To determine which reaction is endothermic, we need to recall the definitions of endothermic and exothermic reactions. An endothermic reaction absorbs energy from its surroundings, while an exothermic reaction releases energy to its surroundings.
Let's analyze each of the given reactions individually:
1. [tex]\( \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} + 58 \ \text{kJ} \)[/tex]
This reaction releases 58 kJ of energy as a product. Therefore, it is exothermic.
2. [tex]\( 6 \text{CO}_2 + 12 \text{H}_2\text{O} + \text{energy} \rightarrow \text{C}_6 \text{H}_{12} \text{O}_6 + 6 \text{O}_2 + 6 \text{H}_2\text{O} \)[/tex]
This reaction includes energy on the reactant side, indicating that it absorbs energy. Therefore, it is endothermic.
3. [tex]\( 2 \text{Na} + \text{Cl}_2 \rightarrow 2 \text{NaCl} + \text{energy} \)[/tex]
This reaction releases energy as a product. Therefore, it is exothermic.
4. [tex]\( 2 \text{C}_2 \text{H}_6 + 7 \text{O}_2 \rightarrow 4 \text{CO}_2 + 6 \text{H}_2\text{O} + 2,502 \ \text{kJ} \)[/tex]
This reaction releases 2,502 kJ of energy as a product. Therefore, it is exothermic.
Based on the analysis of each reaction's energy exchange, we determine that the endothermic reaction is:
[tex]\[ 6 \text{CO}_2 + 12 \text{H}_2\text{O} + \text{energy} \rightarrow \text{C}_6 \text{H}_{12} \text{O}_6 + 6 \text{O}_2 + 6 \text{H}_2\text{O} \][/tex]
Therefore, the index of the endothermic reaction is:
[tex]\[ 2 \][/tex]
