Generating Function for Free Enthalpy

The condition AG(m)+AG(n) = 4G(m+n) suggests Ci = 0. From the coefiBcient expansion AG 2 ) = C + 2iAG 2)l2 means that a propene will be thermodynamically explained as formed from 1.5 ethene units in some way, which does not need to be specified in more detail. In general the partial pressure of the respective oligomer will be found from the coefficients 

Basically, the free enthalpy of polymerization from ethene up to n-olefin is obtained  

If no side reactions would occur then the partial pressures can be summed up to yield the total pressure ptot which will be under standard conditions po. This procedure may serve as normalization. The plot of the free enthalpy against n should give a straight line. From the slope the equilibrium temperature can be obtained. The total pressure must be known. 

From the distribution of olefins the equilibrium temperature can be equated, the free enthalpy of formation being known and other assumptions, i.e., ideal mixture, ideal gas behavior, independence of standard reaction enthalpy, standard reaction entropy of temperature, etc., being valid. The absolute pressure must be known. This is restrictive to methods of measurement of composition. Note that the application for the Gibbs free enthalpy G requires a free exchange of entropy into and from environment and Ifee exchange of volume work during the process. Thus, 

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