2
$\begingroup$

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) ?

$\endgroup$
  • 1
    $\begingroup$ Yes. A 3rd order reaction rate=k[A][B][C]. If both [A] and [B] are in large excess then the rate is solely dependent on [C], pseudo 1st order. The same can be said for any order reaction where only all but one species is in large excess ( and order is of 1 for that species) $\endgroup$ – Leeser Feb 17 '15 at 21:07
  • $\begingroup$ @Leeser Ya , but I am asking is there any other situation when this happens ? ( a situation other than "large excess of species ") $\endgroup$ – Rajesh Feb 22 '15 at 3:54
3
$\begingroup$

Example from biochemistry

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.

Example from process control

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.

Another example, somewhat contrived

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 $A$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.