To identify which reactions are endothermic, we need to consider the enthalpy changes ([tex]\(\Delta H\)[/tex]) for each reaction. An endothermic reaction absorbs energy and thus has a positive [tex]\(\Delta H\)[/tex].
Given the enthalpy changes for the reactions:
1. [tex]\(2 H_2O \rightarrow 2 H_2 + O_2, \Delta H = 484 \, \text{kJ}\)[/tex]
2. [tex]\(C + O_2 \rightarrow CO_2, \Delta H = -394 \, \text{kJ}\)[/tex]
3. [tex]\(H_2 + Br_2 \rightarrow 2 HBr, \Delta H = -73 \, \text{kJ}\)[/tex]
4. [tex]\(2 NH_3 \rightarrow N_2 + 3 H_2, \Delta H = 92 \, \text{kJ}\)[/tex]
We need to select the reactions with positive [tex]\(\Delta H\)[/tex] values as endothermic reactions:
1. [tex]\(2 H_2O \rightarrow 2 H_2 + O_2, \Delta H = 484 \, \text{kJ}\)[/tex]:
[tex]\(\Delta H\)[/tex] is positive, so this reaction is endothermic.
2. [tex]\(C + O_2 \rightarrow CO_2, \Delta H = -394 \, \text{kJ}\)[/tex]:
[tex]\(\Delta H\)[/tex] is negative, so this reaction is exothermic.
3. [tex]\(H_2 + Br_2 \rightarrow 2 HBr, \Delta H = -73 \, \text{kJ}\)[/tex]:
[tex]\(\Delta H\)[/tex] is negative, so this reaction is exothermic.
4. [tex]\(2 NH_3 \rightarrow N_2 + 3 H_2, \Delta H = 92 \, \text{kJ}\)[/tex]:
[tex]\(\Delta H\)[/tex] is positive, so this reaction is endothermic.
Therefore, the endothermic reactions are:
- [tex]\(2 H_2O \rightarrow 2 H_2 + O_2, \Delta H = 484 \, \text{kJ}\)[/tex]
- [tex]\(2 NH_3 \rightarrow N_2 + 3 H_2, \Delta H = 92 \, \text{kJ}\)[/tex]
