Let's analyze the given chemical reaction:
[tex]\[ Ca^{2+}(aq) + 2 OH^-(aq) \rightarrow Ca(OH)_2(s) \][/tex]
Along with the reaction, we are provided the enthalpy change ([tex]\(\Delta H\)[/tex]) for the reaction:
[tex]\[ \Delta H = 16.71 \][/tex]
To determine what this [tex]\(\Delta H\)[/tex] value indicates, let's review the concepts of endothermic and exothermic reactions:
1. Exothermic Reaction:
- In an exothermic reaction, the system releases heat to the surroundings.
- The enthalpy change ([tex]\(\Delta H\)[/tex]) for exothermic reactions is negative ([tex]\( \Delta H < 0 \)[/tex]).
2. Endothermic Reaction:
- In an endothermic reaction, the system absorbs heat from the surroundings.
- The enthalpy change ([tex]\(\Delta H\)[/tex]) for endothermic reactions is positive ([tex]\( \Delta H > 0 \)[/tex]).
Given that the [tex]\(\Delta H\)[/tex] value for our reaction is 16.71 kJ/mol and it is positive, this means that the reaction absorbs heat from the surroundings. Therefore, this characterizes an endothermic reaction.
Thus, the correct interpretation based on the [tex]\(\Delta H\)[/tex] provided is that the reaction is endothermic.
Now, let's match this interpretation with the provided multiple-choice answers:
A. The reaction produces heat.
- This statement would indicate an exothermic reaction ([tex]\( \Delta H < 0 \)[/tex]), which is not the case here.
B. The reaction cannot happen.
- There is no indication from the provided [tex]\(\Delta H\)[/tex] value that the reaction cannot happen. [tex]\(\Delta H\)[/tex] only tells us about heat exchange, not the feasibility of the reaction.
C. The reaction is exothermic.
- This statement suggests a release of heat ([tex]\( \Delta H < 0 \)[/tex]). However, we know that [tex]\(\Delta H\)[/tex] is positive, so this statement is incorrect.
D. The reaction is endothermic.
- This statement correctly indicates that heat is absorbed from the surroundings since [tex]\(\Delta H\)[/tex] is positive ([tex]\( \Delta H > 0 \)[/tex]).
Therefore, the correct answer is:
D. The reaction is endothermic.
