  Chemical reaction network theory is a powerful framework to describe and
analyze chemical systems. While much about the concentration profile in an
equilibrium state can be determined in terms of the graph structure, the
overall reaction's time evolution depends on the network's kinetic rate
function. In this article, we consider the problem of the effective kinetics of
a chemical reaction network regarded as a conversion system from the feeding
species to products. We define the notion of effective kinetics as a partial
solution of a system of non-autonomous ordinary differential equations
determined from a chemical reaction network. Examples of actual calculations
include the Michaelis-Menten mechanism, for which it is confirmed that our
notion of effective kinetics yields the classical formula. Further, we
introduce the notion of straight-line solutions of non-autonomous ordinary
differential equations to formalize the situation where a well-defined reaction
rate exists and consider its relation with the quasi-stationary state
approximation used in microkinetics. Our considerations here give a unified
framework to formulate the reaction rate of chemical reaction networks.
