Second Virial Coefficient of Comp. 2 using Saturated Pressure and Sat. Vapour Fugacity Coefficient Calculator

Second Virial Coefficient Formula:

\[ B_{22} = \frac{\ln(\phi_2^{sat}) \times R \times T_{VLE}}{P_2^{sat}} \]

Second Virial Coefficient 22 (m³):

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1. What is Second Virial Coefficient of Component 2?

Definition: The second virial coefficient B₂₂ describes the contribution of the pair-wise potential of component 2 with itself to the pressure of the gas.

Purpose: It helps in understanding non-ideal gas behavior and is used in equations of state for real gases.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ B_{22} = \frac{\ln(\phi_2^{sat}) \times R \times T_{VLE}}{P_2^{sat}} \]

Where:

\( B_{22} \) — Second virial coefficient of component 2 (m³)
\( \phi_2^{sat} \) — Saturated fugacity coefficient of component 2
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T_{VLE} \) — Temperature of liquid-vapor system (K)
\( P_2^{sat} \) — Saturated pressure of component 2 (Pa)

Explanation: The natural log of the fugacity coefficient is multiplied by the gas constant and temperature, then divided by the saturated pressure.

3. Importance of Second Virial Coefficient

Details: This coefficient is crucial for accurate thermodynamic modeling of real gases, especially in vapor-liquid equilibrium calculations.

4. Using the Calculator

Tips: Enter the saturated fugacity coefficient (unitless), system temperature in Kelvin, and saturated pressure in Pascals. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of B₂₂?
A: It represents the deviation from ideal gas behavior due to interactions between pairs of molecules of component 2.

Q2: What's a typical range for B₂₂?
A: Values are typically small (order of 10⁻⁵ to 10⁻³ m³/mol) and can be positive or negative depending on temperature.

Q3: How does temperature affect B₂₂?
A: Generally, B₂₂ increases with temperature, starting negative at low temperatures and becoming positive at higher temperatures.

Q4: What if my fugacity coefficient is exactly 1?
A: At φ₂ˢᵃᵗ = 1, the gas behaves ideally and B₂₂ would be zero (ideal gas condition).

Q5: Can this be used for mixtures?
A: This calculates B₂₂ for pure component 2. For mixtures, cross coefficients (B₁₂) would also be needed.