Liquid phase mole fraction using Gamma - phi formulation of VLE Calculator

Formula Used:

\[ x_{liquid} = \frac{y_{gas} \times \phi \times P_T}{\gamma \times P_{sat}} \]

Mole Fraction in Vapor Phase (y_gas):

Fugacity Coefficient (φ):

Total Pressure (P_T):

Activity Coefficient (γ):

Saturated Pressure (P_sat):

Mole Fraction in Liquid Phase (x_liquid):

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1. What is Gamma - phi Formulation of VLE?

Definition: The Gamma-phi formulation is a method for calculating vapor-liquid equilibrium (VLE) that accounts for non-ideal behavior in both phases.

Purpose: This calculator determines the liquid phase mole fraction using the Gamma-phi approach, which is essential for distillation design and phase equilibrium calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ x_{liquid} = \frac{y_{gas} \times \phi \times P_T}{\gamma \times P_{sat}} \]

Where:

\( x_{liquid} \) — Mole fraction in liquid phase
\( y_{gas} \) — Mole fraction in vapor phase (0 to 1)
\( \phi \) — Fugacity coefficient (accounts for vapor phase non-ideality)
\( P_T \) — Total system pressure (Pa)
\( \gamma \) — Activity coefficient (accounts for liquid phase non-ideality)
\( P_{sat} \) — Saturation pressure of component (Pa)

Explanation: The formula relates vapor and liquid phase compositions through thermodynamic properties and system conditions.

3. Importance of Gamma-phi Formulation

Details: This approach is crucial for accurate phase equilibrium calculations in chemical processes, especially when dealing with non-ideal mixtures.

4. Using the Calculator

Tips:

Enter vapor phase mole fraction (0-1)
Fugacity coefficient (default 0.95 for near-ideal vapors)
Total system pressure in Pascals
Activity coefficient (default 1.5 for moderately non-ideal liquids)
Saturation pressure in Pascals at system temperature

5. Frequently Asked Questions (FAQ)

Q1: When is the Gamma-phi approach necessary?
A: For systems where both vapor and liquid phases show significant non-ideal behavior, unlike Raoult's Law which assumes ideal behavior.

Q2: How do I determine the fugacity coefficient?
A: Use equations of state (like Peng-Robinson) or experimental data. For near-ideal vapors, φ ≈ 1.

Q3: What affects the activity coefficient?
A: Molecular interactions, temperature, and composition. It's typically >1 for positive deviations from Raoult's Law.

Q4: Can x_liquid exceed 1?
A: No, if you get values >1, check your inputs - likely incorrect P_sat or invalid combination of parameters.

Q5: How does temperature affect the calculation?
A: Temperature primarily affects P_sat (through Antoine equation) and may affect γ and φ.