The thermodynamics of hydrogen bonding in 1-alcohol + water binary mixtures is studied using molecular dynamic (MD) simulation and the polar and perturbed chain form of the statistical associating fluid theory (polar PC-SAFT). The fraction of free monomers in pure saturated liquid water is computed using both TIP4P/2005 and iAMOEBA simulation water models. Results are compared to spectroscopic data available in the literature as well as to polar PC-SAFT. Polar PC-SAFT models hydrogen bonds using single bondable association sites representing electron donors and electron acceptors. The distribution of hydrogen bonds in pure alcohols is computed using the OPLS-AA force field. Results are compared to Monte Carlo (MC) simulations available in the literature as well as to polar PC-SAFT. The analysis shows that hydrogen bonding in pure alcohols is best predicted using a two-site model within the SAFT framework. On the other hand, molecular simulations show that increasing the concentration of water in the mixture increases the average number of hydrogen bonds formed by an alcohol molecule. As a result, a transition in association scheme occurs at high water concentrations where hydrogen bonding is better captured within the SAFT framework using a three-site alcohol model. The knowledge gained in understanding hydrogen bonding is applied to model vapor-liquid equilibrium (VLE) and liquid-liquid equilibrium (LLE) of mixtures using polar PC-SAFT. Predictions are in good agreement with experimental data, establishing the predictive power of the equation of state.