# Vapor Pressure

for an informative description of vapor pressure.

Vapor-liquid processes are quite common, so estimating vapor pressure is vital.

Essentially three ways to do so:

• Clapeyron equation
• Antoine equation
• Cox charts

Clapeyron Equation:

$\frac{dp^*}{dT} = \frac{\Delta \hat H_v}{T(\hat V_g - \hat V_l)}$

which may be reduced (by assuming that $\hat V$ is negligible for the liquid phase, $\hat H_v$ (the latent heat of vaporization : the amount of energy needed to make a substance change phase) is temperature independent, and the gas to be ideal)

$\ln{p^*} = -\frac{\Delta \hat H_v}{RT}+B$

where B is a material-specific constant. This equation is useful at low pressures.

Antoine Equation:

$\log_{10}{p^*}=A-\frac{B}{T+C}$

where A, B, and C are material-specific constants. (NOTE: B is different in each equation! and different from the virial coefficient for that matter!) This empirical relation is useful for a wide range of conditions.

##### Outcome:

Estimate the vapor pressure of liquid components.

##### Test Yourself

Prove that the vapor pressure of water at 100C is 1 atm (using both the Clapeyron and Antoine equations).