Activity Coefficient for Component 1 using NRTL Equation Calculator

✖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 NRTL Equation Coefficient (b21) is the coefficient used in the NRTL equation for component 2 in the binary system. It's independent of concentration and temperature.ⓘ NRTL Equation Coefficient (b21) [b₂₁]			+10% -10%
✖Temperature for NRTL model is the degree or intensity of heat present in a substance or object.ⓘ Temperature for NRTL model [T_NRTL]			+10% -10%
✖NRTL Equation Coefficient (α) is the coefficient used in the NRTL equation which is parameter specific to a particular pair of species.ⓘ NRTL Equation Coefficient (α) [α]			+10% -10%
✖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 NRTL Equation Coefficient (b12) is the coefficient used in the NRTL equation for component 1 in the binary system. It's independent of concentration and temperature.ⓘ NRTL Equation Coefficient (b12) [b₁₂]			+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 NRTL Equation [γ₁]

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Activity Coefficient for Component 1 using NRTL Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
γ₁ = exp((x₂^2)*(((b₂₁/([R]*T_NRTL))*(exp(-(α*b₂₁)/([R]*T_NRTL))/(x₁+x₂*exp(-(α*b₂₁)/([R]*T_NRTL))))^2)+((exp(-(α*b₁₂)/([R]*T_NRTL))*b₁₂/([R]*T_NRTL))/((x₂+x₁*exp(-(α*b₁₂)/([R]*T_NRTL)))^2))))
This formula uses 1 Constants, 1 Functions, 7 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Functions Used

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 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.
NRTL Equation Coefficient (b21) - (Measured in Joule Per Mole) - The NRTL Equation Coefficient (b21) is the coefficient used in the NRTL equation for component 2 in the binary system. It's independent of concentration and temperature.
Temperature for NRTL model - (Measured in Kelvin) - Temperature for NRTL model is the degree or intensity of heat present in a substance or object.
NRTL Equation Coefficient (α) - NRTL Equation Coefficient (α) is the coefficient used in the NRTL equation which is parameter specific to a particular pair of species.
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.
NRTL Equation Coefficient (b12) - (Measured in Joule Per Mole) - The NRTL Equation Coefficient (b12) is the coefficient used in the NRTL equation for component 1 in the binary system. It's independent of concentration and temperature.

STEP 1: Convert Input(s) to Base Unit

Mole Fraction of Component 2 in Liquid Phase: 0.6 --> No Conversion Required
NRTL Equation Coefficient (b21): 0.12 Joule Per Mole --> 0.12 Joule Per Mole No Conversion Required
Temperature for NRTL model: 550 Kelvin --> 550 Kelvin No Conversion Required
NRTL Equation Coefficient (α): 0.15 --> No Conversion Required
Mole Fraction of Component 1 in Liquid Phase: 0.4 --> No Conversion Required
NRTL Equation Coefficient (b12): 0.19 Joule Per Mole --> 0.19 Joule Per Mole No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ₁ = exp((x₂^2)*(((b₂₁/([R]*T_NRTL))*(exp(-(α*b₂₁)/([R]*T_NRTL))/(x₁+x₂*exp(-(α*b₂₁)/([R]*T_NRTL))))^2)+((exp(-(α*b₁₂)/([R]*T_NRTL))*b₁₂/([R]*T_NRTL))/((x₂+x₁*exp(-(α*b₁₂)/([R]*T_NRTL)))^2)))) --> exp((0.6^2)*(((0.12/([R]*550))*(exp(-(0.15*0.12)/([R]*550))/(0.4+0.6*exp(-(0.15*0.12)/([R]*550))))^2)+((exp(-(0.15*0.19)/([R]*550))*0.19/([R]*550))/((0.6+0.4*exp(-(0.15*0.19)/([R]*550)))^2))))

Evaluating ... ...

γ₁ = 1.00002440460362

STEP 3: Convert Result to Output's Unit

1.00002440460362 --> No Conversion Required

FINAL ANSWER

1.00002440460362 ≈ 1.000024 <-- Activity Coefficient of Component 1

(Calculation completed in 00.004 seconds)

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< Local Composition Models Calculators

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 NRTL 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.

Define NRTL Equation Model.

The non-random two-liquid model (abbreviated NRTL model) is an activity coefficient model that correlates the activity coefficients of a compound with its mole fractions in the liquid phase concerned. It is frequently applied in the field of chemical engineering to calculate phase equilibria. The concept of NRTL is based on the hypothesis of Wilson that the local concentration around a molecule is different from the bulk concentration. The NRTL model belongs to the so-called local-composition models. Other models of this type are the Wilson model, the UNIQUAC model, and the group contribution model UNIFAC.

How to Calculate Activity Coefficient for Component 1 using NRTL Equation?

Activity Coefficient for Component 1 using NRTL Equation calculator uses 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)))) to calculate the Activity Coefficient of Component 1, The Activity coefficient for component 1 using NRTL 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 NRTL Equation using this online calculator? To use this online calculator for Activity Coefficient for Component 1 using NRTL Equation, enter Mole Fraction of Component 2 in Liquid Phase (x₂), NRTL Equation Coefficient (b21) (b₂₁), Temperature for NRTL model (T_NRTL), NRTL Equation Coefficient (α) (α), Mole Fraction of Component 1 in Liquid Phase (x₁) & NRTL Equation Coefficient (b12) (b₁₂) and hit the calculate button. Here is how the Activity Coefficient for Component 1 using NRTL Equation calculation can be explained with given input values -> 1.000024 = exp((0.6^2)*(((0.12/([R]*550))*(exp(-(0.15*0.12)/([R]*550))/(0.4+0.6*exp(-(0.15*0.12)/([R]*550))))^2)+((exp(-(0.15*0.19)/([R]*550))*0.19/([R]*550))/((0.6+0.4*exp(-(0.15*0.19)/([R]*550)))^2)))).

FAQ

What is Activity Coefficient for Component 1 using NRTL Equation?

The Activity coefficient for component 1 using NRTL 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((x₂^2)*(((b₂₁/([R]*T_NRTL))*(exp(-(α*b₂₁)/([R]*T_NRTL))/(x₁+x₂*exp(-(α*b₂₁)/([R]*T_NRTL))))^2)+((exp(-(α*b₁₂)/([R]*T_NRTL))*b₁₂/([R]*T_NRTL))/((x₂+x₁*exp(-(α*b₁₂)/([R]*T_NRTL)))^2)))) or 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)))). 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 NRTL Equation Coefficient (b21) is the coefficient used in the NRTL equation for component 2 in the binary system. It's independent of concentration and temperature, Temperature for NRTL model is the degree or intensity of heat present in a substance or object, NRTL Equation Coefficient (α) is the coefficient used in the NRTL equation which is parameter specific to a particular pair of species, 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 NRTL Equation Coefficient (b12) is the coefficient used in the NRTL equation for component 1 in the binary system. It's independent of concentration and temperature.

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

The Activity coefficient for component 1 using NRTL 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((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)))). To calculate Activity Coefficient for Component 1 using NRTL Equation, you need Mole Fraction of Component 2 in Liquid Phase (x₂), NRTL Equation Coefficient (b21) (b₂₁), Temperature for NRTL model (T_NRTL), NRTL Equation Coefficient (α) (α), Mole Fraction of Component 1 in Liquid Phase (x₁) & NRTL Equation Coefficient (b12) (b₁₂). With our tool, you need to enter the respective value for Mole Fraction of Component 2 in Liquid Phase, NRTL Equation Coefficient (b21), Temperature for NRTL model, NRTL Equation Coefficient (α), Mole Fraction of Component 1 in Liquid Phase & NRTL Equation Coefficient (b12) 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 2 in Liquid Phase, NRTL Equation Coefficient (b21), Temperature for NRTL model, NRTL Equation Coefficient (α), Mole Fraction of Component 1 in Liquid Phase & NRTL Equation Coefficient (b12). We can use 1 other way(s) to calculate the same, which is/are as follows -

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)))))

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