Instant Notes

Antoine Equation

Clausius-Clapeyron equation can be written in empirical form as \[\ln P^{\text{sat}} = A - \frac{B}{T}\] A satisfactory relation given by Antoine is of the form \[\ln P^{\text{sat}} = A - \frac{B}{T+C} \tag*{(Antoine equation)}\] The values of the constants \(A,B\) and \(C\) are readily available for many species.

Trouton’s Rule: Trouton’s rule states that the entropy change of vaporization is almost the same value, about 85–88 J/(mol.K), for most of the liquids at their normal boiling points. Since \(\Delta S=\Delta H/T=\lambda/T\), we can also say, that, according to this rule, molar latent heat of vaporization (\(\lambda\)) at normal boiling point is related to the boiling temperature as \[\lambda \approx 10 RT_b \tag{Trouton's rule}\] where \(T_b\) is normal boiling point in Kelvin. This empirical relationship holds good for many systems. Because of its convenience, the rule is used to estimate the enthalpy of vaporization of liquids whose boiling points are known.

Engineering Rule for Vapor Pressure of Water: The following simple formula, which is easy to remember, gives surprisingly good estimates of the vapor pressure for water for temperatures from 100\(^\circ\)C (the normal boiling point) and up to 374\(^\circ\)C (the critical point): \[P_{\ce{H2O}}^{\text{sat}} [\text{bar}] = \left(\frac{T[^\circ\text{C}]}{100} \right)^4\] This formula is very convenient for engineers dealing with steam at various pressure levels. For example, from the formula we estimate \(P^{\text{sat}}= 2.074\) bar at 120\(^\circ\)C (the correct value is = 1.987 bar) and \(P^{\text{sat}}= 81\) bar at 300\(^\circ\)C (the correct value is = 85.88 bar).