(222f) An Estimation Method for the Boyle Temperature

The Boyle temperature, the temperature at which a substance at low pressures behaves like an ideal gas, could be estimated using the Hayden-O’Connell model by finding the zero of the second virial coefficient. However, this model was not designed for estimating the Boyle temperature, but rather to determine the second virial coefficient at far lower temperatures. Furthermore the critical temperature and pressure as well as the dipole moment and the radius of gyration are needed as input parameters, but are not available for all substances.

Analogously to the well-known Guldberg rule that correlates the critical temperature with the normal boiling point, as a rule of thumb the Boyle temperature can be estimated by multiplying the critical temperature with a factor of about 2 to 2.5. However, prediction quality is far lower than it is the case for the Guldberg rule. To overcome this poor prediction a group contribution method was developed, that evaluates the specific factor for every compound. This allows for an improved estimation of the Boyle temperature solely based on the critical temperature and the molecular structure.

A simplified form of the equation used by Joback and Reid for the determination of the critical temperature proved to be suited best. The square term used by Joback and Reid was skipped in our equation, since it is a correction term without physical background and resulted in no improvement of the prediction quality for the Boyle temperature.

Parameter fitting has been done with a training set consisting of 231 compounds and the prediction quality was evaluated using a test set consisting of 49 compounds. The experimental values could be reproduced with an relative error of 4.2 % for the training set and 6.9 % for the test set (the Hayden O’Connell model could only reproduce the experimental data with a relative error of 12 %).