Nitrogen and oxygen gases combine to form nitric oxide: `N_(2)(g) + O_(2)(g) to 2NO(g) `.
Calculate the volume of nitrogen required to produce `30 " dm"^(3)` of NO gas.

Explanation

To solve the problem of calculating the volume of nitrogen required to produce 30 dm³ of nitric oxide (NO) gas, we will follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction between nitrogen and oxygen to form nitric oxide is:
\[ N_2(g) + O_2(g) \rightarrow 2NO(g) \]

### Step 2: Analyze the stoichiometry of the reaction
From the balanced equation, we can see that:
- 1 volume of nitrogen gas (N₂) reacts with 1 volume of oxygen gas (O₂) to produce 2 volumes of nitric oxide (NO).
- This means that for every 1 volume of N₂, we get 2 volumes of NO.

### Step 3: Set up the relationship between volumes
Let \( V \) be the volume of nitrogen gas required. According to the stoichiometry:
- If \( V \) (volume of N₂) produces \( 2V \) (volume of NO), then we can express this relationship as:
\[ 2V = \text{Volume of NO produced} \]

### Step 4: Substitute the known volume of NO
We know from the problem that the volume of NO produced is 30 dm³. Therefore, we can set up the equation:
\[ 2V = 30 \, \text{dm}^3 \]

### Step 5: Solve for V
To find the volume of nitrogen (V), we divide both sides of the equation by 2:
\[ V = \frac{30 \, \text{dm}^3}{2} = 15 \, \text{dm}^3 \]

### Conclusion
Thus, the volume of nitrogen gas required to produce 30 dm³ of nitric oxide is:
\[ \text{Volume of } N_2 = 15 \, \text{dm}^3 \]

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