To determine the final temperature of the calorimeter after the complete combustion of the compound, we need to follow a series of steps, leveraging the known values and the formula [tex]\( q = m C_p \Delta T \)[/tex].
Here’s a step-by-step breakdown of the solution:
1. Identify and Define the Variables:
- Heat released ([tex]\( q \)[/tex]): [tex]\( 14.0 \)[/tex] kJ
- Mass of the calorimeter ([tex]\( m \)[/tex]): [tex]\( 1.20 \)[/tex] kg
- Specific heat capacity of the calorimeter ([tex]\( C_p \)[/tex]): [tex]\( 3.55 \)[/tex] kJ/(kg°C)
- Initial temperature ([tex]\( T_{\text{initial}} \)[/tex]): [tex]\( 22.5 \)[/tex]°C
2. Write the Formula:
The formula relating the heat, mass, specific heat capacity, and temperature change is:
[tex]\[
q = m C_p \Delta T
\][/tex]
3. Isolate ΔT (Change in Temperature):
Rearrange the formula to solve for [tex]\( \Delta T \)[/tex]:
[tex]\[
\Delta T = \frac{q}{m \cdot C_p}
\][/tex]
4. Substitute the Known Values:
Substitute the given values into the formula:
[tex]\[
\Delta T = \frac{14.0 \text{ kJ}}{1.20 \text{ kg} \times 3.55 \text{ kJ/(kg°C)}}
\][/tex]
5. Calculate ΔT:
Perform the calculation:
[tex]\[
\Delta T = \frac{14.0}{1.20 \times 3.55}
\][/tex]
[tex]\[
\Delta T \approx 3.29 \text{°C}
\][/tex]
6. Determine the Final Temperature:
The final temperature ([tex]\( T_{\text{final}} \)[/tex]) is the initial temperature plus the change in temperature:
[tex]\[
T_{\text{final}} = T_{\text{initial}} + \Delta T
\][/tex]
Substitute the values:
[tex]\[
T_{\text{final}} = 22.5 \text{°C} + 3.29 \text{°C}
\][/tex]
[tex]\[
T_{\text{final}} \approx 25.79 \text{°C}
\][/tex]
7. Select the Closest Answer:
Among the provided options, the closest value to [tex]\( 25.79 \text{°C} \)[/tex] is [tex]\( 25.8 \text{°C} \)[/tex].
Hence, the final temperature of the calorimeter is approximately [tex]\( 25.8^{\circ}C \)[/tex].
