6.4 Pseudo first order reaction

  Chemical Kinetics

A second order reactions can be converted into a first order reaction if the other reactant is taken in large excess. Such first order reactions are known as pseudo first order reactions.

Let us take an example: $$A + B \to Products\quad \left( {Rate = k\left[ A \right]\left[ B \right]} \right)$$ As it is a second order reaction, we can write the rate of a reaction as $$k = \frac{{2.303}}{{t(a - b)}}\left[ {\ln \frac{{b(a - x)}}{{a(b - x)}}} \right]{\text{ }}$$ If it is given that the reactant $B$ is taken in excess i.e., $b>>>a$, we can write the rate of a reaction as $$k' = \frac{{2.303}}{{t( - b)}}\left[ {\ln \frac{{(a - x)}}{a}} \right]{\text{ = }}\frac{{2.303}}{{bt}}\left[ {\ln \frac{a}{{a - x}}} \right]$$ In the above reaction, the rate constant $k$ is change to $k'$ which is known as the pseudo first order rate constant which is exactly interpreted as first order reaction rate constant.