Answer :
To determine the reaction rate at different temperatures, we need to use the provided formula:
[tex]\[ \text{Reaction Rate} = \frac{\text{mass of tablet}}{\text{volume of water} \times \text{reaction time}} \][/tex]
Given:
- Mass of tablet = 1000 mg
- Volume of water = 0.200 L
We need to calculate the reaction rate for each provided reaction time:
### Temperature [tex]$3^{\circ} C$[/tex]:
- Reaction time = 138.5 sec
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg}}{0.200 \, \text{L} \times 138.5 \, \text{sec}} \][/tex]
Performing the division:
[tex]\[ \text{Reaction Rate} \approx 36 \, \text{mg/L/sec} \][/tex]
### Temperature [tex]$24^{\circ} C$[/tex]:
- Reaction time = 34.2 sec
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg}}{0.200 \, \text{L} \times 34.2 \, \text{sec}} \][/tex]
Performing the division:
[tex]\[ \text{Reaction Rate} \approx 146 \, \text{mg/L/sec} \][/tex]
### Temperature [tex]$40^{\circ} C$[/tex]:
- Reaction time = 26.3 sec
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg}}{0.200 \, \text{L} \times 26.3 \, \text{sec}} \][/tex]
Performing the division:
[tex]\[ \text{Reaction Rate} \approx 190 \, \text{mg/L/sec} \][/tex]
### Temperature [tex]$65^{\circ} C$[/tex]:
- Reaction time = 14.2 sec
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg}}{0.200 \, \text{L} \times 14.2 \, \text{sec}} \][/tex]
Performing the division:
[tex]\[ \text{Reaction Rate} \approx 352 \, \text{mg/L/sec} \][/tex]
Summarizing the results:
- At [tex]$3^{\circ} C$[/tex], the reaction rate is [tex]$36$[/tex] mg/L/sec.
- At [tex]$24^{\circ} C$[/tex], the reaction rate is [tex]$146$[/tex] mg/L/sec.
- At [tex]$40^{\circ} C$[/tex], the reaction rate is [tex]$190$[/tex] mg/L/sec.
- At [tex]$65^{\circ} C$[/tex], the reaction rate is [tex]$352$[/tex] mg/L/sec.
[tex]\[ \text{Reaction Rate} = \frac{\text{mass of tablet}}{\text{volume of water} \times \text{reaction time}} \][/tex]
Given:
- Mass of tablet = 1000 mg
- Volume of water = 0.200 L
We need to calculate the reaction rate for each provided reaction time:
### Temperature [tex]$3^{\circ} C$[/tex]:
- Reaction time = 138.5 sec
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg}}{0.200 \, \text{L} \times 138.5 \, \text{sec}} \][/tex]
Performing the division:
[tex]\[ \text{Reaction Rate} \approx 36 \, \text{mg/L/sec} \][/tex]
### Temperature [tex]$24^{\circ} C$[/tex]:
- Reaction time = 34.2 sec
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg}}{0.200 \, \text{L} \times 34.2 \, \text{sec}} \][/tex]
Performing the division:
[tex]\[ \text{Reaction Rate} \approx 146 \, \text{mg/L/sec} \][/tex]
### Temperature [tex]$40^{\circ} C$[/tex]:
- Reaction time = 26.3 sec
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg}}{0.200 \, \text{L} \times 26.3 \, \text{sec}} \][/tex]
Performing the division:
[tex]\[ \text{Reaction Rate} \approx 190 \, \text{mg/L/sec} \][/tex]
### Temperature [tex]$65^{\circ} C$[/tex]:
- Reaction time = 14.2 sec
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg}}{0.200 \, \text{L} \times 14.2 \, \text{sec}} \][/tex]
Performing the division:
[tex]\[ \text{Reaction Rate} \approx 352 \, \text{mg/L/sec} \][/tex]
Summarizing the results:
- At [tex]$3^{\circ} C$[/tex], the reaction rate is [tex]$36$[/tex] mg/L/sec.
- At [tex]$24^{\circ} C$[/tex], the reaction rate is [tex]$146$[/tex] mg/L/sec.
- At [tex]$40^{\circ} C$[/tex], the reaction rate is [tex]$190$[/tex] mg/L/sec.
- At [tex]$65^{\circ} C$[/tex], the reaction rate is [tex]$352$[/tex] mg/L/sec.
