Fugacity Calculator
Fugacity Calculator computes the fugacity of a gas using the van der Waals equation for a given temperature, pressure, and gas type.
Formulas Used in Fugacity Calculator
The calculator uses the van der Waals equation and fugacity integral:
van der Waals Equation:
\\[ \left(P + \frac{a}{V^2}\right)(V – b) = RT \\]Fugacity Coefficient:
\\[ \ln \phi = \ln \left(\frac{f}{P}\right) = \int_0^P \left( \frac{V}{RT} – \frac{1}{P} \right) dP \\]For van der Waals gas:
\\[ \ln \phi = \frac{b}{V – b} – \ln \left( \frac{V – b}{V_{\text{ideal}}} \right) – \frac{2a}{RT V} \\]Where:
- \\(P\\): Pressure (bar)
- \\(V\\): Molar volume (L/mol)
- \\(T\\): Temperature (K)
- \\(R\\): Gas constant (0.083144 L bar/(mol K))
- \\(a\\): van der Waals attraction parameter (L² bar/mol²)
- \\(b\\): van der Waals repulsion parameter (L/mol)
- \\(f\\): Fugacity (bar)
- \\(\phi\\): Fugacity coefficient
- \\(V_{\text{ideal}} = RT/P\\): Ideal gas molar volume
Example Calculation
Example: CO₂ at T = 298 K, P = 1 bar, a = 3.592 L² bar/mol², b = 0.04267 L/mol
Solve for \\(V\\) using the van der Waals equation (cubic equation).
Compute: \\(\ln \phi = \frac{b}{V – b} – \ln \left( \frac{V – b}{RT/P} \right) – \frac{2a}{RT V}\\)
Fugacity: \\(f = \phi P\\)