Assume that each tablet's mass was [tex]$1,000 \, \text{mg}$[/tex], and you used [tex]$0.200 \, \text{L}$[/tex] of water each time. Compute the reaction rate to the nearest whole number using the formula below.

[tex]$
\text{Reaction Rate} = \frac{\text{mass of tablet}}{\text{volume of water} \times \text{reaction time}}
$[/tex]

[tex]$3^{\circ} \text{C}$[/tex]
- Reaction time [tex]$= 138.5 \, \text{sec}$[/tex]
- Reaction rate [tex]$=$[/tex] [tex]$\square \, \text{mg/L/sec}$[/tex]

[tex]$24^{\circ} \text{C}$[/tex]
- Reaction time [tex]$= 34.2 \, \text{sec}$[/tex]
- Reaction rate [tex]$=$[/tex] [tex]$\square \, \text{mg/L/sec}$[/tex]

[tex]$40^{\circ} \text{C}$[/tex]
- Reaction time [tex]$= 26.3 \, \text{sec}$[/tex]
- Reaction rate [tex]$=$[/tex] [tex]$\square \, \text{mg/L/sec}$[/tex]

[tex]$65^{\circ} \text{C}$[/tex]
- Reaction time [tex]$= 14.2 \, \text{sec}$[/tex]
- Reaction rate [tex]$=$[/tex] [tex]$\square \, \text{mg/L/sec}$[/tex]



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.