# First Order Chemical Kinetics

I have the following system of reactions: \begin{align} M & \xrightarrow{\lambda(M,W)}M+M \\ W & \xrightarrow{\lambda(M,W)}W+W \\ M & \xrightarrow{\mu} \emptyset \\ W & \xrightarrow{\mu} \emptyset \end{align} Where $$\emptyset$$ encodes no species and $$\lambda(W,M) = \mu+c(N-(W+\delta M))$$ where $$\mu , c , N > 0$$ and $$0 < \delta < 1$$. Both $$\lambda(W,M)$$ and $$\mu$$ are the rates per individual.

I come from a mathematical background and I am trying to apply the Law of Mass action to the above system. I am confused since in the right hand side the $$M$$ and $$W$$ appears twice. What are the rates of of $$M$$ and $$W$$ of the above system?

• As it stands, the system looks quite unchemical. – Ivan Neretin Jan 6 at 18:03
• $\ce{M -> 2M}$ makes no sense chemically. Can you explain the proposed chemistry better? – MaxW Jan 6 at 18:55
• $\ce{M -> \varnothing}$ doesn't make any sense because it is a violation of conservation of matter. It goes to something, even if you don't care what it is. – Zhe Jan 7 at 15:29