Corn farmers in the American Midwest typically use 5.0 ×10^3 kilograms of ammonium nitrate ferti

step 1 Okay, so for this question, they want us to calculate how much nitric acid is needed to fertiliz

Corn farmers in the American Midwest typically use 5.0 ×10^3...

Corn farmers in the American Midwest typically use $5.0 \times 10^{3}$ kilograms of ammonium nitrate fertilizer per square kilometer of cornfield per year. Some of the fertilizer washes into the Mississippi River and eventually flows into the Gulf of Mexico, promoting the growth of algae and endangering other aquatic life. a. Ammonium nitrate can be prepared by the following reaction: $$\mathrm{NH}_{3}(g)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{NH}_{4} \mathrm{NO}_{3}(a q)$$ How much nitric acid would be required to make the fertilizer needed for $1 \mathrm{km}^{2}$ of cornfield per year? b. Ammonium ions dissolved in groundwater may be converted into $\mathrm{NO}_{3}^{-}$ ions by bacterial action: $$\mathrm{NH}_{4}^{+}(a q)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{3}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell)+2 \mathrm{H}^{+}(a q)$$ If $10 \%$ of the ammonium component of $5.0 \times 10^{3}$ kilograms of fertilizer ends up as nitrate ions, how much oxygen would be consumed?

Corn farmers in the American Midwest typically use $5.0 \times 10^{3}$ kilograms of ammonium nitrate fertilizer per square kilometer of cornfield per year. Some of the fertilizer washes into the Mississippi River and eventually flows into the Gulf of Mexico, promoting the growth of algae and endangering other aquatic life.
a. Ammonium nitrate can be prepared by the following reaction:
$$\mathrm{NH}_{3}(g)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{NH}_{4} \mathrm{NO}_{3}(a q)$$
How much nitric acid would be required to make the fertilizer needed for $1 \mathrm{km}^{2}$ of cornfield per year?
b. Ammonium ions dissolved in groundwater may be converted into $\mathrm{NO}_{3}^{-}$ ions by bacterial action:
$$\mathrm{NH}_{4}^{+}(a q)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{3}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell)+2 \mathrm{H}^{+}(a q)$$
If $10 \%$ of the ammonium component of $5.0 \times 10^{3}$ kilograms of fertilizer ends up as nitrate ions, how much oxygen would be consumed?

Key Concepts

Nitrification and the Nitrogen Cycle

Nitrification is a microbial process that converts ammonium ions (NH4+) into nitrate ions (NO3-) and is a key step in the nitrogen cycle. This reaction not only plays a crucial role in environmental chemistry by affecting nutrient dynamics in ecosystems but also is fundamental in understanding how chemical fertilizers may impact water quality through processes such as oxygen consumption during the oxidation of ammonium.

Balanced Chemical Equations

Balanced chemical equations represent the conservation of atoms in chemical reactions, with stoichiometric coefficients indicating the proportions of reactants and products. They serve as the blueprint for performing stoichiometric calculations by providing the necessary mole ratios to determine the amounts of substances consumed or produced in a reaction.

Molar Mass and the Mole Concept

The mole concept is used to relate the mass of a substance to the number of atoms or molecules it contains through its molar mass, which is the mass of one mole of that substance. This conversion is crucial for translating between laboratory-scale mass measurements and the theoretical mole ratios established by the balanced equation.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves using the balanced chemical equation to convert between masses, moles, and molecules of substances, ensuring that the law of conservation of mass is maintained. In problems involving reaction yields or reagent consumption, stoichiometry provides the framework to determine how much of one reactant is needed based on the amount of another product or reactant.

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