We consider the chemical reaction of type \(\text{A }{\mathop{\longrightarrow}\limits_{}^{k_1}} \text{ B}\) which followed by the reaction \(\text{B}+\text{C }{\mathop{\longrightarrow}\limits_{}^{k_2}} \text{ D}\) with rate constants \(k_1\) and \(k_2\). When we assume that both reactions are elementary, then according to the law of mass action we can write down the following system of differential equations for the concentrations of A, B, C, and D: \[ \left\{\begin{aligned} \frac{\dd[\text{A}]}{\dd t} &= -k_1[\text{A}] \\ \\ \frac{\dd[\text{B}]}{\dd t} &=k_1 [\text{A}]-k_2[\text{B}][\text{C}]\\ \\ \frac{\dd[\text{C}]}{\dd t} &=-k_2[\text{B}][\text{C}] \\ \\ \frac{\dd[\text{D}]}{\dd t} &= k_2 [\text{B}][\text{C}]\end{aligned} \right.\]

We consider the chemical reaction of type \(\text{A }{\mathop{\longrightarrow}\limits_{}^{k_1}} \text{ B}\) which is followed by the reaction \(2\,\text{B }{\mathop{\longrightarrow}\limits_{}^{k_2}} \text{ C}\) with rate constants \(k_1\) and \(k_2\). When we assume that both reactions are elementary, we can wrtie down the following system of differential equations for the concentrations of A, B, and C: \[ \left\{\begin{aligned} \frac{\dd[\text{A}]}{\dd t} &= -k_1[\text{A}] \\ \\ \frac{\dd[\text{B}]}{\dd t} &=k_1 [\text{A}]-2k_2[\text{B}]^2\\ \\ \frac{\dd[\text{C}]}{\dd t} &= k_2 [\text{B}]^2\end{aligned} \right.\]