2.1 Procedure to write the rate of a reaction

  Chemical Kinetics

As we know that in any chemical reaction there is a transformation of Reactant $(R)$ to Products $(P)$ i.e., reactants react to form products. Let us assume the reaction be $$R \to P$$

As per standard convention, we define the rate of a reaction by writing the rate of individual reactants and products and then equating them. It should be remembered that rate of reaction is written with negative sign for reactants as the concentration of reactants is decreasing where as with positive sign for products as the concentration of products is increasing in a reaction.

$\therefore$ Rate of reaction of Reactant $R$ is $ - \frac{{d\left[ R \right]}}{{dt}}$

where ${\left[ R \right]}$ represents the concentration of reactant $R$.

$\therefore$ Rate of reaction of Product $P$ is $ - \frac{{d\left[ P \right]}}{{dt}}$

where ${\left[ P \right]}$ represents the concentration of product $P$.

Note: In the above reaction, the stoichiometric coefficient is $1$ in both the reactant and product side. Let us assume a more generalized form of any chemical reaction i.e., $$aA + bB \to cC + dD$$

$\therefore$ Rate of a reaction can be written as $$ - \frac{1}{a}\frac{{d\left[ A \right]}}{{dt}} = - \frac{1}{b}\frac{{d\left[ B \right]}}{{dt}} = \frac{1}{c}\frac{{d\left[ C \right]}}{{dt}} = \frac{1}{d}\frac{{d\left[ D \right]}}{{dt}}$$

$\therefore$ It should always be remembered that rate of any reaction is dependent on concentration as well as stoichiometric coefficients of reactants and products.