Comparison of the Osmotic Virial Equation with the Margules Activity Model for Solid–Liquid Equilibrium
Bibliographic record
Abstract
The main goal of this paper is to compare the general polynomial forms of the osmotic virial equation and the Margules model for the liquid activity coefficients in binary systems. The coefficients/parameters in each model can be calculated based on best fits to experimental phase equilibrium data. Here, the activity coefficient models were combined with the equation of solid-liquid equilibrium. We obtain the coefficients/parameters for the osmotic virial equation and the one- and two-parameter Margules models and compare the accuracy of each model for fitting the experimental data for five water/solute systems: water/glycerol, water/acetic acid, water/propanoic acid, water/mono-ethylene glycol, and water/sulfolane. In obtaining the osmotic virial coefficients, we present a method to fit the equation to the entire range of data including both the ice-formation region and the solute-precipitation region. In expression of the concentration effect of the solute, we showed that the integration constant that arises from the Gibbs-Duhem equation is dependent on the osmotic virial coefficients. The osmotic virial equation is of great interest for its ability to empirically model a very wide range of aqueous solutions and as such is one of the most widely used solution models in biology.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".