Experimental VLE, consistency and fitting

After midterm · Session 2 of 6 · 180 minutes

Soorathep Kheawhom

30 September 2026

The question for today

Does a small fitting error mean the data and model are trustworthy?

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.

Activities inferred from VLE

Under the ideal-vapor approximation with neglected Poynting correction, \gamma_i=\frac{y_iP}{x_iP_i^{sat}(T)}

The absent component at a pure endpoint has no finite measured γ from this ratio. Small x or y amplifies measurement error.

Different tests answer different questions

Diagnostic Evidence and limitation
Area Global signed integral; endpoint coverage matters
Point/local Local deviations; differentiation amplifies noise
Model-based Deviations relative to the chosen model
Herington Empirical temperature-range correction

Agreement across tests strengthens a diagnosis but does not prove the data are correct.

A vapor-pressure error becomes an activity error

Synthetic point: P=100 kPa, x₁=0.4, y₁=0.6 and P₁ˢᵃᵗ=120 kPa.

\gamma_1=\frac{0.6(100)}{0.4(120)}=1.25

Using 150 kPa instead yields γ₁=1.00. The measured mixture data did not change; the inferred liquid behavior did.

An independent check

Check one Antoine saturation pressure and one inferred activity coefficient by hand. Keep the same observations and property convention when comparing models.

One demonstration · 20 minutes

Open the core lab

Load and validate the synthetic example in Lab 08. Inspect its Antoine form and units, then fit one-parameter Margules. Record the residual pattern and one limitation.

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 08, validate the supplied synthetic example and compare one-parameter Margules with NRTL at alpha=0.3 on the same observations. Report one residual pattern and verify one activity coefficient by hand.

Discussion and exit question · 30 minutes

Use 20 minutes to compare results and discuss unexpected behavior.

Does a small fitting error mean the data and model are trustworthy?

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

Required practice · 45–60 minutes

In Lab 08, validate the supplied synthetic example and compare one-parameter Margules with NRTL at alpha=0.3 on the same observations. Report one residual pattern and verify one activity coefficient by hand.

Assessment 2 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: a controlled consistency defect in Lab 03, a fixed held-out comparison, bootstrap fit spread, or your own sourced VLE data. Exact synthetic bootstrap spread does not quantify real measurement uncertainty.

Session appendix · Module reference

Learning path · Offline package

Optional work is additional. Complete the required investigation first.