Question

What is an instantaneous rate of reaction?

Answer 1

Instantaneous rate of reaction:

• “The instantaneous rate is the rate of a reaction at a period of time that is so short that the concentrations of reactants and products change by a negligible amount.”
• The instantaneous rate of reaction can be expressed as the rate of decrease in a concentration of reactants or the rate of increase in the concentration of products.
• Consider a hypothetical reaction, $\mathrm{R}\to \mathrm{P}$
• $1$ mole of the reactant $\mathrm{R}$ produces $1$ mole of the product $\mathrm{P}$.
• If ${\left[\mathrm{R}\right]}_1$ and ${\left[\mathrm{P}\right]}_1$ are the concentrations at time ${\mathrm{t}}_1$ while ${\left[\mathrm{R}\right]}_2$ and ${\left[\mathrm{P}\right]}_2$ are their concentrations at a time ${\mathrm{t}}_2$ then,

$$\begin{gathered} \mathrm{dt}={\mathrm{t}}_2-{\mathrm{t}}_1 \\ \mathrm{d}\left[\mathrm{R}\right]={\left[\mathrm{R}\right]}_2-{\left[\mathrm{R}\right]}_1 \\ \mathrm{d}\left[\mathrm{P}\right]={\left[\mathrm{P}\right]}_2-{\left[\mathrm{P}\right]}_1 \end{gathered}$$

• The rate can be expressed as:

$$\begin{gathered} {\mathrm{r}}_{\mathrm{inst}}=\frac{-\mathrm{d}\left[\mathrm{R}\right]}{\mathrm{dt}} \\ \mathrm{or} \\ {\mathrm{r}}_{\mathrm{inst}}=\frac{\mathrm{d}\left[\mathrm{P}\right]}{\mathrm{dt}} \end{gathered}$$