Excess Gibbs Free Energy using NRTL Equation Calculator

Excess Gibbs Free Energy Formula:

\[ G^E = (x_1x_2RT) \left( \frac{\tau_{21}G_{21}}{x_1 + x_2G_{21}} + \frac{\tau_{12}G_{12}}{x_2 + x_1G_{12}} \right) \]

Mole Fraction of Component 1 (x₁):

Mole Fraction of Component 2 (x₂):

Temperature (T):

NRTL Coefficient (α):

NRTL Coefficient (b₁₂):

J/mol

NRTL Coefficient (b₂₁):

J/mol

Excess Gibbs Free Energy (Gᴱ):

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1. What is Excess Gibbs Free Energy in NRTL Model?

Definition: Excess Gibbs free energy (Gᴱ) represents the difference between the actual Gibbs free energy of a solution and what it would be if the solution were ideal.

Purpose: The NRTL (Non-Random Two-Liquid) model calculates Gᴱ to predict phase equilibria in non-ideal liquid mixtures.

2. How Does the NRTL Equation Work?

The NRTL equation calculates excess Gibbs free energy as:

\[ G^E = (x_1x_2RT) \left( \frac{\tau_{21}G_{21}}{x_1 + x_2G_{21}} + \frac{\tau_{12}G_{12}}{x_2 + x_1G_{12}} \right) \]

Where:

\( x_1, x_2 \) — Mole fractions of components 1 and 2
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Temperature in Kelvin
\( \tau_{12} = b_{12}/RT \), \( \tau_{21} = b_{21}/RT \) — NRTL parameters
\( G_{12} = \exp(-\alpha\tau_{12}) \), \( G_{21} = \exp(-\alpha\tau_{21}) \) — NRTL coefficients
\( \alpha \) — Non-randomness parameter (typically 0.1-0.5)

3. Importance of Excess Gibbs Free Energy

Details: Gᴱ is crucial for predicting vapor-liquid equilibria, activity coefficients, and phase behavior in non-ideal mixtures.

4. Using the Calculator

Tips: Enter mole fractions (must sum to 1), temperature in Kelvin, NRTL coefficients (α, b₁₂, b₂₁). Default values are provided for common systems.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for NRTL parameters?
A: α is usually 0.1-0.5; b₁₂ and b₂₁ are typically 100-5000 J/mol, determined experimentally.

Q2: How do I ensure mole fractions sum to 1?
A: The calculator doesn't enforce this - ensure x₁ + x₂ = 1 for accurate results.

Q3: What temperature units should I use?
A: Temperature must be in Kelvin (K = °C + 273.15).

Q4: Can I use this for multi-component systems?
A: This calculator is for binary systems only. Multi-component NRTL requires additional terms.

Q5: Where can I find NRTL parameters for my system?
A: Check thermodynamic databases like DECHEMA or published literature for your specific components.