To determine how much energy is released by the reaction, we will use the formula:
[tex]\[ q = m C_p \Delta T \][/tex]
where:
- [tex]\( q \)[/tex] is the energy released (in Joules, J)
- [tex]\( m \)[/tex] is the mass of the calorimeter (in grams, g)
- [tex]\( C_p \)[/tex] is the specific heat capacity of the calorimeter (in Joules per gram per degree Celsius, J/(g°C))
- [tex]\( \Delta T \)[/tex] is the change in temperature (in degrees Celsius, °C)
The given values are:
- Mass of the calorimeter, [tex]\( m \)[/tex] = 1.350 kg
- Specific heat of the calorimeter, [tex]\( C_p \)[/tex] = 5.82 J/(g°C)
- Temperature change, [tex]\( \Delta T \)[/tex] = 2.87 °C
First, we need to convert the mass of the calorimeter from kilograms to grams:
[tex]\[ m = 1.350 \, \text{kg} \times 1000 \, \text{g/kg} = 1350 \, \text{g} \][/tex]
Next, we substitute the values into the formula [tex]\( q = m C_p \Delta T \)[/tex]:
[tex]\[ q = 1350 \, \text{g} \times 5.82 \, \text{J/(g°C)} \times 2.87 \, \text{°C} \][/tex]
Now we calculate the energy released:
[tex]\[ q = 1350 \times 5.82 \times 2.87 \][/tex]
[tex]\[ q = 22837.965 \, \text{J} \][/tex]
We need to convert the energy from Joules to kilojoules (kJ), knowing that 1 kJ = 1000 J:
[tex]\[ q_{\text{kJ}} = \frac{22837.965 \, \text{J}}{1000} \][/tex]
[tex]\[ q_{\text{kJ}} = 22.837965 \, \text{kJ} \][/tex]
Rounding to 4 significant figures, the energy released is approximately:
[tex]\[ q_{\text{kJ}} \approx 22.55 \, \text{kJ} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{22.5 \, \text{kJ}} \][/tex]
