Abstract: Thermodynamics of irreversible process offers linear expressions among different physical quantities when there are physical-chemistry changes in the systems close to equilibrium. Extending such existing linear expressions to those systems which are not only far from equilibrium but without dissipative structure formed, a general nonlinear equation is given to express the chemical reaction rate that is the only one in a heterogeneous system. The equation is applied to the catalytic reaction of hydrogen peroxide, i.e., a classical thermodynamic problem, some quartic expressions are obtained in conformity to the experiment data at 298 K and 308 K correspondingly. It shows that the thermodynamics of irreversible process can be applied to those chemical reacting systems which are far from equilibrium if taking the higher terms into consideration. In the higher degree approximation process, however, the different degrees of higher terms require different reactive conditions depending on how far away they are from equilibrium. The extensional application of linear thermodynamic expressions thus provides a new approach to the study on the chemical reactions far from equilibrium.