Vapor Pressure Calculator: Predicting Evaporation, Boiling, and Phase Equilibrium

In 1827, the French engineer Louis Charles Antoine introduced the empirical equation that bears his name while working on the design of steam engines and distillation columns. Antoine's simple three-parameter formula, log₁₀P = A − B/(T + C), became the standard way to estimate the vapor pressure of liquids for engineering handbooks. Yet the underlying physics had been described a century earlier. In 1783, James Watt's experiments on steam showed that the boiling point of water depends on the pressure above it; at lower atmospheric pressure, water boils at a lower temperature. The concept of vapor pressure is central to chemistry, chemical engineering, meteorology, and materials science. It determines whether a liquid evaporates, whether a reaction mixture will boil, and how volatile organic compounds travel through the atmosphere.

Table of Contents

1. What vapor pressure measures
2. The Clausius-Clapeyron equation
3. The Antoine equation
4. Vapor pressure, boiling point, and atmospheric pressure
5. Raoult's law and ideal solutions
6. Worked examples
7. Limitations and non-ideal behavior
8. Frequently Asked Questions

What vapor pressure measures

Vapor pressure is the pressure exerted by a vapor when it is in dynamic equilibrium with its liquid or solid phase in a closed system. At the molecular level, molecules at the surface of a liquid constantly escape into the gas phase (evaporation) while gas molecules return to the liquid (condensation). Equilibrium is reached when these two rates become equal.

Key points:

• Vapor pressure is a function of temperature only for a pure substance.
• Stronger intermolecular forces produce lower vapor pressures because molecules escape less easily.
• Substances with high vapor pressures at room temperature are called volatile (e.g., diethyl ether, ethanol, acetone).
• Substances with very low vapor pressures are called non-volatile (e.g., ionic salts, glycerol, heavy oils).
• The vapor pressure of a liquid equals the external pressure at its boiling point.

The standard enthalpy of vaporization (ΔH_vap) is the heat required to convert one mole of liquid into vapor at constant pressure. Higher ΔH_vap means stronger liquid-phase attractions and therefore lower vapor pressure at a given temperature.

The Clausius-Clapeyron equation

The Clausius-Clapeyron equation is the thermodynamic foundation for the temperature dependence of vapor pressure. For a liquid-vapor equilibrium, it can be written as:

ln(P₂/P₁) = −(ΔH_vap/R) · (1/T₂ − 1/T₁)

where:

• P₁ and P₂ are vapor pressures at absolute temperatures T₁ and T₂ (in kelvin)
• ΔH_vap is the enthalpy of vaporization (J/mol)
• R is the universal gas constant, 8.314 J/(mol·K)

The integrated form is:

ln(P) = −(ΔH_vap/R) · (1/T) + C

A plot of ln(P) versus 1/T gives a straight line with slope −ΔH_vap/R. This relationship allows chemists to determine ΔH_vap from vapor pressure measurements at two or more temperatures.

The Antoine equation

The Antoine equation is an empirical three-parameter fit to experimental vapor pressure data:

log₁₀(P) = A − B/(T + C)

where P is usually in mmHg or bar, T is temperature in °C, and A, B, and C are substance-specific constants valid over a limited temperature range.

Common Antoine constants for selected liquids (P in mmHg, T in °C):

Engineers use the Antoine equation to design distillation columns, evaporators, and HVAC systems where accurate vapor pressure data are essential.

Vapor pressure, boiling point, and atmospheric pressure

A liquid boils when its vapor pressure equals the external pressure. At sea level, atmospheric pressure is about 101.325 kPa (1 atm), so water boils at 100°C. At higher altitudes where atmospheric pressure is lower, water boils at a lower temperature. In Denver, Colorado, where atmospheric pressure is about 83 kPa, water boils near 94°C. In a pressure cooker, the internal pressure is raised above atmospheric, so water boils above 100°C and food cooks faster.

The normal boiling point is defined as the temperature at which the vapor pressure of a liquid equals 1 atm (101.325 kPa). It is a standard property reported for pure compounds.

Raoult's law and ideal solutions

For an ideal solution of two volatile liquids, the total vapor pressure is the sum of the partial pressures of each component:

P_total = χ_A · P°_A + χ_B · P°_B

where χ is the mole fraction of each component in the liquid and P° is the vapor pressure of the pure component at the same temperature. Raoult's law predicts that adding a non-volatile solute lowers the vapor pressure of the solvent proportionally to its mole fraction. This is the basis of colligative properties such as boiling point elevation and freezing point depression.

Worked examples

Example 1: Boiling point from vapor pressure

Water has a vapor pressure of 101.325 kPa at 100°C. At what temperature does water boil on a mountain where atmospheric pressure is 70 kPa?

Use the Clausius-Clapeyron equation with ΔH_vap = 40,650 J/mol: ln(70/101.325) = −(40,650/8.314) · (1/T₂ − 1/373.15) −0.360 = −4,889 · (1/T₂ − 0.002680) 0.0000737 = 1/T₂ − 0.002680 1/T₂ = 0.002754 T₂ = 363 K = 90°C

Water boils at about 90°C on this mountain.

Example 2: Vapor pressure of water at 25°C

Using the Antoine constants for water (P in mmHg, T in °C): log₁₀(P) = 8.07131 − 1730.63/(25 + 233.426) log₁₀(P) = 8.07131 − 1730.63/258.426 = 8.07131 − 6.697 = 1.374 P = 10^1.374 = 23.7 mmHg = 3.16 kPa

This is the saturation vapor pressure of water at 25°C, a key value in humidity and drying calculations.

Example 3: Raoult's law for an ethanol-water solution

A solution contains 0.80 mol fraction water and 0.20 mol fraction ethanol at 25°C. Pure water vapor pressure = 3.16 kPa; pure ethanol vapor pressure = 7.87 kPa. P_total = 0.80 × 3.16 + 0.20 × 7.87 = 2.53 + 1.57 = 4.10 kPa

The vapor above the solution is richer in ethanol than the liquid because ethanol is more volatile.

Limitations and non-ideal behavior

• Non-ideal mixtures: Raoult's law fails for strongly interacting mixtures (e.g., ethanol-water, acetone-chloroform). Activity coefficients must be used.
• Temperature range: Antoine constants are valid only within their specified range; extrapolation leads to large errors.
• Assumptions: The Clausius-Clapeyron equation assumes ΔH_vap is constant and the vapor behaves ideally. Near the critical point, these assumptions break down.
• Associated liquids: Hydrogen-bonded liquids like water and alcohols deviate from simple predictions because of molecular association in the vapor phase.
• Impurities: Dissolved electrolytes lower vapor pressure more strongly than non-electrolytes at the same mole fraction because of dissociation into multiple ions.