After midterm · Session 3 of 6 · 180 minutes
30 September 2026
When does a calculated liquid split represent stable equilibrium?
Before class: 3-page reading · 15–20 minutes
Bring the three preparation answers. Revisit your prediction after one controlled comparison and an independent check.
| 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.
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.
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.
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.
Use the calculated endpoints to close the component balance independently. Check that the tangent supports the entire admitted Gibbs curve.
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.
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.
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.
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 included. With pre-class reading, independent work totals 45–60 minutes.
Choose one extension: NRTL tie-line fitting in Lab 05, paired bootstrap from independent replicates, or feasible three-phase amounts in Lab 06.
Optional paper bridge: recover partial molar properties from tangent intercepts.
Session appendix · Module reference
Learning path · Offline package
Optional work is additional. Complete the required investigation first.