Activity Coefficient for Component 1 using Wilson Equation Calculator

Wilson Equation Formula:

\[ \gamma_1 = \exp\left(\ln(x_1 + x_2 \Lambda_{12}) + x_2\left(\frac{\Lambda_{12}}{x_1 + x_2 \Lambda_{12}} - \frac{\Lambda_{21}}{x_2 + x_1 \Lambda_{21}}\right)\right) \]

Activity Coefficient of Component 1 (γ₁):

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1. What is Activity Coefficient using Wilson Equation?

Definition: The activity coefficient (γ) quantifies the deviation of a component's behavior from ideal solution behavior in liquid mixtures.

Purpose: The Wilson equation provides a thermodynamic model for calculating activity coefficients in non-ideal binary liquid mixtures.

2. How Does the Calculator Work?

The calculator uses the Wilson equation:

\[ \gamma_1 = \exp\left(\ln(x_1 + x_2 \Lambda_{12}) + x_2\left(\frac{\Lambda_{12}}{x_1 + x_2 \Lambda_{12}} - \frac{\Lambda_{21}}{x_2 + x_1 \Lambda_{21}}\right)\right) \]

Where:

\( \gamma_1 \) — Activity coefficient of component 1
\( x_1 \) — Mole fraction of component 1 in liquid phase
\( x_2 \) — Mole fraction of component 2 in liquid phase
\( \Lambda_{12} \) — Wilson equation coefficient for component 1
\( \Lambda_{21} \) — Wilson equation coefficient for component 2

Explanation: The equation accounts for molecular interactions between different components in the mixture.

3. Importance of Activity Coefficient Calculation

Details: Accurate activity coefficients are essential for vapor-liquid equilibrium calculations, distillation design, and chemical process simulations.

4. Using the Calculator

Tips: Enter mole fractions (must sum to 1) and Wilson coefficients (typically determined experimentally or from correlations).

5. Frequently Asked Questions (FAQ)

Q1: What do Wilson coefficients represent?
A: They represent the energy interactions between different molecular pairs in the mixture.

Q2: What range of values do activity coefficients typically have?
A: For most systems, γ ranges between 0.1 and 10, though extreme values are possible.

Q3: When is the Wilson equation most appropriate?
A: For completely miscible liquid mixtures, especially those with similar molecular sizes.

Q4: How do I obtain Wilson coefficients?
A: They are typically determined by fitting experimental vapor-liquid equilibrium data.

Q5: Can this be used for multicomponent systems?
A: The Wilson equation can be extended to multicomponent systems, but this calculator handles binary mixtures only.