Mathematics in Pressbooks: Estimating Vapour Pressure

Vapour pressure([latex]p*[/latex]) is defined as the pressure at which a gas coexists with its solid or liquid phase. Vapour pressure is created by faster molecules that break away from the liquid or solid and enter the gas phase. The vapour pressure of a substance depends on both the substance and its temperature—an increase in temperature increases the vapour pressure. [latex]^{[1]}[/latex]

One empirical method to estimate [latex]p∗[/latex] is the Antoine equation:

[latex]log_{10}(p*)=A-\frac{B}{T+C}[/latex]

where

A, B and C are constants depending on the type of substance

NOTE: Sometimes different sources of data can use different units for temperature, or used [latex]ln[/latex] (base e) instead of [latex]log_{10}[/latex] (base 10).

Consider the calculated result for vapour pressure at 100 °C, compare it with your knowledge of vapour pressure of water. Does it seem accurate?

We know the vapour pressure at 100 °C should be closer to 1 bar as water would boil at 100 °C at 1 atm, this shows the error that might be present in these correlations, especially when taking them outside of their T ranges. As shown below, the value calculated at T=200 °C is more accurate, likely because it is well within the range of temperatures provided for the A, B and C parameters (although there is still some error). Remember these correlations are generalizations, meaning it is rare they are 100% accurate.