SCIENCE · INVESTIGATE AND EXPLAIN

Test ideal and nonideal vapor-composition predictions

For an ideal binary liquid, each partial pressure is its liquid mole fraction times its pure-component vapor pressure at the same temperature.

Learning outcome: Compare xA=.3,.5,.7 at parameter0 and1. Record each partial pressure, total and vapor composition. Identify which changes are due to composition versus the supplied activity correction.

Starting recap

Use chemical amount, dimensional ratios and positive interval endpoints. Distinguish original formula units, independently moving species and a chosen thermodynamic standard.

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At liquid xA=.50 and ideal behavior, pA=30 and pB=10 kPa, total40 kPa and vapor yA=.75. With supplied interaction parameter1, both coefficients exp(.25), total≈51.361 kPa but yA remains.75 at this symmetric composition.

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Predict

Does equal liquid composition imply equal vapor composition when pure vapor pressures differ?

Your prediction and reason

Experiment

Compare xA=.3,.5,.7 at parameter0 and1. Record each partial pressure, total and vapor composition. Identify which changes are due to composition versus the supplied activity correction.

Compare liquid composition, vapor composition and deviation

Worked teaching model · synthetic values · Fictional volatile liquids at one fixed temperature: pure vapor pressures A60 and B20 kPa, ideal vapor. Supplied symmetric Margules illustration lnγA=Aparameter*xB² and lnγB=Aparameter*xA². Parameter0 is ideal Raoult;0..1.5 keeps the declared liquid single-phase model. Not a distillation procedure, measured substance fit or general phase-equilibrium solver.

Liquid mole fraction of A: 0.5 fraction Supplied symmetric interaction parameter: 0 dimensionless

Reset keeps your prediction, captures and practice history.

Axes rescale. Connected samples represent declared equilibrium or activity relationships, not elapsed time. Dashed lines show the concentration-scale gamma=1 reference or ideal Raoult total pressure as named in the model.

Numerical diagram coordinates

liquid mole fraction A	total vapor pressure (kPa)
0	20
0.01	20.4
0.02	20.8
0.03	21.2
0.04	21.6
0.05	22
0.06	22.4
0.07	22.8
0.08	23.2
0.09	23.6
0.1	24
0.11	24.4
0.12	24.8
0.13	25.2
0.14	25.6
0.15	26
0.16	26.4
0.17	26.8
0.18	27.2
0.19	27.6
0.2	28
0.21	28.4
0.22	28.8
0.23	29.2
0.24	29.6
0.25	30
0.26	30.4
0.27	30.8
0.28	31.2
0.29	31.6
0.3	32
0.31	32.4
0.32	32.8
0.33	33.2
0.34	33.6
0.35	34
0.36	34.4
0.37	34.8
0.38	35.2
0.39	35.6
0.4	36
0.41	36.4
0.42	36.8
0.43	37.2
0.44	37.6
0.45	38
0.46	38.4
0.47	38.8
0.48	39.2
0.49	39.6
0.5	40
0.51	40.4
0.52	40.8
0.53	41.2
0.54	41.6
0.55	42
0.56	42.4
0.57	42.8
0.58	43.2
0.59	43.6
0.6	44
0.61	44.4
0.62	44.8
0.63	45.2
0.64	45.6
0.65	46
0.66	46.4
0.67	46.8
0.68	47.2
0.69	47.6
0.7	48
0.71	48.4
0.72	48.8
0.73	49.2
0.74	49.6
0.75	50
0.76	50.4
0.77	50.8
0.78	51.2
0.79	51.6
0.8	52
0.81	52.4
0.82	52.8
0.83	53.2
0.84	53.6
0.85	54
0.86	54.4
0.87	54.8
0.88	55.2
0.89	55.6
0.9	56
0.91	56.4
0.92	56.8
0.93	57.2
0.94	57.6
0.95	58
0.96	58.4
0.97	58.8
0.98	59.2
0.99	59.6
1	60

Dashed reference
liquid mole fraction A	total vapor pressure (kPa)
0	20
0.01	20.4
0.02	20.8
0.03	21.2
0.04	21.6
0.05	22
0.06	22.4
0.07	22.8
0.08	23.2
0.09	23.6
0.1	24
0.11	24.4
0.12	24.8
0.13	25.2
0.14	25.6
0.15	26
0.16	26.4
0.17	26.8
0.18	27.2
0.19	27.6
0.2	28
0.21	28.4
0.22	28.8
0.23	29.2
0.24	29.6
0.25	30
0.26	30.4
0.27	30.8
0.28	31.2
0.29	31.6
0.3	32
0.31	32.4
0.32	32.8
0.33	33.2
0.34	33.6
0.35	34
0.36	34.4
0.37	34.8
0.38	35.2
0.39	35.6
0.4	36
0.41	36.4
0.42	36.8
0.43	37.2
0.44	37.6
0.45	38
0.46	38.4
0.47	38.8
0.48	39.2
0.49	39.6
0.5	40
0.51	40.4
0.52	40.8
0.53	41.2
0.54	41.6
0.55	42
0.56	42.4
0.57	42.8
0.58	43.2
0.59	43.6
0.6	44
0.61	44.4
0.62	44.8
0.63	45.2
0.64	45.6
0.65	46
0.66	46.4
0.67	46.8
0.68	47.2
0.69	47.6
0.7	48
0.71	48.4
0.72	48.8
0.73	49.2
0.74	49.6
0.75	50
0.76	50.4
0.77	50.8
0.78	51.2
0.79	51.6
0.8	52
0.81	52.4
0.82	52.8
0.83	53.2
0.84	53.6
0.85	54
0.86	54.4
0.87	54.8
0.88	55.2
0.89	55.6
0.9	56
0.91	56.4
0.92	56.8
0.93	57.2
0.94	57.6
0.95	58
0.96	58.4
0.97	58.8
0.98	59.2
0.99	59.6
1	60

Calculated evidence under the stated assumptions
Quantity	Value	Unit
A activity coefficient	1	ratio
B activity coefficient	1	ratio
A vapor partial pressure	30	kPa
B vapor partial pressure	10	kPa
Total vapor pressure	40	kPa
Vapor A mole fraction	0.75	fraction
Liquid A mole fraction	0.5	fraction
Vapor minus liquid A fraction	0.25	fraction

Partial pressures determine vapor composition; it is generally different from the liquid composition.

The solid curve is the selected supplied activity model and the dashed line is ideal Raoult behavior. Positive departures do not imply a new chemical species. This symmetric model is a bounded visualization; the pure-pressure ranking alone does not guarantee vapor enrichment for every nonideal composition. No fractionation apparatus or universal boiling diagram is implied.

Retain the species, standard state and ideal/nonideal assumptions with every number. This mathematical packet is not a solution-preparation procedure or evidence of observed laboratory technique.

Partial pressures determine vapor composition; it is generally different from the liquid composition.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Use a liquid composition to predict a vapor composition

For an ideal binary liquid, each partial pressure is its liquid mole fraction times its pure-component vapor pressure at the same temperature. The vapor fractions follow the partial pressures, not the liquid fractions directly. With pA=60 and pB=20 kPa and xA=.50, pA=30,pB=10,total40 and yA=.75.

Explain what separation would require

The vapor is A-enriched in that ideal example because A has the larger pure vapor pressure. Equilibrium vapor enrichment is the basis for a conceptual separation argument, but one equilibrium calculation is not a complete distillation design or proof that repeated separation can reach any purity. No heating or apparatus procedure is requested.

Challenge the ideal assumption with a supplied model

The original bounded illustration uses lnγA=Aparameter xB² and lnγB=Aparameter xA². Multiply each Raoult partial pressure by its own coefficient. At xA=.50 and parameter1, both are exp(.25), so total becomes40exp(.25)≈51.361 kPa while their ratio, and therefore yA=.75, stays unchanged. At asymmetric compositions the coefficients differ.

Keep model and material claims separate

This is the symmetric one-parameter Margules form supplied for comparison, not a fit to named liquids. The parameter range0..1.5 retains the stipulated single-liquid-phase regime. Positive pressure deviation does not identify a unique chemical species or interaction mechanism. Even ranking pure vapor pressures is insufficient to guarantee the same enrichment direction for every nonideal mixture.

Transfer and check

For the ideal model at xA=.25, predict pA=15,pB=15,total30 kPa and yA=.50. Compare that vapor enrichment with the equal-composition case. If an independent total-pressure observation is incompatible with30 kPa, inspect temperature, pure reference pressures, composition and nonideal behavior rather than declaring one cause from a single residual.

Sources and evidence boundary

Conceptual references checked 30 October 2026: Colligative properties, NIST Margules reference. All cases, prose and diagrams are original. Supplied and calculated data are not observed laboratory evidence. No chemical handling, heating, pressurized gas, membrane experiment or clinical application is requested. Retain predictions, contrasting recipes and a changed-case explanation; numerical agreement does not certify independent mastery.

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Public practice checks a specific claim. It does not establish independent mastery.

Can a positive departure from Raoult behavior alone identify a unique microscopic interaction mechanism?

Your explanation and limitations

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Previous: Distinguish analytical concentration from thermodynamic activity Next: Infer dissolved gas from its own partial-pressure constraint

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