What is vapor pressure? I got this question last week from my Junior labmate. Since I work in vapor pressure term every day, I have to learn it well. Below are my note in vapor pressure.
Vapor pressure (also known as equilibrium vapor pressure), is the pressure of a vapor in equilibrium with its non-vapor phases. All liquids and solids have a tendency to evaporate to a gaseous form, and all gases have a tendency to condense back into their original form (either liquid or solid). At any given temperature, for a particular substance, there is a pressure at which the gas of that substance is in dynamic equilibrium with its liquid or solid forms. This is the vapor pressure of that substance at that temperature. The equilibrium vapor pressure is an indication of a liquid’s evaporation rate. It relates to the tendency of molecules and atoms to escape from a liquid or a solid. A substance with a high vapor pressure at normal temperatures is often referred to as volatile.
Fig. 1 Ilustration of Vapor Pressure
Factors that affect vapor pressure are as follows :
- Types of molecules. If the intermolecular forces between molecules are relatively strong, the vapor pressure will be relatively low. And if weak, the vapor pressure will be relatively high.
- Temperature. At a higher temperature, more molecules have enough energy to escape from the liquid or solid. At a lower temperature, fewer molecules have sufficient energy to escape from the liquid or solid.
Many measurement method have been developed to measure the vapor pressure for many substances. And different equations have been presented to correlate vapor pressure as a function of temperature as well. I have learned to used two of these, the Antoine and Wagner Equation.
Antoine ( 1888 ) proposed an equation which has been widely used over limited temperature ranges :
Where T is in Kelvin and P in bar. Values of A, B, and C are tabulated in some references such as Boublik, et al. (1984) and Poling et al. (2000). The Antoine eq. should never be used outside the stated temperature limits. Extrapolation beyond these limits may lead to absurd results. The constants A, B, and C form a set. Never use one constant from one tabulation and the other constant from a different tabulation.
Wagner (1973, 1977) used an elaborate statistical method to develop an equation for representing the vapor pressure behavior of nitrogen and argon over the entire temperature range for which experimental data were avalaible. The equation is :
Where Pvpr is reduced vapor pressure, Tr is reduced temperature, and τis 1-Tr. However, the following form has come to be preferred (Ambrose, 1986; Ambrose and Ghiasse, 1987):
The constants of Wagner Eq. can be found in Poling et al. (2000) and some references.
Now, let make comparison between calculation result of the above two equation applied to calculate the vapor pressure of methanol at 40o C (313.15 K). All the constants I used here were taken from Appendix A Poling et al. (2000). The literature value (Boublik et al., 1984) is 0.35469 bar
Antoine constants are A = 5.20277, B = 1580.080, and C = 239.500
With Eq. (1) :
Pvp = 0.35443 bar
Wagner constants are Tc = 512.64 K, Pc = 80.92 bar, a = -8.63571, b = 1.1798, c = -2.4790, and d = -1.0240
With eq. (3) :
ln Pvpr = -5.43078
ln Pvp = -1.03732
Pvp = 0.35440 bar
If you ask me which equation I prefer to use when all constants are avalaible and you work at high pressures and high temperatures, my answer is Wagner equation 😀 I prefer this Equation since the range of temperature used is larger (see in Appendix A Poling et. al, 2000). Besides, the Antoine eq. should not be used for temperature outside the range listed. While the Wagner eq. may be extrapolated to higher temperature with confidence, although more complex.
There are still some methods to calculate vapor pressure but I will not write here, i.e Clayperon eq., Extended Antoine eq., Ambrose-Walton Corresponding States Method, and Riedel Corresponding-State Method.
For instance calculation and find the Antoine eq. constants online, you may go to NIST Webbook. I see the value is quite different compare than constans avalaible in Poling et. al (2000).
Got a little bit dizzy? hahaha…try to see the Ms. Excel file I upload here to see how to use the Wagner eq. Well sorry I cancel this file…dunno how to upload the Ms. Excel format to wordpress (*can somebody tell me? LOL).
- Bruce E. Poling, John M. Prausnitz, John P. O’Connel. The Properties of Gases and Liquids. Fifth Ed. McGraw-Hill Higher Education. 2000