The kinetics and dynamics for the growth of hydrogen bonding clusters in the Aa-Dd system are considered. The explicit relations between conversions of proton-acceptors and proton-donors and Gibbs free energy are deduced,and then the sol-gel phase transition is predicted to take place and the generalized scaling laws satisfied by the k-th moment and k-th radius near the critical point are given. The conclusions obtained from which are consistent with the statistical descriptions on the system under investigation.