Understand the definition of an exothermic reaction: it is a chemical reaction that releases energy, usually in the form of heat, to the surroundings.
Analyze each given reaction to determine whether it releases or absorbs energy:
1. Electrolysis of water (\$2 H_2O \rightarrow 2 H_2 + O_2$) requires electrical energy input to break water into hydrogen and oxygen, so it is endothermic (absorbs energy).
2. Photosynthesis (\$6 CO_2 + 6 H_2O \rightarrow C_6H_{12}O_6 + 6 O_2$) uses sunlight energy to produce glucose and oxygen, so it is also endothermic (absorbs energy).
3. Melting of ice (\(H_2O(s) \rightarrow H_2O(l)\)) requires heat to change phase from solid to liquid, so it is endothermic (absorbs energy).
4. Combustion of methane (\(CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O\)) releases heat as methane reacts with oxygen to form carbon dioxide and water, making it an exothermic reaction.