An exothermic reaction is one that releases energy in the form of heat. Therefore, we need to identify which of the given reactions releases energy.
Let's analyze each of the given reactions step by step:
1. [tex]\( \text{CH}_4 + 2 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O} + 891 \, \text{kJ} \)[/tex]
- This reaction includes "+ 891 kJ" on the product side, which means it releases 891 kJ of energy as heat. Thus, it is exothermic.
2. [tex]\( \text{NH}_4\text{NO}_3 + \text{H}_2\text{O} + 25 \, \text{kJ} \rightarrow \text{NH}_4^+( \text{aq} ) + \text{NO}_3^-( \text{aq} ) \)[/tex]
- This reaction shows "+ 25 kJ" on the reactant side, indicating it absorbs 25 kJ of energy. Therefore, it is endothermic.
3. [tex]\( 2 \text{H}_2\text{O} + 286 \, \text{kJ} \rightarrow 2 \text{H}_2 + \text{O}_2 \)[/tex]
- Here, "+ 286 kJ" is on the reactant side, signifying that the reaction absorbs 286 kJ of energy. Hence, this reaction is endothermic.
4. [tex]\( \text{N}_2 + \text{O}_2 + 181 \, \text{kJ} \rightarrow 2 \text{NO} \)[/tex]
- In this reaction, "+ 181 kJ" is on the reactant side, meaning it absorbs 181 kJ of energy. So, this reaction is also endothermic.
After reviewing each reaction, the only reaction that releases energy (exothermic) is the first one. Therefore, the exothermic reaction is:
[tex]\[ \text{CH}_4 + 2 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O} + 891 \, \text{kJ} \][/tex]
Thus, the exothermic reaction corresponds to the first reaction, which is Reaction 1.
