Excess Gibbs Free Energy using Van Laar Equation Calculator

Excess Gibbs Free Energy Formula:

\[ G^E = RTx_1x_2 \left( \frac{A'_{12}A'_{21}}{A'_{12}x_1 + A'_{21}x_2} \right) \]

Temperature:

Mole Fraction of Component 1:

Mole Fraction of Component 2:

Van Laar Coefficient (A'12):

Van Laar Coefficient (A'21):

Excess Gibbs Free Energy:

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1. What is Excess Gibbs Free Energy using Van Laar Equation?

Definition: This calculator computes the excess Gibbs free energy for a binary liquid mixture using the Van Laar equation.

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

2. How Does the Calculator Work?

The calculator uses the Van Laar equation:

\[ G^E = RTx_1x_2 \left( \frac{A'_{12}A'_{21}}{A'_{12}x_1 + A'_{21}x_2} \right) \]

Where:

\( G^E \) — Excess Gibbs free energy (J)
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Temperature (K)
\( x_1 \) — Mole fraction of component 1
\( x_2 \) — Mole fraction of component 2
\( A'_{12}, A'_{21} \) — Van Laar coefficients

Explanation: The equation accounts for the non-ideal interactions between different molecules in a binary mixture.

3. Importance of Excess Gibbs Free Energy

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

4. Using the Calculator

Tips: Enter temperature in Kelvin, mole fractions (sum ≤ 1), and Van Laar coefficients. All values must be valid (temperature > 0, mole fractions between 0 and 1).

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Van Laar coefficients?
A: They vary by system but typically range between 0.1 and 3.0 for many common binary mixtures.

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

Q3: Can this be used for multicomponent systems?
A: No, the Van Laar equation is strictly for binary systems. Extensions exist for multicomponent systems.

Q4: What's the relationship between G^E and activity coefficients?
A: The activity coefficients can be derived from the partial derivatives of G^E with respect to composition.

Q5: When is the Van Laar equation most accurate?
A: It works well for moderately non-ideal systems but may not be accurate for highly non-ideal or associating mixtures.