To determine which reaction is exothermic, we need to analyze the energy changes associated with each chemical equation:
1. Reaction 1: [tex]\( CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O + 891 \text{ kJ} \)[/tex]
- This reaction releases 891 kJ of energy, indicated by the positive sign after the products.
- Since energy is released during the reaction, this reaction is exothermic.
2. Reaction 2: [tex]\( 2 H_2O + 286 \text{ kJ} \rightarrow 2 H_2 + O_2 \)[/tex]
- This reaction requires an input of 286 kJ of energy for it to proceed.
- Since energy is absorbed, this reaction is endothermic.
3. Reaction 3: [tex]\( N_2 + O_2 + 181 \text{ kJ} \rightarrow 2 NO \)[/tex]
- This reaction also requires an input of 181 kJ of energy.
- Since energy is absorbed, this reaction is endothermic.
Therefore, the reaction of interest that is exothermic is the first reaction:
[tex]\[ \boxed{1} \][/tex]
In summary, the exothermic reaction is:
[tex]\[ CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O + 891 \text{ kJ} \][/tex]
The numerical answer is [tex]\( \boxed{1} \)[/tex].
