Ideal Gas Gibbs Free Energy using Ideal Gas Mixture Model in Binary System Calculator

Ideal Gas Gibbs Free Energy Formula:

\[ G^{ig} = |(y_1G_1^{ig} + y_2G_2^{ig}) + RT(y_1\ln y_1 + y_2\ln y_2)| \]

Mole Fraction of Component 1 (y₁):

Ideal Gas Gibbs Energy of Component 1 (G₁^ig):

Mole Fraction of Component 2 (y₂):

Ideal Gas Gibbs Energy of Component 2 (G₂^ig):

Temperature (T):

Ideal Gas Gibbs Free Energy (G^ig):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Ideal Gas Gibbs Free Energy in Binary Systems?

Definition: This calculator computes the Gibbs free energy of an ideal gas mixture in a binary system using the ideal gas mixture model.

Purpose: It helps chemical engineers and researchers determine the thermodynamic properties of ideal gas mixtures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G^{ig} = |(y_1G_1^{ig} + y_2G_2^{ig}) + RT(y_1\ln y_1 + y_2\ln y_2)| \]

Where:

\( G^{ig} \) — Ideal gas Gibbs free energy of the mixture (J)
\( y_1, y_2 \) — Mole fractions of components 1 and 2 in vapor phase
\( G_1^{ig}, G_2^{ig} \) — Ideal gas Gibbs free energies of pure components (J)
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Temperature (K)

Explanation: The first term represents the weighted average of pure component Gibbs energies, while the second term accounts for the entropy of mixing.

3. Importance of Gibbs Free Energy Calculation

Details: Gibbs free energy determines the spontaneity of chemical processes and phase equilibria in thermodynamic systems.

4. Using the Calculator

Tips: Enter mole fractions (must sum to 1), component Gibbs energies, and temperature. All values must be valid (temperature > 0, 0 ≤ mole fractions ≤ 1).

5. Frequently Asked Questions (FAQ)

Q1: Why do we take the absolute value of the result?
A: The modulus ensures we get a positive value for Gibbs free energy, which is more meaningful in most thermodynamic analyses.

Q2: What if my mole fractions don't sum to 1?
A: The calculator will still compute a result, but for accurate thermodynamics, mole fractions should properly sum to 1.

Q3: What units should I use?
A: Use consistent units: Joules for energy, Kelvin for temperature, and dimensionless for mole fractions.

Q4: Can this be extended to multicomponent systems?
A: Yes, the formula generalizes to \( G^{ig} = |\sum y_iG_i^{ig} + RT\sum y_i\ln y_i| \) for any number of components.

Q5: When is the ideal gas assumption valid?
A: At low pressures and high temperatures where intermolecular forces become negligible.