The nitrogen in sodium nitrate and in ammonium sulfate is available to plants as fertilizer. Which is the more economical source of nitrogen, a fertilizer containing 30.0% sodium nitrate by weight and costing $9.00 per 100 lb or one containing 20.0% ammonium sulfate by weight and costing $8.10 per 100 lb?

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Calculate the molar mass of sodium nitrate (NaNO_3) and ammonium sulfate ((NH_4)_2SO_4).

Determine the percentage of nitrogen by weight in sodium nitrate and ammonium sulfate using their chemical formulas.

Calculate the amount of nitrogen in 100 lb of each fertilizer based on their respective percentages of sodium nitrate and ammonium sulfate.

Determine the cost per pound of nitrogen for each fertilizer by dividing the cost of 100 lb of fertilizer by the amount of nitrogen in it.

Compare the cost per pound of nitrogen for both fertilizers to determine which is more economical.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Percentage Composition

Percentage composition refers to the mass percentage of each element in a compound. In this context, it helps determine the amount of nitrogen available in each fertilizer type. By calculating the actual nitrogen content based on the percentage and the total weight of the fertilizer, one can compare the two sources effectively.

Cost-Effectiveness

Cost-effectiveness in this scenario involves evaluating the cost per unit of nitrogen provided by each fertilizer. By determining how much nitrogen each fertilizer contributes relative to its price, one can identify which option offers more nitrogen for less money, thus making a more economical choice for fertilization.

Molar Mass and Stoichiometry

Molar mass is the mass of one mole of a substance, which is crucial for converting between grams and moles. Stoichiometry involves the calculation of reactants and products in chemical reactions. Understanding these concepts allows for accurate calculations of nitrogen content in fertilizers, enabling a precise comparison of their economic viability.

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