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Let's solve this step-by-step.

### 1. **Understanding the Reaction**  
The balanced chemical equation given is:
\[
N_2(g) + 3 H_2(g) \rightarrow 2 NH_3(g)
\]
- 1 molecule of \(N_2\) reacts with 3 molecules of \(H_2\) to produce 2 molecules of \(NH_3\).  

### 2. **Available Reactants**
- **Nitrogen molecules (\(N_2\))**: 4  
- **Hydrogen molecules (\(H_2\))**: 9  

### 3. **Determining the Limiting Reactant**  
For every 1 molecule of \(N_2\), we need 3 molecules of \(H_2\). Let’s calculate how many molecules of ammonia can be produced with each reactant.

- **Based on 4 \(N_2\)**:  
  Each \(N_2\) requires 3 \(H_2\). With 4 \(N_2\), we need:
  \[
  4 \times 3 = 12 \, H_2
  \]
  But only **9 \(H_2\)** are available, which is insufficient.  

Thus, **hydrogen (\(H_2\)) is the limiting reactant**.

### 4. **Calculating the Amount of \(NH_3\) Produced**  
Since \(H_2\) is the limiting reactant, let’s see how many molecules of ammonia can be formed from the available 9 molecules of \(H_2\).

- Each group of 3 \(H_2\) produces 2 \(NH_3\).  
  With 9 \(H_2\), we can form:
  \[
  \frac{9}{3} \times 2 = 6 \, NH_3
  \]

### 5. **Remaining Reactants**  
- **Molecules of \(H_2\) left**: All 9 are used up, so **0** molecules remain.  
- **Molecules of \(N_2\) left**: We only used 3 out of 4 \(N_2\).  
  Thus, \(4 - 3 = 1\) molecule of \(N_2\) remains.

---

### **Answers**:
- **Molecules of \(NH_3\)**: 6  
- **Limiting Reactant**: Hydrogen (\(H_2\))  
- **Molecules of \(H_2\) left**: 0  
- **Molecules of \(N_2\) left**: 1  

Let me know if this is clear! Would you like a more detailed explanation on any step?  

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Here are some related questions for further exploration:
1. What would happen if 12 molecules of \(H_2\) were provided instead?
2. How does the concept of limiting reactants apply in industrial ammonia production?
3. What is the theoretical yield of \(NH_3\) if all reactants were in perfect proportion?
4. How can we determine the excess reactant in any chemical reaction?
5. What happens to the leftover \(N_2\) molecules in a real-world chemical reactor?

**Tip**: Always identify the limiting reactant first—it determines the maximum amount of product that can be formed.

Nitrogen and hydrogen combine at a high temperature, in the presence of a catalyst, to produce ammonia. There are four molecules of nitrogen and nine molecules of hydrogen present. When the reaction is complete, how many molecules of NH3 are produced? What is the limiting reactant?

Solve a stoichiometry problem involving the reaction between nitrogen and hydrogen to form ammonia. Determine the limiting reactant and calculate the amount of NH3 produced with 4 molecules of nitrogen and 9 molecules of hydrogen. This problem is ideal for students in Grades 10-12 and explores key chemical reaction concepts.

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