Direct Substitution into the Kinetic Equations

From the definition of the averages of the degree of polymerization it is obvious that in certain cases it is possible to calculate some of them by making use of the kinetic laws directly. There is no need to have the generating function solved as such for equilibrium. 

For example, the second subsidiary equation given already in Eq. (17.8) 

But by changing from s to exp(x) and rewriting the differential, the following elegant relation follows  

The equilibrium constant is A = kp/kdCn o and p is the conversion. Here we have made use of the fact that in equilibrium the rate of formation equals the rate of hydrolysis Vp = kpC = Vd = kpCH20CE- 

As a further example, consider the hydrolysis of a polyester. The loss of ester groups with time is assumed as 

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