A generalized calculation procedure for solving the Thermodynamic Perturbation Theory (TPT1) is found to give reliable numerical estimates of the fraction of non-bonded associating molecules, and their first- and second-order partial derivatives with respect to temperature, density, and mole fractions. This is in contrast to the conventional procedures that rely on specialized equations depending on the number and type of association sites and the number of components in the mixture. This procedure is applicable to SAFT-like equations of state and other models that utilize the TPT1 association term.