Fugacity Coefficient using Gamma-Phi Formulation of VLE Solution

STEP 0: Pre-Calculation Summary
Formula Used
Fugacity Coefficient = (Mole Fraction of Component in Liquid Phase*Activity Coefficient*Saturated pressure)/(Mole Fraction of Component in Vapor Phase*Total Pressure of Gas)
ϕ = (xLiquid*γ*Psat )/(yGas*PT)
This formula uses 6 Variables
Variables Used
Fugacity Coefficient - Fugacity coefficient is the ratio of fugacity to the pressure of that component.
Mole Fraction of Component in Liquid Phase - The Mole Fraction of Component in Liquid Phase can be defined as the ratio of the number of moles a component to the total number of moles of components present in the liquid phase.
Activity Coefficient - Activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances.
Saturated pressure - (Measured in Pascal) - Saturated pressure is the pressure at which a given liquid and its vapour or a given solid and its vapour can co-exist in equilibrium, at a given temperature.
Mole Fraction of Component in Vapor Phase - The Mole Fraction of Component in Vapor Phase can be defined as the ratio of the number of moles a component to the total number of moles of components present in the vapor phase.
Total Pressure of Gas - (Measured in Pascal) - Total pressure of Gas is the sum of all the forces that the gas molecules exert on the walls of their container.
STEP 1: Convert Input(s) to Base Unit
Mole Fraction of Component in Liquid Phase: 0.51 --> No Conversion Required
Activity Coefficient: 1.5 --> No Conversion Required
Saturated pressure: 50000 Pascal --> 50000 Pascal No Conversion Required
Mole Fraction of Component in Vapor Phase: 0.3 --> No Conversion Required
Total Pressure of Gas: 102100 Pascal --> 102100 Pascal No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ϕ = (xLiquid*γ*Psat )/(yGas*PT) --> (0.51*1.5*50000)/(0.3*102100)
Evaluating ... ...
ϕ = 1.24877571008815
STEP 3: Convert Result to Output's Unit
1.24877571008815 --> No Conversion Required
FINAL ANSWER
1.24877571008815 1.248776 <-- Fugacity Coefficient
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Surathkal
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K values for Gamma Phi formulation, Raoult’s Law, Modified Raoult’s Law, and Henry’s Law Calculators

Fugacity Coefficient of Component using K-Value Expression for Gamma-Phi Formulation
​ LaTeX ​ Go Fugacity Coefficient in Raoults Law = (Activity Coefficient in Raoults Law*Saturated Pressure in Gamma-Phi Formulation)/(K value*Total Pressure of Gas)
K-Value of Component using Gamma-Phi Formulation
​ LaTeX ​ Go K value = (Activity Coefficient in Raoults Law*Saturated Pressure in Gamma-Phi Formulation)/(Fugacity Coefficient in Raoults Law*Total Pressure of Gas)
Activity Coefficient of Component using K-Value Expression for Gamma-Phi Formulation
​ LaTeX ​ Go Activity Coefficient in Raoults Law = (K value*Fugacity Coefficient in Raoults Law*Total Pressure of Gas)/Saturated Pressure in Gamma-Phi Formulation
K-Value or Vapour-Liquid Distribution Ratio of Component
​ LaTeX ​ Go K value = Mole Fraction of Component in Vapor Phase/Mole Fraction of Component in Liquid Phase

Fugacity Coefficient using Gamma-Phi Formulation of VLE Formula

​LaTeX ​Go
Fugacity Coefficient = (Mole Fraction of Component in Liquid Phase*Activity Coefficient*Saturated pressure)/(Mole Fraction of Component in Vapor Phase*Total Pressure of Gas)
ϕ = (xLiquid*γ*Psat )/(yGas*PT)

Explain Vapour Liquid Equilibrium (VLE).

An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same (or macroscopically equivalent, the enthalpy change of solution and volume variation in mixing is zero) and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult's law. Deviations from ideality are accommodated by modifying the concentration by an activity coefficient. Analogously, expressions involving gases can be adjusted for non-ideality by scaling partial pressures by a fugacity coefficient.

What is Duhem’s Theorem?

For any closed system formed from known amounts of prescribed chemical species, the equilibrium state is completely determined when any two independent variables are fixed. The two independent variables subject to specification may in general be either intensive or extensive. However, the number of independent intensive variables is given by the phase rule. Thus when F = 1, at least one of the two variables must be extensive, and when F = 0, both must be extensive.

How to Calculate Fugacity Coefficient using Gamma-Phi Formulation of VLE?

Fugacity Coefficient using Gamma-Phi Formulation of VLE calculator uses Fugacity Coefficient = (Mole Fraction of Component in Liquid Phase*Activity Coefficient*Saturated pressure)/(Mole Fraction of Component in Vapor Phase*Total Pressure of Gas) to calculate the Fugacity Coefficient, The Fugacity Coefficient using Gamma-Phi Formulation of VLE formula is defined as the ratio of the product of the liquid phase mole fraction, activity coefficient and the saturated pressure to the product of the vapour phase mole fraction and the total pressure of mixture or solution. Fugacity Coefficient is denoted by ϕ symbol.

How to calculate Fugacity Coefficient using Gamma-Phi Formulation of VLE using this online calculator? To use this online calculator for Fugacity Coefficient using Gamma-Phi Formulation of VLE, enter Mole Fraction of Component in Liquid Phase (xLiquid), Activity Coefficient (γ), Saturated pressure (Psat ), Mole Fraction of Component in Vapor Phase (yGas) & Total Pressure of Gas (PT) and hit the calculate button. Here is how the Fugacity Coefficient using Gamma-Phi Formulation of VLE calculation can be explained with given input values -> 0.423131 = (0.51*1.5*50000)/(0.3*102100).

FAQ

What is Fugacity Coefficient using Gamma-Phi Formulation of VLE?
The Fugacity Coefficient using Gamma-Phi Formulation of VLE formula is defined as the ratio of the product of the liquid phase mole fraction, activity coefficient and the saturated pressure to the product of the vapour phase mole fraction and the total pressure of mixture or solution and is represented as ϕ = (xLiquid*γ*Psat )/(yGas*PT) or Fugacity Coefficient = (Mole Fraction of Component in Liquid Phase*Activity Coefficient*Saturated pressure)/(Mole Fraction of Component in Vapor Phase*Total Pressure of Gas). The Mole Fraction of Component in Liquid Phase can be defined as the ratio of the number of moles a component to the total number of moles of components present in the liquid phase, Activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances, Saturated pressure is the pressure at which a given liquid and its vapour or a given solid and its vapour can co-exist in equilibrium, at a given temperature, The Mole Fraction of Component in Vapor Phase can be defined as the ratio of the number of moles a component to the total number of moles of components present in the vapor phase & Total pressure of Gas is the sum of all the forces that the gas molecules exert on the walls of their container.
How to calculate Fugacity Coefficient using Gamma-Phi Formulation of VLE?
The Fugacity Coefficient using Gamma-Phi Formulation of VLE formula is defined as the ratio of the product of the liquid phase mole fraction, activity coefficient and the saturated pressure to the product of the vapour phase mole fraction and the total pressure of mixture or solution is calculated using Fugacity Coefficient = (Mole Fraction of Component in Liquid Phase*Activity Coefficient*Saturated pressure)/(Mole Fraction of Component in Vapor Phase*Total Pressure of Gas). To calculate Fugacity Coefficient using Gamma-Phi Formulation of VLE, you need Mole Fraction of Component in Liquid Phase (xLiquid), Activity Coefficient (γ), Saturated pressure (Psat ), Mole Fraction of Component in Vapor Phase (yGas) & Total Pressure of Gas (PT). With our tool, you need to enter the respective value for Mole Fraction of Component in Liquid Phase, Activity Coefficient, Saturated pressure, Mole Fraction of Component in Vapor Phase & Total Pressure of Gas and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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