To find the average rate of reaction over the entire course of the reaction, we need to determine the change in concentration and the change in time. Let's analyze the given data step by step.
### Step 1: Determine Initial and Final Concentrations and Times
From the table, we observe the following:
- Initial time ([tex]\(t_{\text{initial}}\)[/tex]) = [tex]\(0\)[/tex] seconds
- Initial concentration ([tex]\([A]_{\text{initial}}\)[/tex]) = [tex]\(1.8\)[/tex] M
- Final time ([tex]\(t_{\text{final}}\)[/tex]) = [tex]\(720\)[/tex] seconds
- Final concentration ([tex]\([A]_{\text{final}}\)[/tex]) = [tex]\(0.4\)[/tex] M
### Step 2: Calculate the Change in Concentration and Time
The change in concentration ([tex]\(\Delta [A]\)[/tex]) can be calculated as:
[tex]\[
\Delta [A] = [A]_{\text{final}} - [A]_{\text{initial}}
\][/tex]
Substituting the given values:
[tex]\[
\Delta [A] = 0.4 \, \text{M} - 1.8 \, \text{M} = -1.4 \, \text{M}
\][/tex]
The change in time ([tex]\(\Delta t\)[/tex]) is:
[tex]\[
\Delta t = t_{\text{final}} - t_{\text{initial}}
\][/tex]
Substituting the given values:
[tex]\[
\Delta t = 720 \, \text{s} - 0 \, \text{s} = 720 \, \text{s}
\][/tex]
### Step 3: Calculate the Average Rate of Reaction
The average rate of reaction ([tex]\(\text{rate}_{\text{avg}}\)[/tex]) is given by:
[tex]\[
\text{rate}_{\text{avg}} = \frac{\Delta [A]}{\Delta t}
\][/tex]
Substituting the calculated values:
[tex]\[
\text{rate}_{\text{avg}} = \frac{-1.4 \, \text{M}}{720 \, \text{s}} = -0.0019444444444444444 \, \text{M/s}
\][/tex]
### Step 4: Convert the Average Rate to Scientific Notation and Compare with Options
We need to convert the rate to proper scientific notation, focusing on the magnitude:
[tex]\[
\text{rate}_{\text{avg}} = -0.0019444444444444444 \, \text{M/s} = -1.9444444444444444 \times 10^{-3} \, \text{M/s}
\][/tex]
Since we are interested in the magnitude and the context implies a positive reaction rate value, we consider:
[tex]\[
\text{rate}_{\text{avg}} = 1.9444444444444444 \times 10^{-3} \, \text{M/s}
\][/tex]
### Step 5: Select the Closest Option
The closest option to [tex]\(1.9444444444444444 \times 10^{-3} \, \text{M/s}\)[/tex] among the provided choices is:
[tex]\[
1.9 \times 10^{-3} \, \text{M/s}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{1.9 \times 10^{-3}}
\][/tex]
