The importance of contributions to real fluid properties by specific interactions has long been recognized. However, it is only recent since such effects have been incorporated into an equation of state. Still the description of some associating systems including organic acids presented difficulties. To explore the solution for such systems, the Veytsman's statistics was extended for dimers and n-mers. Combining the extended statistics with the physical contribution of the present authors' nonrandom lattice fluid model a new Helmholtz's free energy equation was proposed and the resulting equations for pressure and chemical potential were derived. Vapor-liquid equilibria for binary mixtures of organic acids, alcohol, water and alkanes were calculated using the model. The results were found satisfactory for most systems when compared with experimental data.