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Sagot :
To compute the reaction rate at different temperatures, we use the formula:
[tex]\[ \text{Reaction Rate} = \frac{\text{mass of tablet} / \text{volume of water}}{\text{reaction time}} \][/tex]
Given:
- The mass of each tablet is [tex]\(1000 \, \text{mg}\)[/tex].
- The volume of water used each time is [tex]\(0.200 \, \text{L}\)[/tex].
Let's compute the reaction rate for each temperature step-by-step.
### For [tex]\(3^\circ C\)[/tex]:
- Reaction time = 138.5 seconds
- Formula for Reaction Rate:
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{138.5 \, \text{s}} \][/tex]
- First, calculate the concentration:
[tex]\[ \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
- Now, compute the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{138.5 \, \text{s}} \approx 36 \, \text{mg/L/s} \][/tex]
### For [tex]\(24^\circ C\)[/tex]:
- Reaction time = 34.2 seconds
- Formula for Reaction Rate:
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{34.2 \, \text{s}} \][/tex]
- First, calculate the concentration:
[tex]\[ \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
- Now, compute the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{34.2 \, \text{s}} \approx 146 \, \text{mg/L/s} \][/tex]
### For [tex]\(40^\circ C\)[/tex]:
- Reaction time = 26.3 seconds
- Formula for Reaction Rate:
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{26.3 \, \text{s}} \][/tex]
- First, calculate the concentration:
[tex]\[ \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
- Now, compute the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{26.3 \, \text{s}} \approx 190 \, \text{mg/L/s} \][/tex]
### For [tex]\(65^\circ C\)[/tex]:
- Reaction time = 14.2 seconds
- Formula for Reaction Rate:
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{14.2 \, \text{s}} \][/tex]
- First, calculate the concentration:
[tex]\[ \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
- Now, compute the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{14.2 \, \text{s}} \approx 352 \, \text{mg/L/s} \][/tex]
So, the reaction rates are:
- At [tex]\(3^\circ C\)[/tex]: [tex]\(\boxed{36} \, \text{mg/L/s}\)[/tex]
- At [tex]\(24^\circ C\)[/tex]: [tex]\(\boxed{146} \, \text{mg/L/s}\)[/tex]
- At [tex]\(40^\circ C\)[/tex]: [tex]\(\boxed{190} \, \text{mg/L/s}\)[/tex]
- At [tex]\(65^\circ C\)[/tex]: [tex]\(\boxed{352} \, \text{mg/L/s}\)[/tex]
\text{DONE}
[tex]\[ \text{Reaction Rate} = \frac{\text{mass of tablet} / \text{volume of water}}{\text{reaction time}} \][/tex]
Given:
- The mass of each tablet is [tex]\(1000 \, \text{mg}\)[/tex].
- The volume of water used each time is [tex]\(0.200 \, \text{L}\)[/tex].
Let's compute the reaction rate for each temperature step-by-step.
### For [tex]\(3^\circ C\)[/tex]:
- Reaction time = 138.5 seconds
- Formula for Reaction Rate:
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{138.5 \, \text{s}} \][/tex]
- First, calculate the concentration:
[tex]\[ \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
- Now, compute the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{138.5 \, \text{s}} \approx 36 \, \text{mg/L/s} \][/tex]
### For [tex]\(24^\circ C\)[/tex]:
- Reaction time = 34.2 seconds
- Formula for Reaction Rate:
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{34.2 \, \text{s}} \][/tex]
- First, calculate the concentration:
[tex]\[ \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
- Now, compute the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{34.2 \, \text{s}} \approx 146 \, \text{mg/L/s} \][/tex]
### For [tex]\(40^\circ C\)[/tex]:
- Reaction time = 26.3 seconds
- Formula for Reaction Rate:
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{26.3 \, \text{s}} \][/tex]
- First, calculate the concentration:
[tex]\[ \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
- Now, compute the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{26.3 \, \text{s}} \approx 190 \, \text{mg/L/s} \][/tex]
### For [tex]\(65^\circ C\)[/tex]:
- Reaction time = 14.2 seconds
- Formula for Reaction Rate:
[tex]\[ \text{Reaction Rate} = \frac{1000 \, \text{mg} / 0.200 \, \text{L}}{14.2 \, \text{s}} \][/tex]
- First, calculate the concentration:
[tex]\[ \frac{1000 \, \text{mg}}{0.200 \, \text{L}} = 5000 \, \text{mg/L} \][/tex]
- Now, compute the reaction rate:
[tex]\[ \text{Reaction Rate} = \frac{5000 \, \text{mg/L}}{14.2 \, \text{s}} \approx 352 \, \text{mg/L/s} \][/tex]
So, the reaction rates are:
- At [tex]\(3^\circ C\)[/tex]: [tex]\(\boxed{36} \, \text{mg/L/s}\)[/tex]
- At [tex]\(24^\circ C\)[/tex]: [tex]\(\boxed{146} \, \text{mg/L/s}\)[/tex]
- At [tex]\(40^\circ C\)[/tex]: [tex]\(\boxed{190} \, \text{mg/L/s}\)[/tex]
- At [tex]\(65^\circ C\)[/tex]: [tex]\(\boxed{352} \, \text{mg/L/s}\)[/tex]
\text{DONE}
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