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Let’s go step by step to solve this problem.

We are given the balanced chemical equation:

N₂(g) + 3H₂(g) → 2NH₃(g)

This tells us that for every 1 molecule of N₂, we need 3 molecules of H₂ to make 2 molecules of NH₃.

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Part 1a: What are the coefficients?

Coefficients are the numbers in front of each substance in the balanced equation.

- For N₂: there is no number written, which means it’s 1
- For H₂: the number is 3
- For NH₃: the number is 2

✔ So:
- N₂ = 1
- H₂ = 3
- NH₃ = 2

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Part 1b: Draw particle models

We don’t need to draw here, but just to understand:

- N₂ is shown as two circles stuck together (diatomic molecule)
- H₂ is also two small circles stuck together — and we need 3 of them
- NH₃ is one big circle (N) with three small ones (H) around it — and we get 2 of those

The drawing in the image shows:
- One N₂ (two red circles)
- Three H₂ (three pairs of small circles)
- Two NH₃ (each with one big circle and three small ones)

That matches the ratio 1:3:2.

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Part 2a & 2b: Calculate amounts and reduce ratios

We’re told to calculate how many molecules are consumed or produced if the reaction happens:

#### Case 1: Single reaction (happens once)

From the equation:
- N₂ consumed = 1
- H₂ consumed = 3
- NH₃ produced = 2

Ratio N₂ : H₂ : NH₃ = 1 : 3 : 2 → already reduced!

#### Case 2: Reaction occurs 100 times

Multiply each coefficient by 100:

- N₂ = 1 × 100 = 100
- H₂ = 3 × 100 = 300
- NH₃ = 2 × 100 = 200

Ratio = 100 : 300 : 200 → divide all by 100 → 1 : 3 : 2

#### Case 3: Reaction occurs 538 times

Multiply each coefficient by 538:

- N₂ = 1 × 538 = 538
- H₂ = 3 × 538 = let’s calculate:
3 × 500 = 1500
3 × 38 = 114
Total = 1500 + 114 = 1614
- NH₃ = 2 × 538 =
2 × 500 = 1000
2 × 38 = 76
Total = 1000 + 76 = 1076

Ratio = 538 : 1614 : 1076 → divide all by 538 → 1 : 3 : 2

✔ All ratios reduce to 1:3:2 because they’re based on the same balanced equation.

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Final Answer:

For part 1a:
N₂ = 1, H₂ = 3, NH₃ = 2

For part 2 table:

| Situation | N₂ Consumed | H₂ Consumed | NH₃ Produced | Ratio N₂:H₂:NH₃ (reduced) |
|-----------|-------------|-------------|--------------|---------------------------|
| Single reaction | 1 | 3 | 2 | 1:3:2 |
| 100 times | 100 | 300 | 200 | 1:3:2 |
| 538 times | 538 | 1614 | 1076 | 1:3:2 |