real solutions to ideal solutions.


Step 4: Final Answer:
The excess property is defined as the difference between the actual property and the ideal solution property.