The reaction `4N_(2)O+CH_(4) to CO_(2)+2H_(2)O+4N_(2)` takes place in the gaseous state. If all volumes are measured at the same temperature and pressure, calculate the volume of dinitrogen oxide `(N_(2)O)` required to give 150 ml of steam. (N = 14, O = 16, C = 12, H = 1)

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Reaction
The balanced chemical reaction is:
\[ 4 \text{N}_2\text{O} + \text{CH}_4 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O} + 4 \text{N}_2 \]

From this reaction, we can see that 4 moles of dinitrogen oxide (N₂O) produce 2 moles of water (H₂O).

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