SKH Thermodynamics Labs

Lab 08 · Your own VLE data

Can you trust a VLE table before you fit it?

Start with a synthetic isothermal data set at 350 K, then paste your own T, P, x₁, y₁ table with its units and Antoine constants.

Read one row by hand, check the pure-liquid limits of γ, and only then fit a model.

2027 prototype
Review the student workflow

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Core: read one row, inspect the activity coefficients, fit a model and explain the result. Steps 1–5.

Graduate: the core steps plus unit-error signatures, a model comparison and endpoint assumptions in Step 4.

Graduate route. Complete Steps 1–3 with the example and then with your own data. In Step 4, test which checks catch which input mistakes, compare three models and examine endpoint assumptions. Go to the graduate investigation.

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From a table row to activity coefficients

Every unit enters the result
One measured row and the saturation pressures combine into two activity coefficients The measured row gives T, P, x1 and y1. The Antoine equations give each pure-component saturation pressure at that T. Together they give gamma1 and gamma2 by modified Raoult's law. A wrong unit in any box changes both activity coefficients. Measured rowT [K or °C] · P [kPa, Pa, bar] · x₁ · y₁Antoine equationform · A, B, C · T unit · Psat unitγᵢ = yᵢP / (xᵢPᵢˢᵃᵗ)ideal vapor · same P unitsγ₁, γ₂ln γᵢ → 0 for pure i
Check the first row by hand before validating the whole table. A unit mistake usually shows as γ values that are far from 1 everywhere, including where a component is almost pure.

1. Describe the experiment and enter the table

Binary · one run
Pure-component vapor pressures · Antoine

Choose the exact form printed by your source. Valid-range limits are always in K. Constants are not converted when you change a unit.

Comma, semicolon or tab delimiters; dot decimals. At least five interior points, at most 500 rows. Do not include Psat columns.

How the first interior row will be read

Waiting for a table
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Optional. Your choice does not change the calculation.

2. Inspect the activity coefficients

Validate the table to see every row's saturation pressures and activity coefficients, and the pure-liquid checks.

4. Check your understanding

Write first, then compare

Use the synthetic example in Steps 1–3 to answer each question. Then open the explanation and compare. Your answers are saved with your study.

A. Read the first row by hand

Load the example. Use the first-row preview to calculate γ₁ and γ₂ yourself.

Compare with the explanation

At 350 K, P₁sat = 150 kPa and P₂sat = 60 kPa. With x₁ = 0.05, y₁ = 0.3975 and P = 95.12 kPa: γ₁ = 0.3975 × 95.12/(0.05 × 150) = 5.04 and γ₂ = 0.6025 × 95.12/(0.95 × 60) = 1.005.

Component 1 is dilute here, so γ₁ is near its infinite-dilution value, while component 2 is almost pure and γ₂ ≈ 1.

B. What does a wrong pressure unit look like?

Set the P column unit to bar (the numbers are really kPa) and validate again. Compare the pure-liquid checks and the fit with the correct import.

Compare with the explanation

Every P is multiplied by 100, so both γ values are multiplied by 100 and both ln γ rise by ln 100 = 4.61. ln γ₁ at x₁ = 0.95 becomes 4.61 instead of 0.004, which violates the pure-liquid limit. The NRTL fit misses the pressure by 99%.

The ratio γ₁/γ₂ does not change, so the area consistency test of Lab 03 gives the same D = 1.16% and cannot see this mistake. Check the units and the limits before testing consistency.

C. Does a near-perfect fit prove the data are right?

Fit NRTL, then Margules with one and with two parameters. Compare the pressure errors.

Compare with the explanation

NRTL reproduces the pressure to about 10⁻⁶ %, two-parameter Margules to 0.26% and one-parameter Margules to 1.1%. The example was generated by NRTL with τ₁₂ = 0.8 and τ₂₁ = 1.2, which the fit recovers.

A good fit shows that a model can represent the table. It does not show that the measurements are accurate or thermodynamically consistent; Lab 03 tests consistency separately.

4. Investigate what each check can catch

Master's core work

Validate a table in Step 1 before running an investigation.

A. Diagnose input mistakes by their signatures

  1. Re-import the same table under four deliberate misreadings: P as bar, P as Pa, T as °C, and Antoine constants with the wrong T unit.
  2. For each, read the pure-liquid limits, the area D and the NRTL pressure error, or the rejection reason.
  3. Identify which check catches each mistake and which check is blind to it.

B. Compare three activity models

  1. Fit NRTL, one-parameter Margules and two-parameter Margules to the same observations.
  2. Compare the errors, the parameters and the residual pattern in Step 3.
  3. Explain why adding a parameter reduces the error, and what extra data would discriminate between the models.

C. How much does the area test depend on unmeasured endpoints?

  1. Compare the area D with no extension, linear extension and a quadratic fit of ln(γ₁/γ₂).
  2. Explain why the measured interval alone cannot give a full-range verdict.
  3. Name the measurement that would replace the extrapolation.

D. Defend a limited conclusion

The record check only confirms that the sections and calculations are present. Scientific reasoning still needs instructor review.

5. Compare and save

  1. Validate and save the synthetic example.
  2. Validate and save the same table read with P in bar. Compare the limits.
  3. Answer questions A–C in Step 4, then repeat Steps 1–3 with your own data.
  4. Download the complete study, reopen it, and reproduce a saved case.
  1. Validate and save the example and your own data.
  2. Complete investigations A–C and write the graduate claims.
  3. Download the complete study, reopen it, and reproduce a saved case and its investigation record.

Your validated cases will appear here after you add them.

Load the example or enter your own table.

Your table, settings, comparisons and explanations stay in this open page. The study file includes your data table so that it can be reopened.

Model and assumptions

γi = yiP/(xiPisat) assumes an ideal vapor and negligible Poynting and excess-volume corrections. Saturation pressures come from your Antoine constants at each row's T and are never extrapolated beyond the declared range. Fits minimize the unweighted mean of (100 ΔP/P)² and (100 Δy₁)² with bounded multistart Nelder–Mead. Open the current Lab 08 for HE data, isobaric temperature-dependent NRTL and the full consistency suite.