Excess Gibbs Free Energy using NRTL 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%
✖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 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%
✖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%

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

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Excess Gibbs Free Energy using NRTL Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
G^E = (x₁*x₂*[R]*T_NRTL)*((((exp(-(α*b₂₁)/[R]*T_NRTL))*(b₂₁/([R]*T_NRTL)))/(x₁+x₂*exp(-(α*b₂₁)/[R]*T_NRTL)))+(((exp(-(α*b₁₂)/[R]*T_NRTL))*(b₁₂/([R]*T_NRTL)))/(x₂+x₁*exp(-(α*b₁₂)/[R]*T_NRTL))))
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

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

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

Evaluating ... ...

G^E = 0.0255091211453841

STEP 3: Convert Result to Output's Unit

0.0255091211453841 Joule --> No Conversion Required

FINAL ANSWER

0.0255091211453841 ≈ 0.025509 Joule <-- Excess Gibbs Free Energy

(Calculation completed in 00.005 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

Excess Gibbs Free Energy using NRTL Equation Formula

LaTeX Go

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.

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 Excess Gibbs Free Energy using NRTL Equation?

Excess Gibbs Free Energy using NRTL Equation calculator uses 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)))) to calculate the Excess Gibbs Free Energy, The Excess Gibbs Free Energy 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. Excess Gibbs Free Energy is denoted by G^E symbol.

How to calculate Excess Gibbs Free Energy using NRTL Equation using this online calculator? To use this online calculator for Excess Gibbs Free Energy using NRTL Equation, enter Mole Fraction of Component 1 in Liquid Phase (x₁), Mole Fraction of Component 2 in Liquid Phase (x₂), Temperature for NRTL model (T_NRTL), NRTL Equation Coefficient (α) (α), NRTL Equation Coefficient (b21) (b₂₁) & NRTL Equation Coefficient (b12) (b₁₂) and hit the calculate button. Here is how the Excess Gibbs Free Energy using NRTL Equation calculation can be explained with given input values -> 0.025509 = (0.4*0.6*[R]*550)*((((exp(-(0.15*0.12)/[R]*550))*(0.12/([R]*550)))/(0.4+0.6*exp(-(0.15*0.12)/[R]*550)))+(((exp(-(0.15*0.19)/[R]*550))*(0.19/([R]*550)))/(0.6+0.4*exp(-(0.15*0.19)/[R]*550)))).

FAQ

What is Excess Gibbs Free Energy using NRTL Equation?

The Excess Gibbs Free Energy 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 G^E = (x₁*x₂*[R]*T_NRTL)*((((exp(-(α*b₂₁)/[R]*T_NRTL))*(b₂₁/([R]*T_NRTL)))/(x₁+x₂*exp(-(α*b₂₁)/[R]*T_NRTL)))+(((exp(-(α*b₁₂)/[R]*T_NRTL))*(b₁₂/([R]*T_NRTL)))/(x₂+x₁*exp(-(α*b₁₂)/[R]*T_NRTL)))) or 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)))). 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, 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 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 & 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 Excess Gibbs Free Energy using NRTL Equation?

The Excess Gibbs Free Energy 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 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)))). To calculate Excess Gibbs Free Energy using NRTL Equation, you need Mole Fraction of Component 1 in Liquid Phase (x₁), Mole Fraction of Component 2 in Liquid Phase (x₂), Temperature for NRTL model (T_NRTL), NRTL Equation Coefficient (α) (α), NRTL Equation Coefficient (b21) (b₂₁) & NRTL Equation Coefficient (b12) (b₁₂). 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, Temperature for NRTL model, NRTL Equation Coefficient (α), NRTL Equation Coefficient (b21) & 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 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, Temperature for NRTL model, NRTL Equation Coefficient (α), NRTL Equation Coefficient (b21) & NRTL Equation Coefficient (b12). 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*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

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