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This question involves calculating the volume of nitrogen gas (N₂) needed to produce a certain volume of ammonia (NH₃) using the ideal gas law and stoichiometry of the Haber process.

The balanced chemical equation for the Haber process is:

\[
N_2 (g) + 3H_2 (g) \rightarrow 2NH_3 (g)
\]

### Step 1: Use stoichiometry to relate NH₃ to N₂.
From the equation, 1 mole of nitrogen gas (N₂) produces 2 moles of ammonia (NH₃). Therefore, the volume of N₂ needed will be half the volume of NH₃ produced, assuming the same conditions of temperature and pressure.

### Step 2: Calculate the volume of N₂.
We are given:
- Volume of NH₃ = 100.0 L
- Temperature = 30.0°C = 303.15 K (in Kelvin)
- Pressure = 2.50 atm

Using stoichiometry:
\[
\text{Volume of } N_2 = \frac{1}{2} \times \text{Volume of NH₃}
\]
\[
\text{Volume of } N_2 = \frac{1}{2} \times 100.0 \, \text{L} = 50.0 \, \text{L}
\]

### Final Answer:
To produce 100.0 L of NH₃, 50.0 L of N₂ are required.

Would you like further details on how to use the ideal gas law in this context, or have any other questions?

### 5 related questions:
1. How does the ideal gas law relate to gas volumes in chemical reactions?
2. What is the role of the Haber process in industry?
3. How would the required volume of nitrogen change if the pressure or temperature were different?
4. What is the significance of stoichiometry in chemical reactions like this?
5. How does the amount of hydrogen relate to the amount of nitrogen and ammonia produced?

### Tip:
Always remember to check the units when applying gas laws and stoichiometry. Converting temperature to Kelvin and keeping pressure in consistent units (atm, mmHg, etc.) is crucial.

To produce 100.0 L of NH₃ at 30.0°C and 2.50 atm, how many liters of N₂ are needed?

Learn how to calculate the volume of nitrogen gas (N₂) required to produce 100.0 L of ammonia (NH₃) at 30.0°C and 2.50 atm using the ideal gas law and stoichiometry. This problem covers essential concepts such as gas laws and stoichiometric relationships, suitable for high school chemistry students.

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