Liquid stability, LLE and VLLE

After midterm · Session 3 of 6 · 180 minutes

Soorathep Kheawhom

30 September 2026

The question for today

When does a calculated liquid split represent stable equilibrium?

Write your prediction before opening the lab. By the end, support an answer with one controlled comparison and an independent check.

The 180-minute class

Activity Minutes
Opening question and essential concepts 30
One hand calculation 20
One lab demonstration 20
Break 10
Student pair investigation 70
Discussion and exit question 30

The 70-minute investigation is student work with instructor support.

Phase equilibrium includes stability

Equality of chemical potentials identifies stationary candidate states. Stable equilibrium requires the lowest admissible total Gibbs energy.

g_{mix}/RT=\sum_i x_i\ln x_i+g^E/(RT)

A split can lower G even when a homogeneous liquid is locally stable.

The common-tangent conditions

g'(x^\alpha)=g'(x^\beta)=\frac{g(x^\beta)-g(x^\alpha)}{x^\beta-x^\alpha}

The tangent must not lie above g(x) anywhere in the admitted composition interval.

A trivial root xᵅ=xᵝ does not establish two distinct liquid phases.

A lever-rule calculation

Synthetic tie line: x₁ᵅ=0.2, x₁ᵝ=0.8. Feed z₁=0.5.

f_\beta=\frac{z_1-x_1^\alpha}{x_1^\beta-x_1^\alpha}=0.5

For z₁=0.35, fᵝ=0.25. At the same coexistence conditions, the phase amounts change but the tie-line endpoints do not.

An independent check

Use the calculated endpoints to close the component balance independently. Check that the tangent supports the entire admitted Gibbs curve.

One demonstration · 20 minutes

Open the core lab

In Lab 04 select a supported liquid split and save it. Change only overall composition inside the tie line. Compare phase compositions with phase fractions.

Keep one saved baseline for the pair investigation.

Pair investigation · 70 minutes

  • 10 min: predict and record the baseline.
  • 25 min: change one input and calculate.
  • 20 min: exchange roles and check the result by hand.
  • 15 min: prepare one plot or table and a short explanation.

In Lab 04, retain one supported tie line and compare two overall compositions inside it. Verify the lever rule by hand and explain the global stability check.

Discussion and exit question · 30 minutes

Use 20 minutes to compare results and discuss unexpected behavior.

When does a calculated liquid split represent stable equilibrium?

Use the final 10 minutes to explain your answer individually and name one assumption that limits it.

Required practice · 45–60 minutes

In Lab 04, retain one supported tie line and compare two overall compositions inside it. Verify the lever rule by hand and explain the global stability check.

Assessment 3 and independent checkpoint

Retain one study JSON, one comparison and a short explanation. Continue from your classroom case. The hand checkpoint is part of this time budget.

Optional study

Choose one extension: NRTL tie-line fitting in Lab 05, paired bootstrap from independent replicates, or feasible three-phase amounts in Lab 06.

Session appendix · Module reference

Learning path · Offline package

Optional work is additional. Complete the required investigation first.