Step 1: Understanding the Reaction Types Involving Oxygen
Many reactions, especially those involving oxides or compounds containing oxygen, often produce oxygen gas (\(O_2\)) as a product. However, some reactions, particularly hydrolysis or other substitution reactions, may not produce oxygen.
Step 2: Analyze the Given Reaction
The reaction \( \text{XeF}_6 + \text{H}_2\text{O} \rightarrow \) is the hydrolysis of xenon hexafluoride.
When \( \text{XeF}_6 \) reacts with water, it forms xenon oxyfluoride and hydrofluoric acid, but does not release free oxygen gas.
Step 3: Contrast with Other Reactions
In contrast, reactions such as the decomposition of peroxides or some metal oxides can release oxygen gas as a product.
Step 4: Conclusion
Therefore, the reaction of \( \text{XeF}_6 \) with water is the reaction in which oxygen is not produced as a product.