If you put a liquid into a closed space, molecules from the surface of that liquid will evaporate until the entire space is filled with vapor. The pressure created by the evaporating liquid is called the vapor pressure. Knowing the vapor pressure at a specific temperature is important because vapor pressure determines a liquid's boiling point and is related to when a flammable gas will burn. If the vapor of a liquid in your location is hazardous to your health, the vapor pressure helps you determine how much of that liquid will become gas in a given amount of time, and therefore whether the air will be dangerous to breathe. The two equations used to estimate vapor pressure of a pure liquid are the Clausius-Clapeyron equation and the Antoine Equation.

## The Clausius-Clapeyron Equation

Measure the temperature of your liquid using a thermometer or thermocouple. In this example we'll look at benzene, a common chemical used to make several plastics. We'll use benzene at a temperature of 40 degrees Celsius, or 313.15 Kelvin.

Find the latent heat of vaporization for your liquid in a data table. This is the amount of energy it takes to go from a liquid to a gas at a specific temperature. The latent heat of vaporization of benzene at this temperature is 35,030 Joules per mole.

Find the Clausius-Clapeyron constant for your liquid in a data table or from separate experiments that measure vapor pressure at different temperatures. This is just an integration constant that comes from doing the calculus used to derive the equation, and it is unique to each liquid. Vapor pressure constants are often referenced to pressure measured in millimeters of Mercury, or mm of Hg. The constant for the vapor pressure of benzene in mm of Hg is 18.69.

Use the Clausius-Clapeyron Equation to calculate the natural log of the vapor pressure. The Clausius-Clapeyron equation says that the natural log of the vapor pressure is equal to -1 multiplied by the heat of vaporization, divided by the Ideal Gas constant, divided by the temperature of the liquid, plus a constant unique to the liquid.) For this example with benzene at 313.15 degrees Kelvin, the natural log of the vapor pressure is -1 multiplied by 35,030, divided by 8.314, divided by 313.15, plus 18.69, which equals 5.235.

Calculate the vapor pressure of benzene at 40 degrees Celsius by evaluating the exponential function at 5.235, which is 187.8 mm of Hg, or 25.03 kilopascals.

## The Antoine Equation

Neither total volume nor other gases in the same space, such as air, have an effect on the amount of evaporation and resulting vapor pressure, so they do not affect the vapor pressure calculation.

Vapor pressure of a mixture is calculated with Raoult's Law, which adds the vapor pressures of the individual components multiplied by their mole fraction.

The Clausius-Clapeyron and Antoine equations only provide estimates of the vapor pressure at a specific temperature. If knowing the exact vapor pressure is required for your application, you must measure it.

Find the Antoine constants for benzene at 40 degrees Celsius in a data table. These constants are also unique to each liquid, and they are calculated by using non-linear regression techniques on the results of many different experiments that measure the vapor pressure at different temperatures. These constants referenced to mm of Hg for benzene are 6.90565, 1211.033 and 220.790.

Use the Antione Equation to calculate the base 10 log of the vapor pressure. The Antoine Equation, using three constants unique to the liquid, says that the base 10 log of the vapor pressure equals the first constant minus the quantity of the second constant divided by the sum of temperature and the third constant. For benzene, this is 6.90565 minus 1211.033 divided by the sum of 40 and 220.790, which equals 2.262.

Calculate the vapor pressure by raising 10 to the power of 2.262, which equals 182.8 mm of Hg, or 24.37 kilopascals.

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#### References

- Transport Processes and Unit Operations; Christie J. Geankoplis
- Elementary Principles of Chemical Processes; Richard M. Felder and Ronald W. Rousseau
- Purdue University, Bodner Research Web: The Clausius-Clapeyron Equation
- Chemical Reviews: The Antoine Equation for Vapor Pressure Data
- Greener Industry: Benzene

#### Photo Credits

- Perry Harmon/iStock/Getty Images