Excess Gibbs Energy using Wilson Equation Calculator

Excess Gibbs Free Energy Formula:

\[ G^E = (-x_1 \ln(x_1 + x_2 \Lambda_{12}) - x_2 \ln(x_2 + x_1 \Lambda_{21})) \times R \times T \]

Mole Fraction of Component 1 (x₁):

Mole Fraction of Component 2 (x₂):

Wilson Coefficient (Λ₁₂):

Wilson Coefficient (Λ₂₁):

Temperature (T):

Excess Gibbs Free Energy (J):

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1. What is Excess Gibbs Energy using Wilson Equation?

Definition: This calculator estimates the excess Gibbs free energy of a binary liquid mixture using the Wilson equation.

Purpose: It helps chemical engineers and researchers understand non-ideal behavior of liquid mixtures.

2. How Does the Calculator Work?

The calculator uses the Wilson equation:

\[ G^E = (-x_1 \ln(x_1 + x_2 \Lambda_{12}) - x_2 \ln(x_2 + x_1 \Lambda_{21})) \times R \times T \]

Where:

\( G^E \) — Excess Gibbs free energy (J)
\( x_1 \) — Mole fraction of component 1
\( x_2 \) — Mole fraction of component 2
\( \Lambda_{12}, \Lambda_{21} \) — Wilson equation coefficients
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Temperature (K)

3. Importance of Excess Gibbs Energy Calculation

Details: Excess Gibbs energy helps predict phase equilibrium, activity coefficients, and non-ideal behavior in liquid mixtures.

4. Using the Calculator

Tips: Enter mole fractions (must sum to 1), Wilson coefficients, and temperature in Kelvin. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Wilson coefficients?
A: Wilson coefficients are typically between 0.1 and 10, depending on the components and temperature.

Q2: How do I obtain Wilson coefficients?
A: They are determined experimentally from vapor-liquid equilibrium data or estimated using group contribution methods.

Q3: What does a negative excess Gibbs energy mean?
A: Negative values indicate stronger intermolecular forces than in an ideal mixture (attractive interactions dominate).

Q4: Can this be used for multicomponent systems?
A: The Wilson equation can be extended to multicomponent systems, but this calculator handles binary systems only.

Q5: What's the relationship to activity coefficients?
A: The activity coefficients can be derived from the excess Gibbs energy through partial differentiation.