Explicit solution of the reversible isomerization followed by zeroth-order kinetics

An explicit solution to the kinetics problem consisting of a reversible isomerization followed by a zeroth-order process is presented. Exact expressions for the area under the curve and the peak, termination and crossing times were also derived and found to involve the Lambert W function. We discuss in detail the passage to the irreversible limit and test it on the first stages of alcohol elimination in humans. The solution of the generalized problem where both A and B species can undergo a zeroth-order irreversible transformation is presented. The exact solution for the consecutive problem that starts with a zeroth-order kinetics and is followed by a reversible isomerization is also obtained. We comment on the situations where the obtained solutions could be helpful.