Final answer:
The balanced equation for the electrolytic decomposition of water is 2H₂O (l) → 2H₂ (g) + O₂ (g), showing the conversion of water into hydrogen and oxygen gases when subjected to an electric current.
Step-by-step explanation:
The correct balanced equation for the electrolytic decomposition of water is represented by 2H₂O (l) → 2H₂ (g) + O₂ (g). In this process, an electric current is passed through water, causing it to separate into hydrogen gas and oxygen gas. The balanced chemical equation indicates that two molecules of water are decomposed to form two molecules of hydrogen gas and one molecule of oxygen gas.
It is essential to understand that electrolysis involves redox reactions. For the equation to be balanced in terms of mass and charge, we must account for the number of hydrogen and oxygen atoms. The correct answer incorporates the stoichiometry of the reaction, where two moles of hydrogen gas and one mole of oxygen gas are produced per two moles of liquid water consumed.
Using reactants and products in their appropriate states (here, water in the liquid state, and hydrogen and oxygen in the gaseous states) is also crucial for a correctly balanced equation. Therefore, the final answer, which is confirmed by the given reference, is option a) 2H₂O → 2H₂ + O₂, satisfying the requirement of a balanced equation for the decomposition of water via electrolysis.