Question

What do you mean by the rate-determining step?

Answer 1

Rate-determining step:

• “The overall rate of the reaction is controlled by the slowest step in a multi step reaction called the rate-determining step (RDS).”

Example:

• Consider the decomposition of Hydrogen peroxide $\left({\mathrm{H}}_2{\mathrm{O}}_2\right)$:

$2{\mathrm{H}}_2{\mathrm{O}}_2\left(\mathrm{aq}\right)\underset{\mathrm{Alkaline}\mathrm{medium}}{\overset{{\mathrm{I}}^{-}}{\to }}2{\mathrm{H}}_2\mathrm{O}\mathit{\left(}\mathrm{l}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$

• The reaction takes place in two steps:

$$\begin{gathered} \mathrm{Step}1:{\mathrm{H}}_2{\mathrm{O}}_2\left(\mathrm{aq}\right)+{\mathrm{I}}^{-}\left(\mathrm{aq}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)+{\mathrm{IO}}^{-}\left(\mathrm{aq}\right)\left(\mathrm{slow}\right) \\ \mathrm{Step}2:{\mathrm{H}}_2{\mathrm{O}}_2\left(\mathrm{aq}\right)+{\mathrm{IO}}^{-}\left(\mathrm{aq}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)+{\mathrm{I}}^{-}\left(\mathrm{aq}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\left(\mathrm{fast}\right) \end{gathered}$$

• Thus, the rate-determining step is step 1 as it is the slowest step.
• The rate of the reaction can be depicted as:

$\mathrm{Rate}=\frac{-\mathrm{d}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}{\mathrm{dt}}=\mathrm{k}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\left[{\mathrm{I}}^{-}\right]$

Here, $\frac{-\mathrm{d}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}{\mathrm{dt}}$ is the decrease in the concentration of hydrogen peroxide with time.

Here, k is the rate constant, $\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]$ is the concentration of hydrogen peroxide, and $\left[{\mathrm{I}}^{-}\right]$ is the concentration of iodide ion.

• Here, the rate depends on the concentration of hydrogen peroxide and the concentration of iodide ions.