By giving three examples,explain whether the exponents of the concentration terms in a rate law are the same as their stoichiometric coefficients in the balanced chemical reaction.

(N/A) The rate law of a reaction is determined experimentally and does not necessarily correspond to the stoichiometric coefficients of the balanced chemical equation.
$1$. Reaction: $2 NO_{(g)} + O_{2(g)} \rightarrow 2 NO_{2(g)}$
Rate $= k[NO]^2[O_2]^1$. Here,the exponents $(2, 1)$ match the stoichiometric coefficients $(2, 1)$.
$2$. Reaction: $CHCl_{3(g)} + Cl_{2(g)} \rightarrow CCl_{4(g)} + HCl_{(g)}$
Rate $= k[CHCl_3]^1[Cl_2]^{1/2}$. Here,the exponent of $[Cl_2]$ is $1/2$,while its stoichiometric coefficient is $1$. Thus,they do not match.
$3$. Reaction: $CH_3COOC_2H_{5(l)} + H_2O_{(l)} \rightarrow CH_3COOH_{(aq)} + C_2H_5OH_{(aq)}$
Rate $= k[CH_3COOC_2H_5]^1[H_2O]^0$. Here,the exponent of $[H_2O]$ is $0$,while its stoichiometric coefficient is $1$. Thus,they do not match.
Conclusion: The exponents in the rate law are determined by experimental observation and are not always equal to the stoichiometric coefficients of the balanced chemical equation.