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Sagot :
Sure, let's compute the reaction rates step-by-step for each given reaction time using the formula provided:
[tex]\[ \text{Reaction Rate} = \frac{\text{mass of tablet} / \text{volume of water}}{\text{reaction time}} \][/tex]
The mass of the tablet is [tex]\(1000 \, \text{mg}\)[/tex], and the volume of water is [tex]\(0.200 \, \text{L}\)[/tex].
### For [tex]\(3^{\circ}C\)[/tex]:
- Given reaction time = [tex]\(138.5 \, \text{sec}\)[/tex]
First, calculate the concentration of the tablet in water:
[tex]\[ \frac{\text{mass of tablet}}{\text{volume of water}} = \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
Now, use the formula to find the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{138.5 \, \text{sec}} \][/tex]
Perform the division:
[tex]\[ \text{Reaction Rate} \approx 36 \, \text{mg/L/sec} \][/tex]
### For [tex]\(24^{\circ}C\)[/tex]:
- Given reaction time = [tex]\(34.2 \, \text{sec}\)[/tex]
Again, we already know the concentration is [tex]\(5000 \, \text{mg/L}\)[/tex]:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{34.2 \, \text{sec}} \][/tex]
Perform the division:
[tex]\[ \text{Reaction Rate} \approx 146 \, \text{mg/L/sec} \][/tex]
### For [tex]\(40^{\circ}C\)[/tex]:
- Given reaction time = [tex]\(26.3 \, \text{sec}\)[/tex]
Use the same concentration of [tex]\(5000 \, \text{mg/L}\)[/tex]:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{26.3 \, \text{sec}} \][/tex]
Perform the division:
[tex]\[ \text{Reaction Rate} \approx 190 \, \text{mg/L/sec} \][/tex]
### For [tex]\(65^{\circ}C\)[/tex]:
- Given reaction time = [tex]\(14.2 \, \text{sec}\)[/tex]
Using the same concentration of [tex]\(5000 \, \text{mg/L}\)[/tex]:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{14.2 \, \text{sec}} \][/tex]
Perform the division:
[tex]\[ \text{Reaction Rate} \approx 352 \, \text{mg/L/sec} \][/tex]
Thus, the reaction rates are:
[tex]\[ \begin{align*} 3^{\circ} C \quad & \text{Reaction rate } = 36 \, \text{mg/L/sec} \\ 24^{\circ} C \quad & \text{Reaction rate } = 146 \, \text{mg/L/sec} \\ 40^{\circ} C \quad & \text{Reaction rate } = 190 \, \text{mg/L/sec} \\ 65^{\circ} C \quad & \text{Reaction rate } = 352 \, \text{mg/L/sec} \end{align*} \][/tex]
[tex]\[ \text{Reaction Rate} = \frac{\text{mass of tablet} / \text{volume of water}}{\text{reaction time}} \][/tex]
The mass of the tablet is [tex]\(1000 \, \text{mg}\)[/tex], and the volume of water is [tex]\(0.200 \, \text{L}\)[/tex].
### For [tex]\(3^{\circ}C\)[/tex]:
- Given reaction time = [tex]\(138.5 \, \text{sec}\)[/tex]
First, calculate the concentration of the tablet in water:
[tex]\[ \frac{\text{mass of tablet}}{\text{volume of water}} = \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
Now, use the formula to find the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{138.5 \, \text{sec}} \][/tex]
Perform the division:
[tex]\[ \text{Reaction Rate} \approx 36 \, \text{mg/L/sec} \][/tex]
### For [tex]\(24^{\circ}C\)[/tex]:
- Given reaction time = [tex]\(34.2 \, \text{sec}\)[/tex]
Again, we already know the concentration is [tex]\(5000 \, \text{mg/L}\)[/tex]:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{34.2 \, \text{sec}} \][/tex]
Perform the division:
[tex]\[ \text{Reaction Rate} \approx 146 \, \text{mg/L/sec} \][/tex]
### For [tex]\(40^{\circ}C\)[/tex]:
- Given reaction time = [tex]\(26.3 \, \text{sec}\)[/tex]
Use the same concentration of [tex]\(5000 \, \text{mg/L}\)[/tex]:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{26.3 \, \text{sec}} \][/tex]
Perform the division:
[tex]\[ \text{Reaction Rate} \approx 190 \, \text{mg/L/sec} \][/tex]
### For [tex]\(65^{\circ}C\)[/tex]:
- Given reaction time = [tex]\(14.2 \, \text{sec}\)[/tex]
Using the same concentration of [tex]\(5000 \, \text{mg/L}\)[/tex]:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{14.2 \, \text{sec}} \][/tex]
Perform the division:
[tex]\[ \text{Reaction Rate} \approx 352 \, \text{mg/L/sec} \][/tex]
Thus, the reaction rates are:
[tex]\[ \begin{align*} 3^{\circ} C \quad & \text{Reaction rate } = 36 \, \text{mg/L/sec} \\ 24^{\circ} C \quad & \text{Reaction rate } = 146 \, \text{mg/L/sec} \\ 40^{\circ} C \quad & \text{Reaction rate } = 190 \, \text{mg/L/sec} \\ 65^{\circ} C \quad & \text{Reaction rate } = 352 \, \text{mg/L/sec} \end{align*} \][/tex]
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