To solve this problem, let's use the formula for calculating the heat absorbed:
[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]
where:
- [tex]\( q \)[/tex] is the heat absorbed,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( C_p \)[/tex] is the specific heat capacity,
- [tex]\( \Delta T \)[/tex] is the change in temperature.
Here's the step-by-step solution:
1. Convert the mass to grams:
The given mass is [tex]\( 1.400 \, \text{kg} \)[/tex]. We need to convert this mass to grams because the specific heat capacity is given in [tex]\( \text{J}/(\text{g} \cdot ^\circ\text{C}) \)[/tex].
[tex]\[ 1.400 \, \text{kg} = 1.400 \times 1000 \, \text{g} = 1400 \, \text{g} \][/tex]
2. Determine the change in temperature ([tex]\( \Delta T \)[/tex]):
Given that the final temperature is [tex]\( 27.45^\circ \text{C} \)[/tex] and, although the problem didn't mention an initial different temperature, we'll assume there is a meaningful temperature change example where [tex]\( \Delta T = 50^\circ \text{C} \)[/tex].
3. Calculate the heat absorbed (q):
Using the values:
- [tex]\( m = 1400 \, \text{g} \)[/tex],
- [tex]\( C_p = 3.52 \, \text{J}/(\text{g} \cdot ^\circ\text{C}) \)[/tex],
- [tex]\( \delta T = 50^\circ \text{C} \)[/tex]:
[tex]\[
q = m \cdot C_p \cdot \delta T
\][/tex]
Substituting the numbers in:
[tex]\[
q = 1400 \, \text{g} \times 3.52 \, \text{J}/(\text{g} \cdot ^\circ\text{C}) \times 50^\circ \text{C}
\][/tex]
[tex]\[
q = 1400 \times 3.52 \times 50
\][/tex]
[tex]\[
q = 246,400 \, \text{J}
\][/tex]
So the amount of heat absorbed by the reaction is 246,400 J.
However, none of the given options (140 J, 418 J, 1,470 J, 5,170 J) match this value. It appears there might be a misunderstanding or a need for reevaluation of the scenario described to better suit provided option-correct context.
