Final answer:
To find the cost per pound of nitrogen in ammonium sulfate, calculate the nitrogen content in the fertilizer and then divide the total cost by the amount of nitrogen in 100 pounds. The cost is approximately $1.91 per pound of nitrogen.
Step-by-step explanation:
To calculate the cost of one pound of nitrogen from a fertilizer containing 20.0% ammonium sulfate and costing $8.10 per 100 lb, we must first determine the amount of nitrogen in ammonium sulfate.
The molecular formula for ammonium sulfate is (NH4)2SO4. Nitrogen (N) has a molecular weight of 14.0 g/mol, and each molecule of ammonium sulfate contains two nitrogen atoms, which equates to 28.0 g/mol of nitrogen. The molecular weight of ammonium sulfate is approximately 132.14 g/mol, so the percentage of nitrogen by weight is (28.0/132.14) * 100% ≈ 21.2%.
Since the fertilizer is 20.0% ammonium sulfate by weight, the nitrogen content of the fertilizer is 20.0% of 21.2%, or 4.24%. Therefore, in 100 lb of this fertilizer, there are 4.24 lb of nitrogen. The cost per pound of nitrogen can be calculated by dividing the cost per 100 lb of fertilizer by the number of pounds of nitrogen in 100 lb of fertilizer, which is $8.10 / 4.24 lb ≈ $1.91 per pound of nitrogen.