Vapor Pressure Calculator — Clausius–Clapeyron Equation and Raoult's Law

What is Vapor Pressure?

Vapor pressure is the pressure exerted by the vapor molecules of a substance in a closed system at thermodynamic equilibrium — meaning the molecules are both vaporizing and condensing at the same rate at a particular pressure and temperature.

Vapor pressure is directly related to the kinetic energy of a molecule. Light molecules, those with high kinetic energy, or those with weak intermolecular forces, have higher vapor pressures and therefore a higher volatility — the tendency to vaporize. For example, acetone evaporates much faster than water at room temperature, because its vapor pressure is nearly 10 times higher.

The Clausius–Clapeyron Equation

The Clausius–Clapeyron equation describes the relationship between vapor pressure and temperature of a liquid. It is accurate for the phase transition between liquid and gas (vaporization) or solid and gas (sublimation).

The equation in its integrated form used by this calculator is:

P₂ = P₁ × exp(−ΔH / R × (1/T₂ − 1/T₁))

Where:

• P₂ — Vapor pressure at the target temperature T₂ (the result)
• P₁ — Known vapor pressure at the reference temperature T₁
• ΔH — Enthalpy (molar heat) of vaporization in J/mol
• R — Universal gas constant: 8.314 J/(mol·K)
• T₁, T₂ — Temperatures in Kelvin

This formula assumes that ΔH remains constant across the temperature range, which is a reasonable approximation for moderate temperature differences. For wide temperature ranges, the actual ΔH varies and the result will be approximate.

What is the Enthalpy of Vaporization?

The enthalpy of vaporization (ΔH_vap), also called the latent heat of vaporization, is the amount of thermal energy that must be absorbed per mole of a substance to convert it from liquid to gas at constant pressure. It reflects the strength of intermolecular forces:

• Water: 40,650 J/mol — high due to strong hydrogen bonds
• Ethanol: 38,560 J/mol — moderate hydrogen bonding
• Methanol: 35,270 J/mol
• Benzene: 30,720 J/mol — weaker, only van der Waals forces
• Acetone: 29,100 J/mol
• Diethyl ether: 26,520 J/mol — highly volatile

Clausius–Clapeyron Equation — an Example

Question: What is the vapor pressure of water at 50°C (323.15 K), given that its boiling point is 100°C (373.15 K) at 101,325 Pa, and ΔH_vap = 40,650 J/mol?

Using the equation:

P₂ = 101,325 × exp(−40,650 / 8.314 × (1/323.15 − 1/373.15))
P₂ = 101,325 × exp(−4,888 × 0.000415)
P₂ = 101,325 × exp(−2.028)
P₂ ≈ 101,325 × 0.1315 ≈ 13,327 Pa ≈ 13.3 kPa

The accepted value at 50°C is about 12.3 kPa. The small difference arises because ΔH varies slightly with temperature — the Clausius–Clapeyron equation is an approximation.

How to Calculate Vapor Pressure — Raoult's Law

For solutions and mixtures, Raoult's law relates the vapor pressure of an ideal solution to the mole fractions and pure vapor pressures of its components:

P_A = x_A × P°_A

Where:

• P_A — Partial vapor pressure of component A above the solution
• x_A — Mole fraction of A in the liquid phase (0 to 1)
• P°_A — Vapor pressure of pure component A at the same temperature

For a binary mixture (A + B), the total vapor pressure is:

P_total = x_A × P°_A + x_B × P°_B

Note that x_B = 1 − x_A. Raoult's law is exact for ideal solutions and provides a good approximation for mixtures of chemically similar substances.

Raoult's Law — an Example

Question: A binary mixture contains 40 mol% ethanol (x_A = 0.40) in water (x_B = 0.60) at 25°C. The pure vapor pressures are: P°_ethanol = 7.869 kPa, P°_water = 3.169 kPa. What is the total vapor pressure?

P_ethanol = 0.40 × 7.869 = 3.148 kPa
P_water = 0.60 × 3.169 = 1.901 kPa
P_total = 3.148 + 1.901 = 5.049 kPa

Frequently Asked Questions

Does vapor pressure depend on temperature?

Yes. Vapor pressure increases exponentially with temperature (described by the Clausius–Clapeyron equation). At higher temperatures, more molecules have enough energy to escape into the gas phase.

What is the vapor pressure of water at 25°C?

Approximately 3.169 kPa (23.77 mmHg or 0.0313 atm). This is the reference value used in many calculations.

At what vapor pressure does a liquid boil?

A liquid boils when its vapor pressure equals the external (atmospheric) pressure. At sea level (101.325 kPa), water boils at 100°C. At altitude, where atmospheric pressure is lower, water boils below 100°C.

What is the difference between vapor pressure and boiling point?

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. The boiling point is the temperature at which the vapor pressure equals external pressure. Both describe the same physical property from different perspectives.

What are the units of vapor pressure?

Common units include Pascal (Pa), kilopascal (kPa), millimeters of mercury (mmHg or Torr), atmosphere (atm), and in American engineering: pounds per square inch (psi) and inches of mercury (inHg). This calculator outputs results in all of these units simultaneously.

When does Raoult's law fail?

Raoult's law applies only to ideal solutions — mixtures where intermolecular forces between unlike molecules are similar to those between like molecules. Real solutions (e.g., ethanol–water) deviate from ideality: positive deviations occur when unlike-molecule interactions are weaker than like-molecule ones (actual P > Raoult's P), and negative deviations when they are stronger.