Answered

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

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

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

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

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

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



Answer :

GinnyAnswer
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]

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