In an experiment, 0.1 moles of M, a group 1 metal, react with sufficient oxygen to give 0.05 moles of compound X. Compound X is then allowed to react with water, and a hydroxide is the only product. In a separate experiment, 0.1 moles of the metal reacts with water to give 0.1 moles of a hydroxide and 0.05 moles of a gas, Y. Identify the metal and compounds X and Y. Write balanced chemical equations for the reactions described.