Raoult Bubble–Dew Lever Rule

Worked Example: Tie Line and Lever Rule

Consider a binary mixture with Volatility ratio 2, Liquid composition 0.25, and Overall composition 0.5. Let us derive the pressure, vapor composition, and phase status. We use basic arithmetic to find these values from the inputs.

1. The bubble pressure is P = x × alpha + (1 - x) = 0.25 × 2 + (1 - 0.25) = 1.25.
2. The equilibrium vapor composition is y = x × alpha / P = 0.25 × 2 / 1.25 = 0.4.
3. The dew pressure at vapor y is 1 / (y / alpha + 1 - y) = 1 / (0.4 / 2 + 1 - 0.4) = 1.25.
4. The overall composition z is 0.5. Since z > y (0.5 > 0.4), the entire mixture is vapor.
5. The vapor fraction is 1.0, and the phase status is Vapor.

Exploring the P-x-y Diagram

Change the interactive controls to see how the equilibrium shifts. You will explore a simple P-x-y visualization in the module view to verify calculations.

1. Open the module and set Volatility ratio to 2.
2. Set Liquid composition to 0.5. Observe the bubble pressure rising to 1.5, and equilibrium vapor composition to 0.6666666666666666.
3. Set Overall composition to 0.5. Now, the overall composition equals the liquid composition (z = x). The vapor fraction drops to 0.0, and the phase status becomes Two phase.

Model Limitations

This model describes an isothermal ideal binary mixture with normalized saturation pressures. It assumes Raoult's law is perfectly obeyed without nonideal azeotropes. Furthermore, degenerate endpoints purposefully omit single-phase inferences outside the selected tie line to prevent division by zero.

No temperature solver or real chemical property database is used; all behaviors are derived purely from the relative volatility ratio and provided compositions. This restricts the module strictly to isothermal systems obeying idealized rules.

References

This module implements textbook formulas for vapor-liquid equilibrium (VLE) without complex derivations. It uses basic relations directly to demonstrate the tie line and lever rule over composition domains.

• NPTEL: Vapour Liquid Equilibrium in Ideal Solutions: Supports the isothermal P-x-y diagram formulas and the lever rule applied in this module.