Excess Gibbs Energy using Wilson Equation Calculator

✖The mole fraction of component 1 in liquid phase can be defined as the ratio of the number of moles a component 1 to the total number of moles of components present in the liquid phase.ⓘ Mole Fraction of Component 1 in Liquid Phase [x₁]			+10% -10%
✖The mole fraction of component 2 in liquid phase can be defined as the ratio of the number of moles a component 2 to the total number of moles of components present in the liquid phase.ⓘ Mole Fraction of Component 2 in Liquid Phase [x₂]			+10% -10%
✖The Wilson Equation Coefficient (Λ12) is the coefficient used in the Wilson equation for component 1 in the binary system.ⓘ Wilson Equation Coefficient (Λ12) [Λ₁₂]			+10% -10%
✖The Wilson Equation Coefficient (Λ21) is the coefficient used in the Wilson equation for component 2 in the binary system.ⓘ Wilson Equation Coefficient (Λ21) [Λ₂₁]			+10% -10%
✖Temperature for Wilson Equation is the degree or intensity of heat present in a substance or object.ⓘ Temperature for Wilson Equation [T_Wilson]			+10% -10%

✖Excess Gibbs Free Energy is the Gibbs energy of a solution in excess of what it would be if it were ideal.ⓘ Excess Gibbs Energy using Wilson Equation [G^E]

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Excess Gibbs Energy using Wilson Equation

Formula

`"G"^{"E"} = (-"x"_{"1"}*ln("x"_{"1"}+"x"_{"2"}*"Λ"_{"12"})-"x"_{"2"}*ln("x"_{"2"}+"x"_{"1"}*"Λ"_{"21"}))*"[R]"*"T"_{"Wilson"}`

Example

`"184.9797J"=(-"0.4"*ln("0.4"+"0.6"*"0.5")-"0.6"*ln("0.6"+"0.4"*"0.55"))*"[R]"*"85K"`

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Excess Gibbs Energy using Wilson Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Excess Gibbs Free Energy = (-Mole Fraction of Component 1 in Liquid Phase*ln(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*Wilson Equation Coefficient (Λ12))-Mole Fraction of Component 2 in Liquid Phase*ln(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*Wilson Equation Coefficient (Λ21)))*[R]*Temperature for Wilson Equation
G^E = (-x₁*ln(x₁+x₂*Λ₁₂)-x₂*ln(x₂+x₁*Λ₂₁))*[R]*T_Wilson
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Excess Gibbs Free Energy - (Measured in Joule) - Excess Gibbs Free Energy is the Gibbs energy of a solution in excess of what it would be if it were ideal.
Mole Fraction of Component 1 in Liquid Phase - The mole fraction of component 1 in liquid phase can be defined as the ratio of the number of moles a component 1 to the total number of moles of components present in the liquid phase.
Mole Fraction of Component 2 in Liquid Phase - The mole fraction of component 2 in liquid phase can be defined as the ratio of the number of moles a component 2 to the total number of moles of components present in the liquid phase.
Wilson Equation Coefficient (Λ12) - The Wilson Equation Coefficient (Λ12) is the coefficient used in the Wilson equation for component 1 in the binary system.
Wilson Equation Coefficient (Λ21) - The Wilson Equation Coefficient (Λ21) is the coefficient used in the Wilson equation for component 2 in the binary system.
Temperature for Wilson Equation - (Measured in Kelvin) - Temperature for Wilson Equation is the degree or intensity of heat present in a substance or object.

STEP 1: Convert Input(s) to Base Unit

Mole Fraction of Component 1 in Liquid Phase: 0.4 --> No Conversion Required
Mole Fraction of Component 2 in Liquid Phase: 0.6 --> No Conversion Required
Wilson Equation Coefficient (Λ12): 0.5 --> No Conversion Required
Wilson Equation Coefficient (Λ21): 0.55 --> No Conversion Required
Temperature for Wilson Equation: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G^E = (-x₁*ln(x₁+x₂*Λ₁₂)-x₂*ln(x₂+x₁*Λ₂₁))*[R]*T_Wilson --> (-0.4*ln(0.4+0.6*0.5)-0.6*ln(0.6+0.4*0.55))*[R]*85

Evaluating ... ...

G^E = 184.979715088552

STEP 3: Convert Result to Output's Unit

184.979715088552 Joule --> No Conversion Required

FINAL ANSWER

184.979715088552 ≈ 184.9797 Joule <-- Excess Gibbs Free Energy

(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Surathkal

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Excess Gibbs Free Energy using NRTL Equation

Go Excess Gibbs Free Energy = (Mole Fraction of Component 1 in Liquid Phase*Mole Fraction of Component 2 in Liquid Phase*[R]*Temperature for NRTL model)*((((exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b21))/[R]*Temperature for NRTL model))*(NRTL Equation Coefficient (b21)/([R]*Temperature for NRTL model)))/(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b21))/[R]*Temperature for NRTL model)))+(((exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b12))/[R]*Temperature for NRTL model))*(NRTL Equation Coefficient (b12)/([R]*Temperature for NRTL model)))/(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b12))/[R]*Temperature for NRTL model))))

Activity Coefficient for Component 2 using NRTL Equation

Go Activity Coefficient of Component 2 = exp((Mole Fraction of Component 1 in Liquid Phase^2)*(((NRTL Equation Coefficient (b12)/([R]*Temperature for NRTL model))*(exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b12))/([R]*Temperature for NRTL model))/(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b12))/([R]*Temperature for NRTL model))))^2)+((exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b21))/([R]*Temperature for NRTL model))*(NRTL Equation Coefficient (b21)/([R]*Temperature for NRTL model)))/((Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b21))/([R]*Temperature for NRTL model)))^2))))

Activity Coefficient for Component 1 using NRTL Equation

Go Activity Coefficient of Component 1 = exp((Mole Fraction of Component 2 in Liquid Phase^2)*(((NRTL Equation Coefficient (b21)/([R]*Temperature for NRTL model))*(exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b21))/([R]*Temperature for NRTL model))/(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b21))/([R]*Temperature for NRTL model))))^2)+((exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b12))/([R]*Temperature for NRTL model))*NRTL Equation Coefficient (b12)/([R]*Temperature for NRTL model))/((Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b12))/([R]*Temperature for NRTL model)))^2))))

Activity Coefficient for Component 1 using Wilson Equation

Go Activity Coefficient of Component 1 = exp((ln(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*Wilson Equation Coefficient (Λ12)))+Mole Fraction of Component 2 in Liquid Phase*((Wilson Equation Coefficient (Λ12)/(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*Wilson Equation Coefficient (Λ12)))-(Wilson Equation Coefficient (Λ21)/(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*Wilson Equation Coefficient (Λ21)))))

Activity Coefficient for Component 2 using Wilson Equation

Go Activity Coefficient of Component 2 = exp((ln(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*Wilson Equation Coefficient (Λ21)))-Mole Fraction of Component 1 in Liquid Phase*((Wilson Equation Coefficient (Λ12)/(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*Wilson Equation Coefficient (Λ12)))-(Wilson Equation Coefficient (Λ21)/(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*Wilson Equation Coefficient (Λ21)))))

Excess Gibbs Energy using Wilson Equation

Go Excess Gibbs Free Energy = (-Mole Fraction of Component 1 in Liquid Phase*ln(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*Wilson Equation Coefficient (Λ12))-Mole Fraction of Component 2 in Liquid Phase*ln(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*Wilson Equation Coefficient (Λ21)))*[R]*Temperature for Wilson Equation

Activity Coefficient for Component 1 for Infinite Dilution using NRTL Equation

Go Activity Coefficient 1 for infinite dilution = exp((NRTL Equation Coefficient (b21)/([R]*Temperature for NRTL model))+(NRTL Equation Coefficient (b12)/([R]*Temperature for NRTL model))*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b12))/([R]*Temperature for NRTL model)))

Activity Coefficient for Component 2 for Infinite Dilution using NRTL Equation

Go Activity Coefficient 2 for Infinite Dilution = exp((NRTL Equation Coefficient (b12)/([R]*Temperature for NRTL model))+(NRTL Equation Coefficient (b21)/([R]*Temperature for NRTL model))*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b21))/([R]*Temperature for NRTL model)))

Activity Coefficient for Component 2 for Infinite Dilution using Wilson Equation

Go Activity Coefficient 2 for Infinite Dilution = exp(ln(Wilson Equation Coefficient (Λ21))+1-Wilson Equation Coefficient (Λ12))

Activity Coefficient for Component 1 for Infinite Dilution using Wilson Equation

Go Activity Coefficient 1 for infinite dilution = -ln(Wilson Equation Coefficient (Λ12))+1-Wilson Equation Coefficient (Λ21)

Excess Gibbs Energy using Wilson Equation Formula

What is Gibbs Free Energy?

The Gibbs free energy (or Gibbs energy) is a thermodynamic potential that can be used to calculate the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. The Gibbs free energy measured in joules in SI) is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system (can exchange heat and work with its surroundings, but not matter). This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.

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 Excess Gibbs Energy using Wilson Equation?

Excess Gibbs Energy using Wilson Equation calculator uses Excess Gibbs Free Energy = (-Mole Fraction of Component 1 in Liquid Phase*ln(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*Wilson Equation Coefficient (Λ12))-Mole Fraction of Component 2 in Liquid Phase*ln(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*Wilson Equation Coefficient (Λ21)))*[R]*Temperature for Wilson Equation to calculate the Excess Gibbs Free Energy, The Excess Gibbs Energy using Wilson Equation formula is defined as a function of the parameters independent of concentration and temperature and mole fraction in the liquid phase of components 1 & 2 in the binary system. Excess Gibbs Free Energy is denoted by G^E symbol.

How to calculate Excess Gibbs Energy using Wilson Equation using this online calculator? To use this online calculator for Excess Gibbs Energy using Wilson Equation, enter Mole Fraction of Component 1 in Liquid Phase (x₁), Mole Fraction of Component 2 in Liquid Phase (x₂), Wilson Equation Coefficient (Λ12) (Λ₁₂), Wilson Equation Coefficient (Λ21) (Λ₂₁) & Temperature for Wilson Equation (T_Wilson) and hit the calculate button. Here is how the Excess Gibbs Energy using Wilson Equation calculation can be explained with given input values -> 184.9797 = (-0.4*ln(0.4+0.6*0.5)-0.6*ln(0.6+0.4*0.55))*[R]*85.

FAQ

What is Excess Gibbs Energy using Wilson Equation?

The Excess Gibbs Energy using Wilson Equation formula is defined as a function of the parameters independent of concentration and temperature and mole fraction in the liquid phase of components 1 & 2 in the binary system and is represented as G^E = (-x₁*ln(x₁+x₂*Λ₁₂)-x₂*ln(x₂+x₁*Λ₂₁))*[R]*T_Wilson or Excess Gibbs Free Energy = (-Mole Fraction of Component 1 in Liquid Phase*ln(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*Wilson Equation Coefficient (Λ12))-Mole Fraction of Component 2 in Liquid Phase*ln(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*Wilson Equation Coefficient (Λ21)))*[R]*Temperature for Wilson Equation. The mole fraction of component 1 in liquid phase can be defined as the ratio of the number of moles a component 1 to the total number of moles of components present in the liquid phase, The mole fraction of component 2 in liquid phase can be defined as the ratio of the number of moles a component 2 to the total number of moles of components present in the liquid phase, The Wilson Equation Coefficient (Λ12) is the coefficient used in the Wilson equation for component 1 in the binary system, The Wilson Equation Coefficient (Λ21) is the coefficient used in the Wilson equation for component 2 in the binary system & Temperature for Wilson Equation is the degree or intensity of heat present in a substance or object.

How to calculate Excess Gibbs Energy using Wilson Equation?

The Excess Gibbs Energy using Wilson Equation formula is defined as a function of the parameters independent of concentration and temperature and mole fraction in the liquid phase of components 1 & 2 in the binary system is calculated using Excess Gibbs Free Energy = (-Mole Fraction of Component 1 in Liquid Phase*ln(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*Wilson Equation Coefficient (Λ12))-Mole Fraction of Component 2 in Liquid Phase*ln(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*Wilson Equation Coefficient (Λ21)))*[R]*Temperature for Wilson Equation. To calculate Excess Gibbs Energy using Wilson Equation, you need Mole Fraction of Component 1 in Liquid Phase (x₁), Mole Fraction of Component 2 in Liquid Phase (x₂), Wilson Equation Coefficient (Λ12) (Λ₁₂), Wilson Equation Coefficient (Λ21) (Λ₂₁) & Temperature for Wilson Equation (T_Wilson). With our tool, you need to enter the respective value for Mole Fraction of Component 1 in Liquid Phase, Mole Fraction of Component 2 in Liquid Phase, Wilson Equation Coefficient (Λ12), Wilson Equation Coefficient (Λ21) & Temperature for Wilson Equation 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 Excess Gibbs Free Energy?

In this formula, Excess Gibbs Free Energy uses Mole Fraction of Component 1 in Liquid Phase, Mole Fraction of Component 2 in Liquid Phase, Wilson Equation Coefficient (Λ12), Wilson Equation Coefficient (Λ21) & Temperature for Wilson Equation. We can use 1 other way(s) to calculate the same, which is/are as follows -

Excess Gibbs Free Energy = (Mole Fraction of Component 1 in Liquid Phase*Mole Fraction of Component 2 in Liquid Phase*[R]*Temperature for NRTL model)*((((exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b21))/[R]*Temperature for NRTL model))*(NRTL Equation Coefficient (b21)/([R]*Temperature for NRTL model)))/(Mole Fraction of Component 1 in Liquid Phase+Mole Fraction of Component 2 in Liquid Phase*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b21))/[R]*Temperature for NRTL model)))+(((exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b12))/[R]*Temperature for NRTL model))*(NRTL Equation Coefficient (b12)/([R]*Temperature for NRTL model)))/(Mole Fraction of Component 2 in Liquid Phase+Mole Fraction of Component 1 in Liquid Phase*exp(-(NRTL Equation Coefficient (α)*NRTL Equation Coefficient (b12))/[R]*Temperature for NRTL model))))

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