Sure, let’s walk through the problem step by step.
### Step 1: Identify the initial and final temperatures
Given:
- Initial temperature ([tex]\( T_{\text{initial}} \)[/tex]): [tex]\( 25.00 ^{\circ} \text{C} \)[/tex]
- Final temperature ([tex]\( T_{\text{final}} \)[/tex]): [tex]\( 28.54 ^{\circ} \text{C} \)[/tex]
### Step 2: Calculate the change in temperature
The change in temperature ([tex]\( \Delta T \)[/tex]) is calculated as the difference between the final and initial temperatures:
[tex]\[
\Delta T = T_{\text{final}} - T_{\text{initial}}
\][/tex]
Substituting the given values:
[tex]\[
\Delta T = 28.54 ^{\circ} \text{C} - 25.00 ^{\circ} \text{C} = 3.54 ^{\circ} \text{C}
\][/tex]
The exact value (without rounding) is:
[tex]\[
\Delta T = 3.539999999999999 ^{\circ} \text{C}
\][/tex]
### Step 3: Identify the heat capacity of the calorimeter
Given:
- Heat capacity ([tex]\( C \)[/tex]): [tex]\( 5860 \, \text{J/}^{\circ} \text{C} \)[/tex]
### Step 4: Calculate the heat of reaction
The heat of reaction [tex]\( q_{\text{rxn}} \)[/tex] is given by the formula:
[tex]\[
q_{\text{rxn}} = C \times \Delta T
\][/tex]
Substitute the known values:
[tex]\[
q_{\text{rxn}} = 5860 \, \text{J/}^{\circ} \text{C} \times 3.539999999999999 ^{\circ} \text{C}
\][/tex]
Performing the multiplication:
[tex]\[
q_{\text{rxn}} = 5860 \times 3.539999999999999 = 20744.399999999994 \, \text{J}
\][/tex]
### Final Answer:
The heat of reaction is:
[tex]\[
q_{\text{rxn}} = 20744.399999999994 \, \text{J}
\][/tex]
Thus, during the reaction, the heat released (or absorbed) by the calorimeter and the water is approximately [tex]\( 20744.40 \, \text{J} \)[/tex] when rounded to two decimal places. If you do not require rounding, you can use the value [tex]\( 20744.399999999994 \, \text{J} \)[/tex].
