Total Pressure for Binary Liquid System for Dew-Bubble Point Calculations with Modified Raoult's Law Calculator

Total Pressure Formula:

\[ P_T = (x_1 \times \gamma_1 \times P_{1}^{sat}) + (x_2 \times \gamma_2 \times P_{2}^{sat}) \]

Mole Fraction of Component 1 (x₁):

Activity Coefficient of Component 1 (γ₁):

Saturated Pressure of Component 1 (P₁^sat):

Mole Fraction of Component 2 (x₂):

Activity Coefficient of Component 2 (γ₂):

Saturated Pressure of Component 2 (P₂^sat):

Total Pressure (P_T):

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1. What is Total Pressure for Binary Liquid System?

Definition: This calculator computes the total pressure of a binary liquid system using Modified Raoult's Law, which accounts for non-ideal behavior through activity coefficients.

Purpose: Essential for dew-bubble point calculations in vapor-liquid equilibrium studies, particularly in chemical engineering and thermodynamics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_T = (x_1 \times \gamma_1 \times P_{1}^{sat}) + (x_2 \times \gamma_2 \times P_{2}^{sat}) \]

Where:

\( P_T \) — Total system pressure (Pa)
\( x_1, x_2 \) — Mole fractions of components 1 and 2 in liquid phase
\( \gamma_1, \gamma_2 \) — Activity coefficients for components 1 and 2
\( P_{1}^{sat}, P_{2}^{sat} \) — Saturation pressures of pure components 1 and 2 (Pa)

Explanation: The total pressure is the sum of partial pressures of both components, each calculated as the product of mole fraction, activity coefficient, and pure component vapor pressure.

3. Importance of This Calculation

Details: Accurate pressure calculations are crucial for designing distillation columns, predicting phase behavior, and optimizing separation processes in chemical industries.

4. Using the Calculator

Tips: Enter mole fractions (must sum to 1), activity coefficients (typically >1 for positive deviation), and saturation pressures. Default values are provided as examples.

5. Frequently Asked Questions (FAQ)

Q1: What is Modified Raoult's Law?
A: It extends ideal Raoult's Law by incorporating activity coefficients to account for non-ideal interactions between molecules.

Q2: When should I use this calculator?
A: For binary systems where activity coefficients are known and non-ideal behavior is significant (common with polar or associating molecules).

Q3: How do I obtain activity coefficients?
A: They can be determined experimentally or estimated using thermodynamic models like UNIQUAC or NRTL.

Q4: What if my mole fractions don't sum to 1?
A: The calculator will still compute a result, but for meaningful physical interpretation, x₁ + x₂ should equal 1.

Q5: Can this be extended to multicomponent systems?
A: Yes, the principle extends to more components by adding terms for each additional component.