Vapour Fugacity Coefficient of Comp. 1 using Sat. Pressure and Second Virial Coefficients Calculator

Fugacity Coefficient Formula:

\[ \phi_1 = \exp\left(\frac{B_{11}(P - P_1^{sat}) + P(y_2^2)(2B_{12} - B_{11} - B_{22})}{RT}\right) \]

Second Virial Coefficient B11:

m³

System Pressure (P):

Saturated Pressure of Component 1 (P₁ˢᵃᵗ):

Mole Fraction of Component 2 in Vapour (y₂):

Second Virial Coefficient B12:

m³

Second Virial Coefficient B22:

m³

System Temperature (T):

Fugacity Coefficient of Component 1 (φ₁):

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1. What is Fugacity Coefficient of Component 1?

Definition: The fugacity coefficient (φ₁) is a measure of non-ideality for component 1 in a vapor mixture, representing the ratio of its fugacity to its partial pressure.

Purpose: It helps chemical engineers account for real gas behavior in phase equilibrium calculations, particularly in vapor-liquid equilibrium systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \phi_1 = \exp\left(\frac{B_{11}(P - P_1^{sat}) + P(y_2^2)(2B_{12} - B_{11} - B_{22})}{RT}\right) \]

Where:

\( \phi_1 \) — Fugacity coefficient of component 1
\( B_{11}, B_{12}, B_{22} \) — Second virial coefficients (m³)
\( P \) — System pressure (Pa)
\( P_1^{sat} \) — Saturated pressure of component 1 (Pa)
\( y_2 \) — Mole fraction of component 2 in vapor phase
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T \) — System temperature (K)

3. Importance of Fugacity Coefficient Calculation

Details: Accurate fugacity coefficients are essential for modeling phase equilibria, designing separation processes, and predicting vapor-liquid equilibrium compositions in chemical engineering applications.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Default values are provided for quick testing. Temperature must be in Kelvin, pressures in Pascals, and virial coefficients in cubic meters.

5. Frequently Asked Questions (FAQ)

Q1: What do the second virial coefficients represent?
A: They describe pairwise molecular interactions between components (B11 for 1-1, B22 for 2-2, B12 for 1-2 interactions).

Q2: When is this calculation most important?
A: For systems at moderate pressures where gas behavior deviates from ideality but higher-order virial terms can be neglected.

Q3: What if I don't know the virial coefficients?
A: They can be estimated from equations of state or experimental data. Many databases provide these values for common compounds.

Q4: How does temperature affect the result?
A: Higher temperatures generally make gases behave more ideally (φ₁ closer to 1), while lower temperatures increase non-ideality.

Q5: What does a fugacity coefficient of 1 mean?
A: The component behaves ideally - its fugacity equals its partial pressure.