Let's go through each part of the question step by step:
(a) Write a balanced equation for the overall reaction:
To determine the overall reaction, we need to sum the individual steps of the proposed mechanism. Let’s write down the steps again:
1. [tex]\( N_2O_5 \leftrightarrows NO_3 + NO_2 \)[/tex] (fast; equilibrium)
2. [tex]\( NO_3 + NO_2 \rightarrow 2 NO_2 + O \)[/tex] (slow)
3. [tex]\( N_2O_5 + O \rightarrow 2 NO_2 + O_2 \)[/tex] (fast)
Adding these steps together:
- From Step 1: [tex]\( N_2O_5 \rightarrow NO_3 + NO_2 \)[/tex]
- From Step 2: [tex]\( NO_3 + NO_2 \rightarrow 2 NO_2 + O \)[/tex]
- From Step 3: [tex]\( N_2O_5 + O \rightarrow 2 NO_2 + O_2 \)[/tex]
Combining these steps:
[tex]\[ N_2O_5 + N_2O_5 + NO_3 + NO_2 + O \rightarrow NO_3 + NO_2 + 2 NO_2 + O + 2 NO_2 + O_2 \][/tex]
Simplifying, we get:
[tex]\[ 2 N_2O_5 \rightarrow 4 NO_2 + O_2 \][/tex]
Thus, the balanced equation for the overall reaction is:
[tex]\[ 2 N_2O_5 \rightarrow 4 NO_2 + O_2 \][/tex]
(b) Determine the molecularity of the slow reaction.
The slow step (rate-determining step) of the reaction mechanism is:
[tex]\[ NO_3 + NO_2 \rightarrow 2 NO_2 + O \][/tex]
The molecularity of a reaction is determined by the number of reactant molecules involved in this elementary step. Here, there are two reactant molecules involved, [tex]\( NO_3 \)[/tex] and [tex]\( NO_2 \)[/tex].
Therefore, the molecularity of the slow reaction is second order.
(c) Determine the intermediate species.
An intermediate species is one that is formed in one step of the mechanism and consumed in another; it does not appear in the overall balanced equation. From the given mechanism:
The intermediate species:
- [tex]\( NO_3 \)[/tex]: It is produced in step 1 and consumed in step 2.
- [tex]\( O \)[/tex] can also be considered an intermediate since it is produced in step 2 and consumed in step 3.
However, the most prominent intermediate as evident from the mechanism is [tex]\( NO_3 \)[/tex].
Thus, the intermediate species is NO_3.
(d) Write the rate law for the proposed mechanism.
The rate of the reaction is determined by the slowest step, which is the rate-determining step. The rate law is derived from this slow step.
The slow step is:
[tex]\[ NO_3 + NO_2 \rightarrow 2 NO_2 + O \][/tex]
Thus, the rate law is given by the concentration of the reactants in this step:
[tex]\[ \text{Rate} = k[NO_3][NO_2] \][/tex]
So, the rate law for the proposed mechanism is:
[tex]\[ \text{Rate} = k[NO_3][NO_2] \][/tex]
Summary:
- Overall reaction: [tex]\( 2 N_2O_5 \rightarrow 4 NO_2 + O_2 \)[/tex]
- Molecularity of the slow reaction: Second order
- Intermediate species: [tex]\( NO_3 \)[/tex]
- Rate law: [tex]\( \text{Rate} = k[NO_3][NO_2] \)[/tex]
