The optimal molar ratio of adipic acid to hexamethylenediamine for the synthesis of nylon-6,6 with the highest yield and purity is 1:1. This is because the reaction between adipic acid and hexamethylenediamine is a condensation polymerization reaction, where each monomer reacts with the other in a 1:1 stoichiometric ratio to form the nylon-6,6 polymer. Maintaining this equimolar ratio ensures that both reactants are consumed completely, maximizing the yield and purity of the final product.