Calculate Vapor Pressure From Enthalpy And Entropy

Estimate equilibrium vapor pressure using thermodynamic inputs with instant visualization.

How to Calculate Vapor Pressure from Enthalpy and Entropy: A Practical Expert Guide

Vapor pressure is one of the most important thermodynamic properties in chemical engineering, environmental modeling, process safety, atmospheric science, and pharmaceutical formulation. In practice, people often know or can estimate a compound’s enthalpy of vaporization and entropy of vaporization, then need to convert those values into an equilibrium vapor pressure at a target temperature. This is exactly where the relationship between Gibbs free energy, equilibrium constants, and phase change thermodynamics becomes useful.

The core idea is simple: at phase equilibrium, the chemical potential of the liquid and vapor phases are equal. If you model vaporization as an equilibrium process and assume that enthalpy and entropy changes do not vary strongly over the selected temperature range, you can estimate vapor pressure with an exponential expression. Even though this is an approximation, it is often highly informative and physically meaningful, especially when you need fast engineering estimates before moving to more sophisticated equations of state or multi-parameter correlations.

1) The Governing Equation

Start with the standard thermodynamic relationship:

ΔG° = ΔH° – TΔS°

For an equilibrium process, the standard Gibbs free energy also relates to the equilibrium constant:

ΔG° = -RT ln(K)

For vaporization, if we define K = P/P° (ideal vapor assumption), we obtain:

ln(P/P°) = (ΔS°/R) – (ΔH°/(RT))

Therefore:

P = P° × exp[(ΔS°/R) – (ΔH°/(RT))]

where R = 8.314462618 J/mol·K, T is absolute temperature in K, ΔH is in J/mol, ΔS is in J/mol·K, and P° is your reference pressure standard state.

2) Why Unit Discipline Matters

• Convert ΔH to J/mol before calculation.
• Convert ΔS to J/mol·K before calculation.
• Convert temperature to Kelvin.
• Keep your pressure units consistent with the selected reference pressure P°.

A common source of large error is mixing kJ/mol with J/mol or using Celsius directly in the exponential term. Since the formula includes ΔH/(RT), even small unit mistakes can change calculated pressure by orders of magnitude.

3) Interpreting the Physics

The equation has two competing terms: entropy contribution (ΔS/R) and enthalpy penalty (ΔH/RT). At low temperatures, the enthalpy term dominates and vapor pressure is low. As temperature rises, ΔH/(RT) decreases, the exponent becomes less negative, and vapor pressure increases rapidly. This is why volatility can change dramatically with modest temperature increases.

In process design, this exponential sensitivity controls evaporation rates, flash behavior, distillation profiles, storage emissions, and inhalation risk predictions. In environmental systems, it influences atmospheric partitioning and transport behavior for volatile compounds.

4) Typical Reference Data and Trends

The table below lists representative thermodynamic values near normal boiling points for selected liquids. Values are commonly reported in thermodynamic compilations such as NIST. The entropy of vaporization shown here is estimated as ΔSvap ≈ ΔHvap/Tb, which illustrates Trouton-type behavior for many non-associating liquids.

Compound	Normal Boiling Point Tb (K)	ΔHvap at Tb (kJ/mol)	Estimated ΔSvap (J/mol·K)	Interpretation
Water	373.15	40.65	108.9	Higher entropy change due to strong liquid-phase hydrogen bonding
Ethanol	351.52	38.56	109.7	Polar, hydrogen bonding, strong intermolecular effects
Benzene	353.25	30.72	86.9	Closer to Trouton-type behavior for non-associating liquids
Acetone	329.45	29.10	88.3	Moderate polarity with comparatively lower vaporization enthalpy
n-Hexane	341.88	28.85	84.4	Typical hydrocarbon volatility behavior

5) Real Vapor Pressure Statistics Example: Water

For many users, water is a useful benchmark because high-quality reference values are easy to obtain and familiar. The values below show the rapid increase of saturation vapor pressure with temperature. This non-linear rise is exactly what the exponential model captures.

Temperature (°C)	Saturation Vapor Pressure (kPa)	Saturation Vapor Pressure (mmHg)	Approximate Multiplication vs 25°C
25	3.17	23.8	1.0×
40	7.38	55.4	2.3×
60	19.9	149.4	6.3×
80	47.4	355.5	15.0×
100	101.3	760.0	32.0×

6) Step-by-Step Workflow for Engineers and Scientists

1. Select or estimate ΔH and ΔS for the vaporization process and confirm the state assumptions.
2. Convert ΔH to J/mol and ΔS to J/mol·K.
3. Convert operating temperature to Kelvin.
4. Choose a reference pressure standard P° (often 1 bar or 1 atm).
5. Compute ln(P/P°) = (ΔS/R) – (ΔH/RT).
6. Exponentiate to recover P, then convert to desired units (kPa, bar, atm, mmHg).
7. Validate against trusted data if available, especially near critical process limits.

7) Model Limitations You Should Not Ignore

• ΔH and ΔS can vary with temperature; assuming constants introduces error across wide ranges.
• Ideal vapor behavior may fail at high pressures.
• Mixtures require activity coefficients or fugacity approaches, not pure-component formula alone.
• Near the critical region, simple exponential forms lose reliability.
• Reference-state definitions must match your source data.

For narrow ranges, the constant-parameter model is often very practical. For high-accuracy work over broad temperature spans, use Antoine, Wagner, DIPPR-style correlations, or EOS-based flash methods with fitted parameters and validated property packages.

8) When to Prefer This Method

This enthalpy-entropy method is excellent for rapid calculations, educational demonstrations, early-stage design estimates, and sensitivity analysis. It is especially useful when you have thermodynamic state-function estimates but lack detailed vapor pressure coefficients. Because the equation is physically interpretable, it also provides better intuition than purely empirical fits.

It is less suitable when your objective is regulatory-grade prediction accuracy over very broad conditions, or when complex molecular interactions dominate the system. In those cases, this calculator should be treated as a high-quality screening tool, followed by a validated property model.

9) Authoritative Data and Learning References

• NIST Chemistry WebBook (.gov) for thermophysical and vapor pressure data.
• Physical chemistry educational explanation from university-hosted materials (.edu mirror availability varies).
• Penn State meteorology notes on vapor pressure concepts (.edu).

10) Practical Takeaway

If you remember one thing, remember this: vapor pressure grows exponentially with temperature because the free-energy balance between liquid and vapor shifts rapidly as thermal energy increases. By combining enthalpy and entropy terms in the Gibbs-equilibrium expression, you can produce technically meaningful vapor pressure estimates with minimal input data. Use careful units, validate against trusted references, and apply the method in the temperature window where your assumptions are valid.