Does the data
tell one story?

1. What did the article report?

2. What can these measurements test here?

For an isobaric path, temperature changes with composition. Gibbs–Duhem includes the excess-enthalpy term: Σxᵢ d ln γᵢ = −Hᴱ/(RT²) dT. Setting this term to zero is not generally valid. No independent Hᴱ data or full-range endpoint estimates are supplied in this exercise, so the partial area is a diagnostic, not a pass/fail test.

Pure endpoints do not specify the absent component’s infinite-dilution γ. This lab does not fill those gaps using the same NRTL model being evaluated.

3. Is the NRTL equation itself consistent?

The derivative check holds T = 350 K fixed. It verifies the model equation and does not certify the experimental data. A small fitting residual answers a different question again.

NIST: area tests and the isobaric correction ↗

Start with the article’s NRTL model at 350 K, over the full composition range including model limits. Add δ(1−x₁)² to ln γ₁ while leaving ln γ₂ unchanged. These are synthetic activity data, not modified article observations.

A₊ and A₋ are positive and negative area magnitudes. D = 100|A₊−A₋|/(A₊+A₋). The exact signed integral for this perturbation is δ/3. Full-range area cancellation is necessary under these fixed-T, fixed-P activity-model assumptions; it is not sufficient to validate arbitrary data.

Barbieri, C.; De Guido, G.; Moioli, S. Vapor-liquid equilibrium data for the binary system isopropanol+water at 60 kPa and 80 kPa. The Journal of Chemical Thermodynamics 198 (2024), 107342. Numerical data: Tables 4–7, p. 7. The original PDF and figures are not redistributed.

Ideal vapor and negligible Poynting corrections are assumed. Antoine: log₁₀(P/bar) = A−B/(T/K+C). NIST 2-propanol: A = 4.8610, B = 1357.427, C = −75.814, 329.92–362.41 K. NIST water: A = 5.0768, B = 1659.793, C = −45.854, 334–363 K. Joint domain: 334–362.41 K. No extrapolation; model curves have gaps outside it. All original observations remain visible.

The article’s Table 7 prints b in 1/K; Eq. (2), τ = a+b/T, requires b in K. We use the printed numerical values with Eq. (2). The article’s parameters were fitted using a wider literature collection. This exercise uses only its 40 newly reported observations and different property assumptions. It does not reproduce the Aspen regression or Table 6.

Teaching objective: mean squared residual of ln γ across both components. Fit uses five starting points, bounded Nelder–Mead, −3 ≤ τ₁₂, τ₂₁ ≤ 8, fixed α = 0.47. Average expanded uncertainties are reported, but are not treated as independent pointwise weights. Errors in x, y, T and P and their correlations are not modeled. No parameter confidence intervals are claimed.

Bubble curves solve ΣxᵢγᵢPᵢˢᵃᵗ/P − 1 = 0 by bisection. A sampled liquid-curvature check is shown; this study does not solve flash or LLE. Area integration is piecewise linear over measured valid compositions, split exactly at zero crossings.

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