Many chemical reactions demonstrate a very similar evolution of reagent concentrations in time, although their species are quite different. This can be linked with a universal stochastic behavior of reagents. In this paper we show what role in understanding chemical kinetics stochastic models play. To support this concept, we consider two interesting cases known in the literature as first- and second-order reactions. The former has a stretched exponential decay in time for its reagent concentration, and the latter evolves hyperbolically. We have established that the behavior can be explained by limit theorems of probability theory. The reaction evolution is directly connected with different behavior motivations in reagent populations. The reason for the universal kinetics is found in the indices of the corresponding probability distribution functions. They are macroscopic parameters measured in chemical experiments. Such an approach allows ones to discover what happens with molecular populations in microscopic dynamics.