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

Total Pressure Formula:

\[ P_T = \frac{1}{\left(\frac{y_1}{\gamma_1 \cdot P_{1}^{sat}} + \frac{y_2}{\gamma_2 \cdot P_{2}^{sat}}\right)} \]

Mole Fraction of Component 1 in Vapour Phase (y₁):

Activity Coefficient of Component 1 (γ₁):

Saturated Pressure of Component 1 (P₁^sat):

Mole Fraction of Component 2 in Vapour Phase (y₂):

Activity Coefficient of Component 2 (γ₂):

Saturated Pressure of Component 2 (P₂^sat):

Total Pressure of Gas (P_T):

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1. What is Total Pressure for Binary Vapour System?

Definition: This calculator determines the total pressure of a binary vapour system using Modified Raoult's Law, accounting for non-ideal behavior through activity coefficients.

Purpose: It's essential for dew-bubble point calculations in chemical engineering, particularly for vapor-liquid equilibrium (VLE) analysis of non-ideal mixtures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_T = \frac{1}{\left(\frac{y_1}{\gamma_1 \cdot P_{1}^{sat}} + \frac{y_2}{\gamma_2 \cdot P_{2}^{sat}}\right)} \]

Where:

\( P_T \) — Total pressure of the gas mixture (Pa)
\( y_1 \) — Mole fraction of component 1 in vapour phase
\( \gamma_1 \) — Activity coefficient of component 1
\( P_{1}^{sat} \) — Saturated pressure of component 1 (Pa)
\( y_2 \) — Mole fraction of component 2 in vapour phase
\( \gamma_2 \) — Activity coefficient of component 2
\( P_{2}^{sat} \) — Saturated pressure of component 2 (Pa)

Explanation: The formula accounts for the non-ideal behavior of components through their activity coefficients, modifying Raoult's Law for more accurate calculations.

3. Importance of Total Pressure Calculation

Details: Accurate pressure calculations are crucial for designing separation processes like distillation, predicting phase behavior, and ensuring proper operation of chemical processes.

4. Using the Calculator

Tips: Enter the mole fractions (must sum to 1), activity coefficients (typically >1 for positive deviation from ideality), and saturated pressures. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for activity coefficients?
A: For ideal mixtures, γ=1. For non-ideal mixtures, γ can range from 0.1 to 10 or more, depending on the system.

Q2: How do I obtain saturated vapor pressures?
A: Use Antoine equation or vapor pressure tables for pure components at the system temperature.

Q3: What if my mole fractions don't sum to 1?
A: The calculator will still compute, but results may not be physically meaningful. Ensure y₁ + y₂ = 1 for accurate results.

Q4: When is Modified Raoult's Law necessary?
A: When dealing with non-ideal mixtures where molecular interactions cause deviations from ideal behavior.

Q5: Can this be extended to multicomponent systems?
A: Yes, the principle can be extended, but the formula becomes more complex with additional terms for each component.