Total Pressure using Gamma-Phi Formulation of VLE Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Pressure of Gas = (Mole Fraction of Component in Liquid Phase*Activity Coefficient*Saturated pressure)/(Mole Fraction of Component in Vapor Phase*Fugacity Coefficient)
PT = (xLiquid*γ*Psat )/(yGas*ϕ)
This formula uses 6 Variables
Variables Used
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.
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.
Fugacity Coefficient - Fugacity coefficient is the ratio of fugacity to the pressure of that component.
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
Fugacity Coefficient: 0.95 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PT = (xLiquid*γ*Psat )/(yGas*ϕ) --> (0.51*1.5*50000)/(0.3*0.95)
Evaluating ... ...
PT = 134210.526315789
STEP 3: Convert Result to Output's Unit
134210.526315789 Pascal --> No Conversion Required
FINAL ANSWER
134210.526315789 134210.5 Pascal <-- Total Pressure of Gas
(Calculation completed in 00.004 seconds)

Credits

Created by Shivam Sinha
National Institute Of Technology (NIT), Surathkal
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Verified by Pragati Jaju
College Of Engineering (COEP), Pune
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18 K values for Gamma/Phi formulation, Raoult’s Law, Modified Raoult’s Law, and Henry’s Law Calculators

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

Total Pressure using Gamma-Phi Formulation of VLE Formula

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

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 Total Pressure using Gamma-Phi Formulation of VLE?

Total Pressure using Gamma-Phi Formulation of VLE calculator uses Total Pressure of Gas = (Mole Fraction of Component in Liquid Phase*Activity Coefficient*Saturated pressure)/(Mole Fraction of Component in Vapor Phase*Fugacity Coefficient) to calculate the Total Pressure of Gas, The Total Pressure 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 fugacity coefficient of mixture or solution. Total Pressure of Gas is denoted by PT symbol.

How to calculate Total Pressure using Gamma-Phi Formulation of VLE using this online calculator? To use this online calculator for Total Pressure 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) & Fugacity Coefficient (ϕ) and hit the calculate button. Here is how the Total Pressure using Gamma-Phi Formulation of VLE calculation can be explained with given input values -> 134210.5 = (0.51*1.5*50000)/(0.3*0.95).

FAQ

What is Total Pressure using Gamma-Phi Formulation of VLE?
The Total Pressure 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 fugacity coefficient of mixture or solution and is represented as PT = (xLiquid*γ*Psat )/(yGas*ϕ) or Total Pressure of Gas = (Mole Fraction of Component in Liquid Phase*Activity Coefficient*Saturated pressure)/(Mole Fraction of Component in Vapor Phase*Fugacity Coefficient). 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 & Fugacity coefficient is the ratio of fugacity to the pressure of that component.
How to calculate Total Pressure using Gamma-Phi Formulation of VLE?
The Total Pressure 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 fugacity coefficient of mixture or solution is calculated using Total Pressure of Gas = (Mole Fraction of Component in Liquid Phase*Activity Coefficient*Saturated pressure)/(Mole Fraction of Component in Vapor Phase*Fugacity Coefficient). To calculate Total Pressure 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) & Fugacity Coefficient (ϕ). 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 & Fugacity Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Total Pressure of Gas?
In this formula, Total Pressure of Gas uses Mole Fraction of Component in Liquid Phase, Activity Coefficient, Saturated pressure, Mole Fraction of Component in Vapor Phase & Fugacity Coefficient. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Total Pressure of Gas = (Activity Coefficient in Raoults Law*Saturated Pressure in Gamma-Phi Formulation)/(K value*Fugacity Coefficient in Raoults Law)
  • Total Pressure of Gas = Saturated Pressure in Raoults Law/K value
  • Total Pressure of Gas = (Activity Coefficient in Raoults Law*Saturated Pressure in Raoults Law)/K value
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