On the inapplicability of mixing rules based on the infinite pressure reference state for equations of state which use the hard-sphere repulsive term

The mixing rules for cubic equations of state, Wong-Sandler, Huron-Vidal and modifications have been developed because the residual Helmholtz energy gives a finite limit at infinite pressure for these equations. When the hard-sphere model is used, for the repulsive term of the equation of state, it can be shown that the residual Helmhltz energy goes to infinity at infinite pressure. It is shown that for real fluids the physically true limit is the one obtained from the hard-sphere model. Unfortunately the divergencies do not cancel out in the evaluation of the excess Helmholtz free energy, making these types of mixing rules inapplicable to these equations of state.