Write general reaction and its differential rate equation and rate law.

$(a)$ General Reaction : $\mathrm{aA}+\mathrm{bB} \rightarrow \mathrm{cC}+\mathrm{dD} \ldots$ $(i)$

Where $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and $\mathrm{d}$ are the stoichiometric coefficients of reactants and products.

$(b)$ Rate expression : Rate $\propto[\mathrm{A}]^{x}[\mathrm{~B}]^{y} \quad \ldots$ $(ii)$

Where, exponents $x$ and $y$ may or may not be equal to the stoichiometric coefficients (a and $(b)$ of the reactants. Above equation $(ii)$ can also be written as:

Rate $=k[\mathrm{~A}]^{x}[\mathrm{~B}]^{y}$

$\therefore-\frac{\mathrm{d}[\mathrm{R}]}{\mathrm{dt}}=k[\mathrm{~A}]^{x}[\mathrm{~B}]^{y}$

Where $k$ is a proportionality constant and is called rate constant. The proportionality constant $k$ of differential rate equation is called rate constant.

$(c)$ Rate law or rate expression : Rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.

$\text { For example : } 2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{2(\mathrm{~g})}$

The differential form of this rate expression is given as Rate $=-\frac{\mathrm{d}[\mathrm{R}]}{\mathrm{dt}}=k\left[\mathrm{NO}_{2}\right]^{2}\left[\mathrm{O}_{2}\right]$

Where, $x=2=$ coefficient of $\mathrm{NO}$

and $\quad y=1=$ coefficient of $\mathrm{O}_{2}$ (Coefficient of $\mathrm{O}_{2}$ is not written but it is accepted)