Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. It only takes a minute to sign up.
Sign up to join this community
The pseudo 1st order reaction happens when one of the reactant is in large excess and its concentration doesnt change during the reaction .
Is there any other such situation when a certain higher order reaction turns out to become a pseudo first order kinetic reaction (except the situation where an N$^{th}$ order reaction has N-1 species in large excess) ?
The Michaelis-Menten equation for enzyme kinetics is an example.
$v=\frac{k_{cat}E_0S}{K_S+S}$ where $S$ is substrate concentration and $E$ in enzyme concentration.
At low $S$ ($S\ll K_S$), the reaction is 2nd order with $v=\frac{k_{cat}}{K_S}E_0S$, i.e. first order in both enzyme and in substrate. However at high $S$ ($S\gg K_S$), the reaction is first order only in enzyme with $v=k_{cat}E_0$, and is zero-order in substrate. The substrate concentration doesn't have to be in molar excess to other reactants.
In chemical engineering, nonlinear systems such as higher-order reactions occuring in a continuous process at steady-state are often modeled using linear (which you can think of as first-order reactions) systems as an approximation for developing process control techniques. A MATLAB documentation page has some good information.
As a last example, consider an unstable molecule $A$. It can decompose to $B$ by two entirely separate elementary mechanisms. The first is $\ce{A + A -> B + B}$. The second is $\ce{A -> B}$. At high concentrations of $A$, the second-order kinetics will dominate and the decomposition of $A$ will be second order. But lower the concentration enough, and the reaction will become first order in $A$ because the rate the bimolecular reaction will be dwarfed by the unimolecular route at low $A$.
