Week 2 follow-up · A guided Lab 08 review
19 October 2026
Your feedback asked for clearer unit conventions, a guided demonstration and more explanation of the results.
Open: Lab 08 and the three-page Lab guide.
We will use one synthetic dataset throughout this review. Follow along for 15 minutes at the start of Session 3. The last three slides are optional reference material.
Keep your original worksheet. Add corrections beside it. This review adds no attendance submission.
At the same measured temperature, modified Raoult’s law gives
y_iP=x_i\gamma_iP_i^{sat},\qquad \gamma_i=\frac{y_iP}{x_iP_i^{sat}}.
Assumptions here: ideal vapor and negligible Poynting correction. Use the same pressure unit in numerator and denominator.
Your action: Locate these quantities on guide page 1 before opening any fit.
| Worksheet page 2, Section C | Lab 08 synthetic example | |
|---|---|---|
| Equilibrium temperature | 50 °C = 323.15 K | 350 K = 76.85 °C |
| Temperature in Antoine equation | °C | K |
| Constants | A = 4, B = 1000, C = 200 | Supplied separately for each component |
| Purpose | Practice equation conventions | Work with a complete VLE dataset |
Your action: Select Load synthetic example in Lab 08. Use its own constants. Keep the Section C constants in that paper exercise.
Both examples are synthetic teaching data.
| Setting or display | Meaning | Lab example |
|---|---|---|
| Measured-data temperature unit | Unit of the numbers in the input file | 350 with K selected |
| Temperature inside Antoine equation | Convention attached to A, B and C | Insert 350 in this K correlation |
| Valid temperature limits | Range fields always use K | 300–390 K |
The calculated observation table always displays K and kPa.
Your action: Check all three locations on guide page 2. An equivalent measured input is 76.85 with °C selected. Merely relabeling 350 as °C changes the temperature.
Your action: After validation, locate x_1=0.5 in Imported observations. Use guide page 1.
| Input observation | Value | Calculated property at 350 K | Value |
|---|---|---|---|
| T | 350 K | P_1^{sat} | 150 kPa |
| P | 158.707198 kPa | P_2^{sat} | 60 kPa |
| x_1 | 0.500000 | \ln\gamma_1 | 0.399813 |
| y_1 | 0.704857 | \ln\gamma_2 | 0.445568 |
P_1^{sat} and P_2^{sat} come from the two Antoine correlations. They are not the total mixture pressure P.
\gamma_1=\frac{0.704857144627\,(158.707198211)}{0.5\,(150)} \approx 1.491545
\gamma_2=\frac{(1-0.704857144627)\,(158.707198211)}{(1-0.5)\,(60)} \approx 1.561377
All pressures are in kPa. Both results are dimensionless.
Your action: Calculate \gamma_1 and compare it with \exp(0.399813), allowing for display rounding. The table reports ln γ, so comparing 1.491545 directly with 0.399813 compares different quantities.
Agreement checks the calculation with the chosen inputs. Real property accuracy needs an independent reference.
Your action: Follow guide page 2 and repeat these steps in the open Lab.
Select Pressure and vapor residuals in View. Guide page 2 explains Excel/CSV preparation and reopening saved studies.
Default synthetic dataset: 19 observations at 350 K. Same property inputs and fitting objective.
| Fitted model | Mean absolute pressure error (%) | Mean absolute y_1 error (percentage points) |
|---|---|---|
| Margules, one parameter | 1.14098 | 0.675676 |
| NRTL, α = 0.3 | About 1.14\times10^{-6} | About 3.83\times10^{-7} |
Small final digits may vary. The data generator uses NRTL, so near-exact recovery is expected.
Your action: Name each metric and its unit in worksheet E2. A mole-fraction error of 0.01 equals 1 percentage point. Near-zero training error alone does not establish consistency or prediction.
| Check | Evidence it supplies |
|---|---|
| Hand calculation versus Lab | Agreement for this calculation with the chosen equation and inputs |
| P^{sat} versus independent measurements or a trusted reference | External support for the property inputs at the same T |
| Applicable thermodynamic diagnostic | Agreement with a constraint, under stated assumptions |
| Data excluded from fitting | Evidence about prediction on those held-out observations |
Your action: On guide page 3, identify which check you have actually performed. Describe any remaining checks as future work.
The synthetic example has no real-fluid measurements against which to validate its property constants.
For a binary liquid at fixed T and P, Gibbs–Duhem requires
x_1\,d\ln\gamma_1+x_2\,d\ln\gamma_2=0.
The two activity coefficients are linked. A fitted model can obey this relation while only approximating inconsistent measurements.
Lab 08 assumes negligible excess-volume pressure effects for its isothermal diagnostics. Isobaric diagnostics need their temperature correction and, for the differential test, independent H^E data.
Your action: Read the diagnostic’s applicability message. With incomplete composition coverage and No extrapolation, a full-area verdict is unavailable. Not assessed is not a pass or a failure.
Your action: Answer these on paper before the next slide. No form submission is required.
Use guide pages 1–2 for units and page 3 for the types of evidence. Then check the answers on the next slide.
Your action: Add one correction to your worksheet if needed. Return to Session 3: liquid stability.
Next we ask whether an equilibrium calculation gives the lowest admissible Gibbs energy. A good VLE fit alone does not settle that question.
Optional: Use guide page 2 when preparing your own dataset.
The supplied template uses 350 K and kPa. A CSV contains observations only. It does not set or restore the Lab’s units or constants. Excel workbooks (.xlsx) must first be saved as CSV.
| File | What it contains | How to use it |
|---|---|---|
| Observation CSV | Raw T, P, x1, y1 | Import as data, then set units and properties |
| Complete study JSON | Controls, sources and recorded results | Study workspace, load JSON, Restore, then validate/refit |
| Fitted residuals CSV | Calculated residual table | Open in a spreadsheet to inspect/export results |
If results differ: compare the raw data, units, component order, equation form, sources and model settings first. Then check convergence and parameter-bound warnings.
Keep the JSON and a screenshot of any error. Guide page 2 gives the exact restore steps. You do not need to edit JSON by hand.
Finding: On the same 350 K synthetic dataset, NRTL reproduces the training observations more closely than one-parameter Margules.
Evidence: Mean absolute pressure error decreases from about 1.14098% to 0.00000114%, with the same property inputs and fitting objective.
Limit: The generator uses NRTL. This comparison establishes model recovery on these observations. Thermodynamic consistency, real-fluid property accuracy and prediction each require their own applicable evidence.
Your action: Use this structure for worksheet F, with your own saved results. Include the metric, units, controlled inputs and a limitation.