Certainly! Let's go through the reaction rate calculations for each temperature step by step.
The formula for calculating the reaction rate is:
[tex]\[
\text{Reaction Rate} = \frac{\text{mass of tablet} / \text{volume of water}}{\text{reaction time}}
\][/tex]
Given:
- Mass of each tablet = [tex]\(1000 \text{ mg}\)[/tex]
- Volume of water = [tex]\(0.200 \text{ L}\)[/tex]
First, we need to calculate the value of [tex]\(\frac{\text{mass of tablet}}{\text{volume of water}}\)[/tex]:
[tex]\[
\frac{1000 \text{ mg}}{0.200 \text{ L}} = 5000 \text{ mg/L}
\][/tex]
Now, for each temperature, we will use this value to calculate the reaction rate.
### 3°C
Reaction time = 138.5 seconds
[tex]\[
\text{Reaction Rate} = \frac{5000 \text{ mg/L}}{138.5 \text{ sec}} \approx 36.1 \text{ mg/L/sec}
\][/tex]
To the nearest whole number:
[tex]\[
\text{Reaction Rate} \approx 36 \text{ mg/L/sec}
\][/tex]
### 24°C
Reaction time = 34.2 seconds
[tex]\[
\text{Reaction Rate} = \frac{5000 \text{ mg/L}}{34.2 \text{ sec}} \approx 146.2 \text{ mg/L/sec}
\][/tex]
To the nearest whole number:
[tex]\[
\text{Reaction Rate} \approx 146 \text{ mg/L/sec}
\][/tex]
### 40°C
Reaction time = 26.3 seconds
[tex]\[
\text{Reaction Rate} = \frac{5000 \text{ mg/L}}{26.3 \text{ sec}} \approx 190.1 \text{ mg/L/sec}
\][/tex]
To the nearest whole number:
[tex]\[
\text{Reaction Rate} \approx 190 \text{ mg/L/sec}
\][/tex]
### 65°C
Reaction time = 14.2 seconds
[tex]\[
\text{Reaction Rate} = \frac{5000 \text{ mg/L}}{14.2 \text{ sec}} \approx 352.1 \text{ mg/L/sec}
\][/tex]
To the nearest whole number:
[tex]\[
\text{Reaction Rate} \approx 352 \text{ mg/L/sec}
\][/tex]
Therefore, the reaction rates to the nearest whole number for each temperature are:
[tex]\[
\begin{array}{l}
3^\circ \text{C} \quad \text{Reaction Rate} = 36 \text{ mg/L/sec} \\
24^\circ \text{C} \quad \text{Reaction Rate} = 146 \text{ mg/L/sec} \\
40^\circ \text{C} \quad \text{Reaction Rate} = 190 \text{ mg/L/sec} \\
65^\circ \text{C} \quad \text{Reaction Rate} = 352 \text{ mg/L/sec} \\
\end{array}
\][/tex]
