"A complex reaction consists of a number of steps. The overall rate of the reaction depends on the' slowest step" Illustrate the above statement with ąn example and also mention the mechanism.

Sure, here are the step-by-step solutions: **Step 1:** Identify the slowest step in the reaction mechanism. The slowest step in a reaction mechanism is also known as the rate-determining step. It determines the overall rate of the reaction. In this case, the given reaction mechanism is: Therefore, the slowest step in this mechanism is the above step. **Step 2:** Determine the order of the reaction. The rate law of a reaction can be expressed as: $r=k[A{]}^m[B{]}^n$ where r is the rate of the reaction, k is the rate constant, A and B are the reactants, and m and n are the orders of the reaction with respect to A and B, respectively. In this case, since there is only one reactant, we can simplify the rate law to: $r=k[N_2{O}_5{]}^m$ To determine the order of the reaction, we can perform experiments with different initial concentrations of $(N_2{\left(O\right)}_5$ and measure the corresponding rates. If the rate of the reaction changes by a factor of 2 when the concentration of $(N_2{\left(O\right)}_5$ is doubled, then the reaction is first-order with respect to $(N_2{\left(O\right)}_5$. Therefore, we can write: $(r)=(k)[(N_2{O}_5)]$ This indicates that the reaction is first-order with respect to $(N_2{\left(O\right)}_5$. **Step 3:** Write the overall balanced equation for the reaction. The overall balanced equation for the reaction can be written as: {2}{\left({N}\right)}_{{{2}}}{\left({O}\right)}_{{{5}}}\rightarrow{4}{\left({N}{O}\right)}_{{{2}}}+{\left({O}\right)}_{{{2}}}} **Step 4:** Write the rate law for the reaction. As we determined in Step 2, the rate law for the reaction is: $(r)=(k)[(N_2{O}_5)]$ **Step 5:** Combine the slowest step with the overall balanced equation to get the rate law. The slowest step in the reaction mechanism is: {\left({N}\right)}_{{{2}}}{{\left({O}\right)}_{{{5}}}^{{{2}}}}\rightarrow{\left({s}{l}{o}{w}\right)}{\left({N}{O}\right)}_{{{2}}}+{\left({N}{O}\right)}_{{{3}}}}{\left({N}\right)}_{{{2}}}{{\left({O}\right)}_{{{5}}}^{{{2}}}}\rightarrow{\left({s}{l}{o}{w}\right)}{\left({N}{O}\right)}_{{{2}}}+{\left({N}{O}\right)}_{{{3}}}} Using this slowest step and the overall balanced equation, we can write the rate law as: $(r)=(k)[(N_2{O}_5)]$ which matches the rate law we obtained in Step 4. Therefore, the rate law for the given reaction is $(r)=(k)[(N_2{O}_5)]$, and the slowest step in the reaction mechanism is ${\left({N}\right)}_{{{2}}}{{\left({O}\right)}_{{{5}}}^{{{2}}}}\rightarrow{\left({s}{l}{o}{w}\right)}{\left({N}{