Activity Coefficient for Component 1 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%

✖Activity Coefficient of Component 1 is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances.ⓘ Activity Coefficient for Component 1 using Wilson Equation [γ₁]

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Activity Coefficient for Component 1 using Wilson Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))))
γ₁ = exp((ln(x₁+x₂*Λ₁₂))+x₂*((Λ₁₂/(x₁+x₂*Λ₁₂))-(Λ₂₁/(x₂+x₁*Λ₂₁))))
This formula uses 2 Functions, 5 Variables

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)
exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Activity Coefficient of Component 1 - Activity Coefficient of Component 1 is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances.
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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ₁ = exp((ln(x₁+x₂*Λ₁₂))+x₂*((Λ₁₂/(x₁+x₂*Λ₁₂))-(Λ₂₁/(x₂+x₁*Λ₂₁)))) --> exp((ln(0.4+0.6*0.5))+0.6*((0.5/(0.4+0.6*0.5))-(0.55/(0.6+0.4*0.55))))

Evaluating ... ...

γ₁ = 0.718533794512143

STEP 3: Convert Result to Output's Unit

0.718533794512143 --> No Conversion Required

FINAL ANSWER

0.718533794512143 ≈ 0.718534 <-- Activity Coefficient of Component 1

(Calculation completed in 00.004 seconds)

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Excess Gibbs Free Energy using NRTL Equation

LaTeX 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 1 using NRTL Equation

LaTeX 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

LaTeX 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)))))

Excess Gibbs Energy using Wilson Equation

LaTeX 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 using Wilson Equation Formula

LaTeX Go

What is Activity Coefficient?

An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behavior 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 Activity Coefficient for Component 1 using Wilson Equation?

Activity Coefficient for Component 1 using Wilson Equation calculator uses 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))))) to calculate the Activity Coefficient of Component 1, The Activity Coefficient for Component 1 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. Activity Coefficient of Component 1 is denoted by γ₁ symbol.

How to calculate Activity Coefficient for Component 1 using Wilson Equation using this online calculator? To use this online calculator for Activity Coefficient for Component 1 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) and hit the calculate button. Here is how the Activity Coefficient for Component 1 using Wilson Equation calculation can be explained with given input values -> 0.718534 = exp((ln(0.4+0.6*0.5))+0.6*((0.5/(0.4+0.6*0.5))-(0.55/(0.6+0.4*0.55)))).

FAQ

What is Activity Coefficient for Component 1 using Wilson Equation?

The Activity Coefficient for Component 1 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 γ₁ = exp((ln(x₁+x₂*Λ₁₂))+x₂*((Λ₁₂/(x₁+x₂*Λ₁₂))-(Λ₂₁/(x₂+x₁*Λ₂₁)))) or 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))))). 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.

How to calculate Activity Coefficient for Component 1 using Wilson Equation?

The Activity Coefficient for Component 1 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 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))))). To calculate Activity Coefficient for Component 1 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). 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) 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 Activity Coefficient of Component 1?

In this formula, Activity Coefficient of Component 1 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). We can use 1 other way(s) to calculate the same, which is/are as follows -

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))))

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