Let's solve this step by step:
1. Given data:
- Initial temperature ([tex]\( T_i \)[/tex]): [tex]\( 28.50^{\circ} C \)[/tex]
- Final temperature ([tex]\( T_f \)[/tex]): [tex]\( 27.45^{\circ} C \)[/tex]
- Mass ([tex]\( m \)[/tex]): [tex]\( 1.400 \, \text{kg} \)[/tex]
- Specific heat ([tex]\( C_p \)[/tex]): [tex]\( 3.52 \, \text{J} / (\text{g} \cdot {}^{\circ}C) \)[/tex]
2. Convert the mass from kilograms to grams:
- Mass ([tex]\( m \)[/tex]) [tex]\( = 1.400\, \text{kg} \times 1000 \frac{\text{g}}{\text{kg}} = 1400 \, \text{g} \)[/tex]
3. Calculate the temperature change ([tex]\( \Delta T \)[/tex]):
- [tex]\( \Delta T = T_f - T_i = 27.45^{\circ} C - 28.50^{\circ} C = -1.05^{\circ} C \)[/tex]
4. Calculate the heat absorbed ([tex]\( q \)[/tex]) using the formula [tex]\( q = m C_p \Delta T \)[/tex]:
- [tex]\( q = 1400 \, \text{g} \times 3.52 \, \text{J} / (\text{g} \cdot {}^{\circ} C) \times -1.05^{\circ} C = -5174.4 \, \text{J} \)[/tex]
Since the temperature is decreasing, the heat absorbed by the reaction is negative, indicating that heat is released by the reaction.
Thus, the absolute value of heat released is [tex]\( \boxed{5170 \, \text{J}} \)[/tex], which matches one of the answer choices provided. Therefore, the answer is [tex]\( 5170 \, \text{J} \)[/tex].
