………...mol of `N_(2)` are needed to produce 3.8 mol of `NH_(3)` by reaction with hydrogen.

Answer

To determine how many moles of \( N_2 \) are needed to produce 3.8 moles of \( NH_3 \), we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction between nitrogen and hydrogen to form ammonia is:
\[ N_2 + 3H_2 \rightarrow 2NH_3 \]

### Step 2: Analyze the stoichiometry
From the balanced equation, we can see that:
- 1 mole of \( N_2 \) produces 2 moles of \( NH_3 \).

### Step 3: Set up a proportion
We need to find out how many moles of \( N_2 \) are required to produce 3.8 moles of \( NH_3 \). We can set up a proportion based on the stoichiometry:
\[ \frac{1 \text{ mole of } N_2}{2 \text{ moles of } NH_3} = \frac{x \text{ moles of } N_2}{3.8 \text{ moles of } NH_3} \]

### Step 4: Solve for \( x \)
Cross-multiplying gives us:
\[ 1 \times 3.8 = 2 \times x \]
This simplifies to:
\[ 3.8 = 2x \]
Now, divide both sides by 2:
\[ x = \frac{3.8}{2} = 1.9 \]

### Conclusion
Thus, 1.9 moles of \( N_2 \) are needed to produce 3.8 moles of \( NH_3 \).