The rate equation for a reaction mechanism is determined by the slowest step (the rate-determining step).
This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
The rate equation for a reaction mechanism is determined by the slowest step (the rate-determining step).
The given mechanism is:
1. $\text{N}_2\text{O}_5\text{(g)} \to \text{N}_2\text{O}_3\text{(g)} + \text{O}_2\text{(g)}$ (Slow step)
2. $\text{N}_2\text{O}_3\text{(g)} \to \text{NO(g)} + \text{NO}_2\text{(g)}$ (Fast step)
3. $\text{NO(g)} + \text{N}_2\text{O}_5\text{(g)} \to 3\text{NO}_2\text{(g)}$ (Fast step)
The slow step is the first step:
$$ \text{N}_2\text{O}_5\text{(g)} \to \text{N}_2\text{O}_3\text{(g)} + \text{O}_2\text{(g)} $$
For an elementary step, the rate law can be written directly from the stoichiometry of the reactants in that step. In this slow step, one molecule of $\text{N}_2\text{O}_5$ reacts.
Therefore, the rate equation for the reaction is:
$$ \text{Rate} = k[\text{N}_2\text{O}_5] $$
The rate equation for the reaction is $\boxed{\text{Rate} = k[\text{N}_2\text{O}_5]}$.
