SCIENCE · INVESTIGATE AND EXPLAIN

Find a boiling condition without extrapolating a fit

Invert a bounded empirical vapor-pressure relation and separate missing support from physical impossibility.

Learning outcome: Convert pressure units, check a fitted interval and interpret a conditional boiling temperature.

Starting recap

A logarithm reverses exponentiation. One bar is 100 kPa. A fitted equation has a declared temperature interval.

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Try

A water correlation ending at 343 K cannot establish the ordinary atmospheric boiling temperature merely because its algebra can be evaluated outside that interval.

Open the experiment

Predict

Predict how decreasing external pressure changes a supported boiling temperature. Decide whether every requested pressure must produce an answer from this fit.

Your prediction and reason

Experiment

For water compare 20 and 100 kPa; for ethanol compare 20, 100 and 5 kPa. Capture one supported and one unsupported case, explaining the plotted intersection or its absence.

Infer a boiling condition only within the fitted range

Reference fitted coefficients · conditional phase-equilibrium calculations · A bulk pure liquid is assumed present. Boiling criterion Psat(T)=external pressure; inverted roots are reported only inside the selected source interval. No mixture, nucleation, hydrostatic or heating-rate model.

Pure substance reference: Water substance External pressure: 20 kPa

Reset keeps your prediction, captures and practice history.

Match external pressure to a supported saturation curve

Water: requested external pressure 20 kPa = 0.2 bar. The selected fit covers 293–343 K and saturation pressures 2.37206–31.08531 kPa.

T = B/[A − log₁₀(P/bar)] − C = 333.28155 K = 60.13155 °C. Substituting it back into the forward equation gives 20 kPa. Display digits describe arithmetic, not new measurement precision.

This activity assumes a bulk pure liquid and uses Pₛₐₜ(T) = external pressure as the boiling criterion. Evaporation can occur below a boiling condition. External total pressure is not automatically the vapor's partial pressure in an air-containing headspace; the closed-inventory lesson has no air. Hydrostatic pressure, nucleation, mixtures and heating dynamics are outside this calculation.

Try 20 kPa for both substances, then 100 kPa for water and 5 kPa for ethanol. Explain the two missing-support results without claiming physical impossibility. These fits are intentionally not stitched together or silently extrapolated.

Empirical fit, units and assumptions

NIST Chemistry WebBook: Water, Gubkov, Fermor et al. (1964), accessed 28 October 2026. NIST calculated these coefficients from the authors' data: A=6.20963, B=2354.731, C=7.559, valid 293–343 K. log₁₀(P/bar)=A−B/(T/K+C). No coefficient uncertainty or covariance is supplied in the selected row. This is a frozen empirical correlation, not a new measurement or a first-principles force simulation.

Supported inversion: 333.2815 K.

The calculated temperature is conditional on the selected empirical correlation and bulk-liquid equilibrium criterion; fit uncertainty is not supplied.

Observation to attach to a capture

Captures retain the selected substance, temperature and inventory or external pressure. Replay reconstructs a conditional calculation from frozen reference coefficients; it is not a new measurement, rate experiment or validated extrapolation.

Understand

A calculation can lack source support

Select water and 20 kPa. Predict what changing external pressure does before reading the intersection. Then try 100 kPa. The absence of a supported answer does not mean water cannot boil at that pressure: this selected water fit ends at 343 K.

For a bulk pure liquid with negligible hydrostatic correction, the equilibrium boiling criterion is Pₛₐₜ(T) = P_external. Lower external pressure gives a lower boiling temperature within a monotone supported interval. This is not a heating-rate or bubble-nucleation simulation.

Convert kPa to bar by dividing by 100. Inverting the displayed Antoine relation gives

T = B/[A − log₁₀(P_bar)] − C.

First calculate the saturation pressures at the published interval endpoints. Only if the requested pressure lies between them does this activity evaluate the inverse. It then substitutes the supported temperature back into the forward equation. The dashed pressure line and curve share fixed axes; the curve stops at its source boundaries.

Compare, refuse and transfer

For ethanol compare 20 with 100 kPa. Both can be checked against its selected interval. Then try 5 kPa and explain why a lower pressure can fall outside support just as a higher pressure can. Save one supported recipe and one refusal, with the evidence needed to extend the analysis.

A calculation outside this interval might happen to be close to a measured value, but closeness is not established by this source contract. Obtain a suitable correlation or measurement rather than treating algebraic extrapolation as validated evidence. Missing coefficient covariance and uncertainty also prevent a supported numerical confidence interval here.

In an air-filled container, total pressure includes air plus vapor partial pressure. Saturation of vapor above a liquid does not require its partial pressure to equal the whole atmosphere. The boiling criterion here compares saturation pressure with external total pressure; the earlier sealed-container activity explicitly excluded air. Do not substitute one pressure for the other.

Water and ethanol are both molecular liquids. Intermolecular attractions matter to their phase behavior, but this comparison does not hold every other molecular property fixed. The selected temperatures are conditional calculations from fitted coefficients, not new laboratory observations.

Sources and continuation

NIST water correlation and temperature ranges.
NIST ethanol correlation and temperature ranges.
Revisit finite vapor inventory to explain why insufficient material cannot reach saturation.
Contrast the existing normal-boiling-point evidence with these pressure-dependent calculations.

Apply

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

Explain why the external total pressure used for boiling differs from a substance’s partial pressure in air. Identify which extra source data would be needed for an unsupported case.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Test when adding substance changes vapor pressure Next: Infer dry gas from water levels and a wet pressure

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