Kinetics of Homogeneous Polycondensations

If a dicarboxylic acid, HOOC—R—COOH, is condensed irreversibly with a glycol, HO—R —OH, then the decrease in concentration of the carboxyl groups depends on the molar concentrations of carboxyl groups, hydroxyl groups, and catalyst K  

Starting with equimolar concentrations of hydroxyl and carboxyl groups, [COOH] = [OH]. The molar concentration of carboxyl groups [COOH] at time t is related to the original molar concentration [COOH]o through the degree of reaction p. With these conditions, equation (17-14), and constant catalyst concentration, equation (17-46) becomes, after integration. 

In polycondensations that have no added catalyst, the carboxyl groups act as catalyst. Equation (17-46) then becomes 

---