I was wondering how to write down the deterministic rate equation for a bimolecular reaction with similar particles.
e.g.
$$ \ce{A ->[k_+] 2B} $$
and
$$ \ce{2B ->[k_-] A} $$
Now the rate equations for the above reactions are:
$$ \mathrm{\frac{\delta A}{\delta t}= - k_{+} A + k_{-} B^2} $$
$$ \mathrm{\frac{\delta B}{\delta t}= 2 k_{+} A - 2 k_{-} B^2} $$
Now I have included a factor of 2 in the second equation to conserve $\mathrm{A + \frac{B}{2}}$.
But I don't understand the reasoning for this factor of 2 in the second equation.