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Activity Coefficient for Component 2 using NRTL Equation Formula

GoActivity Coefficient for Component 2 using Wilson Equation Formula

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Activity coefficient of component 2 is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances. Check FAQs

γ 2 = \exp (({x 1}^{2}) \cdot (((\frac{b 12}{[R] \cdot T NRTL}) \cdot {(\frac{\exp (- \frac{α \cdot b 12}{[R] \cdot T NRTL})}{x 2 + x 1 \cdot \exp (- \frac{α \cdot b 12}{[R] \cdot T NRTL})})}^{2}) + (\frac{\exp (- \frac{α \cdot b 21}{[R] \cdot T NRTL}) \cdot (\frac{b 21}{[R] \cdot T NRTL})}{{(x 1 + x 2 \cdot \exp (- \frac{α \cdot b 21}{[R] \cdot T NRTL}))}^{2}})))

γ₂ - Activity Coefficient of Component 2?x₁ - Mole Fraction of Component 1 in Liquid Phase?b₁₂ - NRTL Equation Coefficient (b12)?T_NRTL - Temperature for NRTL model?α - NRTL Equation Coefficient (α)?x₂ - Mole Fraction of Component 2 in Liquid Phase?b₂₁ - NRTL Equation Coefficient (b21)?[R] - Universal gas constant?[R] - Universal gas constant?[R] - Universal gas constant?[R] - Universal gas constant?[R] - Universal gas constant?[R] - Universal gas constant?

Activity Coefficient for Component 2 using NRTL Equation Example

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Here is how the Activity Coefficient for Component 2 using NRTL Equation equation looks like with Values.

Here is how the Activity Coefficient for Component 2 using NRTL Equation equation looks like with Units.

Here is how the Activity Coefficient for Component 2 using NRTL Equation equation looks like.

1 = \exp (({0.4}^{2}) \cdot (((\frac{0.19}{8.3145 \cdot 550}) \cdot {(\frac{\exp (- \frac{0.15 \cdot 0.19}{8.3145 \cdot 550})}{0.6 + 0.4 \cdot \exp (- \frac{0.15 \cdot 0.19}{8.3145 \cdot 550})})}^{2}) + (\frac{\exp (- \frac{0.15 \cdot 0.12}{8.3145 \cdot 550}) \cdot (\frac{0.12}{8.3145 \cdot 550})}{{(0.4 + 0.6 \cdot \exp (- \frac{0.15 \cdot 0.12}{8.3145 \cdot 550}))}^{2}})))

1 = \exp (({0.4}^{2}) \cdot (((\frac{0.19J/mol}{8.3145 \cdot 550K}) \cdot {(\frac{\exp (- \frac{0.15 \cdot 0.19J/mol}{8.3145 \cdot 550K})}{0.6 + 0.4 \cdot \exp (- \frac{0.15 \cdot 0.19J/mol}{8.3145 \cdot 550K})})}^{2}) + (\frac{\exp (- \frac{0.15 \cdot 0.12J/mol}{8.3145 \cdot 550K}) \cdot (\frac{0.12J/mol}{8.3145 \cdot 550K})}{{(0.4 + 0.6 \cdot \exp (- \frac{0.15 \cdot 0.12J/mol}{8.3145 \cdot 550K}))}^{2}})))

1 = \exp (({0.4}^{2}) \cdot (((\frac{0.19}{8.3145 \cdot 550}) \cdot {(\frac{\exp (- \frac{0.15 \cdot 0.19}{8.3145 \cdot 550})}{0.6 + 0.4 \cdot \exp (- \frac{0.15 \cdot 0.19}{8.3145 \cdot 550})})}^{2}) + (\frac{\exp (- \frac{0.15 \cdot 0.12}{8.3145 \cdot 550}) \cdot (\frac{0.12}{8.3145 \cdot 550})}{{(0.4 + 0.6 \cdot \exp (- \frac{0.15 \cdot 0.12}{8.3145 \cdot 550}))}^{2}})))

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Activity Coefficient for Component 2 using NRTL Equation Solution

Follow our step by step solution on how to calculate Activity Coefficient for Component 2 using NRTL Equation?

FIRST Step Consider the formula

γ 2 = \exp (({x 1}^{2}) \cdot (((\frac{b 12}{[R] \cdot T NRTL}) \cdot {(\frac{\exp (- \frac{α \cdot b 12}{[R] \cdot T NRTL})}{x 2 + x 1 \cdot \exp (- \frac{α \cdot b 12}{[R] \cdot T NRTL})})}^{2}) + (\frac{\exp (- \frac{α \cdot b 21}{[R] \cdot T NRTL}) \cdot (\frac{b 21}{[R] \cdot T NRTL})}{{(x 1 + x 2 \cdot \exp (- \frac{α \cdot b 21}{[R] \cdot T NRTL}))}^{2}})))

Next Step Substitute values of Variables

∴

γ 2 = \exp (({0.4}^{2}) \cdot (((\frac{0.19J/mol}{[R] \cdot 550K}) \cdot {(\frac{\exp (- \frac{0.15 \cdot 0.19J/mol}{[R] \cdot 550K})}{0.6 + 0.4 \cdot \exp (- \frac{0.15 \cdot 0.19J/mol}{[R] \cdot 550K})})}^{2}) + (\frac{\exp (- \frac{0.15 \cdot 0.12J/mol}{[R] \cdot 550K}) \cdot (\frac{0.12J/mol}{[R] \cdot 550K})}{{(0.4 + 0.6 \cdot \exp (- \frac{0.15 \cdot 0.12J/mol}{[R] \cdot 550K}))}^{2}})))

Next Step Substitute values of Constants

∴

γ 2 = \exp (({0.4}^{2}) \cdot (((\frac{0.19J/mol}{8.3145 \cdot 550K}) \cdot {(\frac{\exp (- \frac{0.15 \cdot 0.19J/mol}{8.3145 \cdot 550K})}{0.6 + 0.4 \cdot \exp (- \frac{0.15 \cdot 0.19J/mol}{8.3145 \cdot 550K})})}^{2}) + (\frac{\exp (- \frac{0.15 \cdot 0.12J/mol}{8.3145 \cdot 550K}) \cdot (\frac{0.12J/mol}{8.3145 \cdot 550K})}{{(0.4 + 0.6 \cdot \exp (- \frac{0.15 \cdot 0.12J/mol}{8.3145 \cdot 550K}))}^{2}})))

Next Step Prepare to Evaluate

∴

γ 2 = \exp (({0.4}^{2}) \cdot (((\frac{0.19}{8.3145 \cdot 550}) \cdot {(\frac{\exp (- \frac{0.15 \cdot 0.19}{8.3145 \cdot 550})}{0.6 + 0.4 \cdot \exp (- \frac{0.15 \cdot 0.19}{8.3145 \cdot 550})})}^{2}) + (\frac{\exp (- \frac{0.15 \cdot 0.12}{8.3145 \cdot 550}) \cdot (\frac{0.12}{8.3145 \cdot 550})}{{(0.4 + 0.6 \cdot \exp (- \frac{0.15 \cdot 0.12}{8.3145 \cdot 550}))}^{2}})))

Next Step Evaluate

∴

γ 2 = 1.00001084639206

LAST Step Rounding Answer

∴

γ 2 = 1

Activity Coefficient for Component 2 using NRTL Equation Formula Elements

Variables

Constants

Functions

Activity Coefficient of Component 2

Activity coefficient of component 2 is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances.

Symbol: γ₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

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.

Symbol: x₁

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

NRTL Equation Coefficient (b12)

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.

Symbol: b₁₂

Measurement: Energy Per MoleUnit: J/mol

Note: Value can be positive or negative.

Temperature for NRTL model

Temperature for NRTL model is the degree or intensity of heat present in a substance or object.

Symbol: T_NRTL

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

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.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

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.

Symbol: x₂

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

NRTL Equation Coefficient (b21)

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.

Symbol: b₂₁

Measurement: Energy Per MoleUnit: J/mol

Note: Value can be positive or negative.

Universal gas constant