To find the reaction rate for each temperature, we use the formula:
[tex]\[
\text{Reaction Rate} = \frac{\text{mass of tablet} / \text{volume of water}}{\text{reaction time}}
\][/tex]
Given:
- Mass of tablet = [tex]\(1000 \, \text{mg}\)[/tex]
- Volume of water = [tex]\(0.200 \, \text{L}\)[/tex]
For each temperature, we will plug in the reaction time to find the reaction rate. Let's do this step-by-step:
### 1. At [tex]\(3^{\circ} C\)[/tex]:
- Reaction time = [tex]\(138.5 \, \text{sec}\)[/tex]
[tex]\[
\text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{138.5 \, \text{sec}} = \frac{5000 \, \text{mg/L}}{138.5 \, \text{sec}}
\][/tex]
Calculating this:
[tex]\[
\text{Reaction Rate} \approx 36 \, \text{mg/L/sec}
\][/tex]
### 2. At [tex]\(24^{\circ} C\)[/tex]:
- Reaction time = [tex]\(34.2 \, \text{sec}\)[/tex]
[tex]\[
\text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{34.2 \, \text{sec}} = \frac{5000 \, \text{mg/L}}{34.2 \, \text{sec}}
\][/tex]
Calculating this:
[tex]\[
\text{Reaction Rate} \approx 146 \, \text{mg/L/sec}
\][/tex]
### 3. At [tex]\(40^{\circ} C\)[/tex]:
- Reaction time = [tex]\(26.3 \, \text{sec}\)[/tex]
[tex]\[
\text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{26.3 \, \text{sec}} = \frac{5000 \, \text{mg/L}}{26.3 \, \text{sec}}
\][/tex]
Calculating this:
[tex]\[
\text{Reaction Rate} \approx 190 \, \text{mg/L/sec}
\][/tex]
### 4. At [tex]\(65^{\circ} C\)[/tex]:
- Reaction time = [tex]\(14.2 \, \text{sec}\)[/tex]
[tex]\[
\text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{14.2 \, \text{sec}} = \frac{5000 \, \text{mg/L}}{14.2 \, \text{sec}}
\][/tex]
Calculating this:
[tex]\[
\text{Reaction Rate} \approx 352 \, \text{mg/L/sec}
\][/tex]
So, the reaction rates to the nearest whole number are:
- At [tex]\(3^{\circ} C\)[/tex], the reaction rate = [tex]\(36 \, \text{mg/L/sec}\)[/tex]
- At [tex]\(24^{\circ} C\)[/tex], the reaction rate = [tex]\(146 \, \text{mg/L/sec}\)[/tex]
- At [tex]\(40^{\circ} C\)[/tex], the reaction rate = [tex]\(190 \, \text{mg/L/sec}\)[/tex]
- At [tex]\(65^{\circ} C\)[/tex], the reaction rate = [tex]\(352 \, \text{mg/L/sec}\)[/tex]
