To determine the final temperature of the bomb calorimeter, we need to follow these steps:
1. Identify the given values:
- Initial temperature of the calorimeter, [tex]\( T_{\text{initial}} = 22.5^\circ C \)[/tex]
- Mass of the calorimeter, [tex]\( m = 1.20 \, \text{kg} \)[/tex]
- Convert the mass from kilograms to grams, since the specific heat is given in J/(g*°C):
[tex]\[ m = 1.20 \, \text{kg} \times 1000 \, \frac{\text{g}}{\text{kg}} = 1200 \, \text{g} \][/tex]
- Specific heat of the calorimeter, [tex]\( C_p = 3.55 \, \frac{\text{J}}{\text{g} \cdot \text{°C}} \)[/tex]
- Heat released by the combustion, [tex]\( q = 14.0 \, \text{kJ} \)[/tex]
- Convert the heat from kilojoules to joules:
[tex]\[ q = 14.0 \, \text{kJ} \times 1000 \, \frac{\text{J}}{\text{kJ}} = 14000 \, \text{J} \][/tex]
2. Use the heat transfer equation [tex]\( q = m C_p \Delta T \)[/tex] where [tex]\( \Delta T \)[/tex] is the change in temperature. Rearrange the equation to solve for [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = \frac{q}{m C_p} \][/tex]
3. Substitute the given values into the formula:
[tex]\[ \Delta T = \frac{14000 \, \text{J}}{1200 \, \text{g} \times 3.55 \, \frac{\text{J}}{\text{g} \cdot \text{°C}}} \][/tex]
4. Calculate the change in temperature:
[tex]\[ \Delta T = \frac{14000}{1200 \times 3.55} \approx \frac{14000}{4260} \approx 3.29^\circ C \][/tex]
5. Determine the final temperature of the calorimeter:
[tex]\[ T_{\text{final}} = T_{\text{initial}} + \Delta T \][/tex]
[tex]\[ T_{\text{final}} = 22.5^\circ C + 3.29^\circ C = 25.79^\circ C \][/tex]
Given the calculations, the final temperature of the calorimeter is approximately [tex]\( 25.8^\circ C \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{25.8^\circ C} \][/tex]
