We present a general framework for the application of a transform technique, probability generating functions (pgf), to mass balances that describe free radical reactions, in particular synthesis or modification of polyolefins. Contributions of specific reactions to the mass balances are identified and transformed separately, so that a modular approach is possible for the construction of the pgf balance equations for different free radical processes. This simplifies the transformation step hopefully making the method useful to more people. Three examples taken from the literature are transformed using this modular method showing its ease of use. In Part 11 of this work, the resulting transforms are inverted to recover the complete molecular weight distribution.