### Pseudo-First order

A very important case is that of pseudo-first order kinetics.  This is when a reaction is 2nd order overall but is first order with respect to two reactants.  This is a very common kinetic scheme.

$\rm{rate = k[A][B]}$

where A and B are some generic reactants.   Now the kinetics of this reaction can be a bit complicated.  The initial rate depends on both A and B and as the reaction proceeds both A and B are changing in concentration and affecting the rate.

When trying to understand this reaction, we can as experimentalists try to set up conditions that simplify things.  The easiest way to do this is to try to eliminate the concentration dependence of one of the reactants.  We can do this by making the initial concentrations of one of the reactants very very high compared to the other.  For example, if we had a reaction

$\rm{CH_3Br + OH^- \rightarrow CH_3OH + Br^-}$

For this reaction the rate law is

$\rm{rate = k[OH^-][CH_3Br]}$

Imagine we had an initial concentration of CH3Br of 100 μM and and an initial concentration of OH- of 10 mM.   Now even if all of the CH3Br has reacted the concentration of OH- will be essentially unchanged.  Therefore during the course of the reaction, the concentration of OH- will be essentially constant.  This makes the reaction "like a first order reaction", thus the name pseudo-first order.

$\rm{rate = k[OH^-][CH_3Br]= k(constant)[CH_3Br] = k'[CH_3Br]}$

Since only concentration of CH3Br would change during the reaction, the rate would only change due to the changes in the CH3Br reaction.  Because the reaction is first order with respect to CH3Br, the kinetics would appear to be first order with a new "pseudo-first order rate constant",  k'.  The value of this rate constant would depend on the value of the overall rate constant, k, and the initial (fixed) concentration of OH-.