Vapor Pressure – Definition and How to Calculate It

Vapor pressure (or vapour pressure) is the equilibrium pressure of a vapor above its liquid or solid state in a closed container. In this type of closed system, some molecules of a liquid or solid have enough kinetic energy to escape at the surface and enter the vapor (gas) phase. Meanwhile, some vapor molecules collide with the liquid or solid surface and change their phase. The kinetic energy of vapor molecules causes them to hit the walls and lid of a container, producing vapor pressure.

The point where the number of molecules escaping the liquid (or solid) equals the number of molecules returning from the vapor phase back to liquid (or solid) is the saturated vapor pressure. In a closed container, the evaporation rate and condensation rate are equal at saturated vapor pressure. In an open container, vapor pressure rises as temperature increases until the temperature reaches the boiling point. Saturated vapor pressure occurs at the boiling point temperature, which in turn depends on atmospheric pressure. So, at 1 atm of pressure, the saturated vapor pressure of water occurs at 100 ^°C (212 ^°F). In other words, vapor pressure equals atmospheric pressure at a liquid’s boiling point.

A substance with a high vapor pressure is said to be volatile. Examples of volatile substances include gasoline and rubbing alcohol (liquids) and paradichlorobenzene (solid). In an open container, molecules of a liquid that escape as vapor do not strike a container and reach an equilibrium pressure. Instead, vapor molecules evaporate. A nonvolatile liquid has a vapor pressure lower than that of water and only slowly evaporates. A volatile liquid has a high vapor pressure and quickly evaporates.

Factors That Affect Vapor Pressure

The most important factors affecting vapor pressure are temperature and type of molecules:

• Temperature: Temperature has the greatest effect on vapor pressure. As temperature increases, vapor pressure increases. As temperature decreases, vapor pressure decreases. This makes sense, as imparting thermal energy gives molecules more kinetic energy. The graph of the relationship between vapor pressure and temperature is curve. However, the graph of natural logarithm of vapor pressure versus temperature is a straight line.
• Intermolecular forces: The forces between molecules and thus the chemical composition of a substance affect its vapor pressure. For example, water contains strong hydrogen bonds, so it has a lower vapor pressure than gasoline, which has weaker intermolecular forces acting between its molecules.

There are also factors that do not affect vapor pressure:

• Quantity of liquid or solid: The amount of matter does not affect a substance’s vapor pressure. For example, the vapor pressure of a droplet of water is the same as the vapor pressure of a pool of water.
• Surface area: The surface area does not affect vapor pressure. However, evaporation occurs much faster with a large surface area than a small one. For example, water in a glass takes longer to evaporate than the same volume of water spilled onto a counter.

Vapor Pressure of Water

The vapor pressure of water depends on its temperature. The vapor pressure of water at room temperature (25 ^°C) is 23.8 mm Hg, 0.0313 atm, or 23.8 torr, or 3.17 kPa. At its freezing point (0 ^°C), the vapor pressure of water is 4.6 torr. At its boiling point (100 ^°C), the vapor pressure of water is 658.0 torr (atmospheric pressure).

Table of Vapor Pressure Values

This table lists vapor pressure values for liquids near room temperature (20-25 ^°C or 68-77 ^°F):

How to Calculate Vapor Pressure

There are several vapor pressure formulas, but two common ones are Raoult’s law and the Clausius-Clapeyron equation.

Calculate Vapor Pressure Using Raoult’s Law

Raoult’s law relates the vapor pressure of a solution (P_solution) to the vapor pressure of the solvent (P_solvent) and mole fraction of the solvent (X_solvent):

P_solution = P_solventX_solvent

For example, find the vapor pressure of a solution of simple syrup consisting of 1 liter water an 1 liter sucrose.

First, find the mole fraction of the solvent. In this case, the solvent is water.

• Mass of 1 liter of water: 1000 grams
• Mass of 1 liter of sucrose: 1056.7 g
• Moles (water): 1000 grams × 1 mol/18.015 g = 55.51 moles
• Moles (sucrose): 1056.7 grams × 1 mol/342.2965 g = 3.08 moles (using the molar mass of sucrose from its chemical formula, C₁₂H₂₂O₁₁.)
• Total moles: 55.51 + 3.08 = 58.59 moles
• Mole fraction of water: 55.51/58.59 = 0.947

Next, find the solvent vapor pressure. The easiest way to do this is to look up the value on a table. The vapor pressure of water at 25 ^°C is 23.8 mm Hg.

Next, plug the values into Raoult’s law:

• P_solution = P_solventX_solvent
• P_solution = (23.8 mm Hg)(0.947)
• P_solution = 22.54 mm Hg

Calculate Vapor Pressure Using the Clausius-Clapeyron Equation

The Clausius-Clapeyron equation relates the rise in vapor pressure with increasing temperature. The natural logarithm (ln) changes the nonlinear relationship between vapor pressure and temperature into a linear relationship.

ln P = -(ΔH_vap/R)(1/T) + C

• lnP is the natural logarithm of the vapor pressure
• ΔH_vap is the enthalpy of vaporization
• R is the ideal or universal gas constant [8.314 J/(mol•K)]
• T is the absolute temperature (Kelvin)
• C is the y-intercept, which is constant for a given line

If you measure the vapor pressures and temperatures of two points, you can find the enthalpy of vaporization. Similarly, if you know the enthalpy of vaporization and the vapor pressure at one temperature, you can find the vapor pressure at another temperature.

ln(P₁/P₂) = -(ΔH_vap/R)(1/T₁ – 1/T₂)

Usually, this sort of problem involves graphing the natural log of pressure versus temperature and then looking up the desired value on the resulting chart. The slope of the line (C) is ΔH_vap. Or, you consult a reference that gives you ΔH_vap and vapor pressure at some temperature.

References

• Perry, R.H.; Green, D.W., eds. (1997). Perry’s Chemical Engineers’ Handbook (7th ed.). McGraw-Hill. ISBN 978-0-07-049841-9.
• Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey (2002). General Chemistry (8th ed.). Prentice Hall. ISBN 978-0-13-014329-7.
• Sinnot, R.K. (2005). Chemical Engineering Design (4th ed.). Butterworth-Heinemann. ISBN 978-0-7506-6538-4.
• Wagner, W. (1973). “New vapour pressure measurements for argon and nitrogen and a new method for establishing rational vapour pressure equations”. Cryogenics. 13 (8): 470–482. doi:10.1016/0011-2275(73)90003-9