To determine the average rate of the reaction:
[tex]\[ 2 \text{NO} (g) + \text{O}_2 (g) \longrightarrow 2 \text{NO}_2 (g) \][/tex]
given the concentration data, we proceed as follows:
1. Identify the initial and final concentrations and times:
- Initial concentration of NO: [tex]\([NO]_{\text{initial}} = 0.0300 \, M\)[/tex] at [tex]\( t_{\text{initial}} = 5.0 \, \text{s}\)[/tex]
- Final concentration of NO: [tex]\([NO]_{\text{final}} = 0.0225 \, M\)[/tex] at [tex]\( t_{\text{final}} = 650.0 \, \text{s}\)[/tex]
2. Calculate the change in concentration of NO ([tex]\(\Delta [NO]\)[/tex]):
[tex]\[ \Delta [NO] = [NO]_{\text{initial}} - [NO]_{\text{final}} \][/tex]
[tex]\[ \Delta [NO] = 0.0300 \, M - 0.0225 \, M \][/tex]
[tex]\[ \Delta [NO] = 0.0075 \, M \][/tex]
3. Calculate the change in time ([tex]\(\Delta t\)[/tex]):
[tex]\[ \Delta t = t_{\text{final}} - t_{\text{initial}} \][/tex]
[tex]\[ \Delta t = 650.0 \, \text{s} - 5.0 \, \text{s} \][/tex]
[tex]\[ \Delta t = 645.0 \, \text{s} \][/tex]
4. Determine the average rate of reaction:
The average rate of the reaction is given by the change in concentration per unit time. For the reaction involving NO, we use the rate of decrease of [tex]\([NO]\)[/tex].
[tex]\[ \text{Average rate} = \frac{\Delta [NO]}{\Delta t} \][/tex]
[tex]\[ \text{Average rate} = \frac{0.0075 \, M}{645.0 \, s} \][/tex]
[tex]\[ \text{Average rate} = 1.1627906976744185 \times 10^{-5} \, \text{M/s} \][/tex]
Therefore, the average rate of the reaction during this time period is [tex]\(1.1627906976744185 \times 10^{-5} \, \text{M/s}\)[/tex].
