To determine how much energy is released by the reaction, we will use the formula for heat transfer:
[tex]\[ q = m C_p \Delta T \][/tex]
Here,
- [tex]\( q \)[/tex] stands for the heat energy released,
- [tex]\( m \)[/tex] represents the mass of the calorimeter,
- [tex]\( C_p \)[/tex] is the specific heat capacity of the calorimeter,
- [tex]\( \Delta T \)[/tex] is the change in temperature.
Given:
- The mass of the calorimeter, [tex]\( m \)[/tex], is 1.350 kg. First, we need to convert this mass to grams (since the specific heat capacity is in J/(g·°C)):
[tex]\[ 1.350 \, \text{kg} \times 1000 \, \text{g/kg} = 1350 \, \text{g} \][/tex]
- The specific heat capacity, [tex]\( C_p \)[/tex], is 5.82 J/(g·°C).
- The change in temperature, [tex]\( \Delta T \)[/tex], is 2.87°C.
Using the heat transfer formula:
[tex]\[ q = m C_p \Delta T \][/tex]
[tex]\[ q = 1350 \, \text{g} \times 5.82 \, \frac{\text{J}}{\text{g} \cdot \, ^{\circ} \text{C}} \times 2.87 \, ^{\circ} \text{C} \][/tex]
Multiply these values:
[tex]\[ q = 1350 \times 5.82 \times 2.87 \][/tex]
[tex]\[ q = 22549.59 \, \text{J} \][/tex]
To convert Joules to kilojoules (since 1 kJ = 1000 J):
[tex]\[ q = \frac{22549.59 \, \text{J}}{1000} \][/tex]
[tex]\[ q = 22.55 \, \text{kJ} \][/tex]
Therefore, the energy released by the reaction is approximately 22.5 kJ. So, the correct answer is:
[tex]\[ \boxed{22.5 \, \text{kJ}} \][/tex]
