Suppose a certain fertilizer has the following composition: ingredient ammonium phosphate ((NH₂)¸PO4) a ((NH,),CO) potassium sulfate (K₂SO4) urea inert ingredients percent by mass 14% 36% 44% 6% What should the first (nitrogen) number on the bag label be? That is, calculate the percent by mass of nitrogen in this fertilizer. Round your answer to the nearest percent.
Suppose a certain fertilizer has the following composition: ingredient ammonium phosphate ((NH₂)¸PO4) a ((NH,),CO) potassium sulfate (K₂SO4) urea inert ingredients percent by mass 14% 36% 44% 6% What should the first (nitrogen) number on the bag label be? That is, calculate the percent by mass of nitrogen in this fertilizer. Round your answer to the nearest percent.
Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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
Transcribed Image Text:To help farmers and gardeners, commercial fertilizers have a big three-number "NPK" label on the bag that gives the amounts of three key plant nutrients: nitrogen, phosphorus, and potassium. For example, a bag of "10–10–10" fertilizer has 10% by mass nitrogen, 10% by mass potassium as potash (K₂O), and 10% by mass phosphorus as phosphate (P₂O₅).
Suppose a certain fertilizer has the following composition:
| Ingredient | Percent by Mass |
|---------------------------------|-----------------|
| Ammonium phosphate ((NH₄)₃PO₄) | 14% |
| Urea ((NH₂)₂CO) | 36% |
| Potassium sulfate (K₂SO₄) | 44% |
| Inert ingredients | 6% |
What should the first (nitrogen) number on the bag label be? That is, calculate the percent by mass of nitrogen in this fertilizer. Round your answer to the nearest percent.
**Explanation:**
To find the nitrogen content, we calculate the contribution of nitrogen from each nitrogen-containing compound.
1. **Ammonium phosphate ((NH₄)₃PO₄)**:
- Contains three ammonium ions, each with one nitrogen atom.
- Molar mass of ammonium phosphate ≈ 149 g/mol
- Molar mass of nitrogen in (NH₄)₃PO₄ = 3 x 14 g/mol = 42 g/mol
- Percent nitrogen in (NH₄)₃PO₄ = (42/149) x 100 ≈ 28.19%
- Contribution to fertilizer: 14% (mass) x 28.19% ≈ 3.9466%
2. **Urea ((NH₂)₂CO)**:
- Contains two nitrogen atoms.
- Molar mass of urea ≈ 60 g/mol
- Molar mass of nitrogen in urea = 2 x 14 g/mol = 28 g/mol
- Percent nitrogen in urea = (28/60) x 100 ≈ 46.67%
- Contribution to fertilizer: 36% (mass) x 46.67% ≈ 16.8%
Add both contributions:
3.9466% +
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