After midterm · Session 2 of 6 · 180 minutes
30 September 2026
Does a small fitting error mean the data and model are trustworthy?
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.
\mu_i=\mu_i^\circ+RT\ln a_i,\qquad a_i=\gamma_i x_i
The activity is dimensionless; γ is its correction relative to an ideal liquid solution using the pure-liquid standard.
Residual: real fluid minus ideal gas at the same T, P and composition.
Excess: real mixture minus ideal solution at the same T, P and composition.
\gamma_i=\frac{y_iP}{x_iP_i^{sat}(T)}
This inversion assumes ideal vapor and negligible Poynting correction. Convergence, consistency and prediction are separate checks.
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.
Check one Antoine saturation pressure and one inferred activity coefficient by hand. Keep the same observations and property convention when comparing models.
Load and validate the synthetic example in Lab 08. Inspect its Antoine form and units, then fit one-parameter Margules. Compare predicted P and y with one observed point, then inspect the residual pattern.
Keep one saved baseline for the pair investigation.
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.
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.
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 included. With pre-class reading, independent work totals 45–60 minutes.
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.