Question

Large quantities of fertilizer are washed into the Mississippi River from agricultural land in the Midwest. The excess nutrients collect in the Gulf of Mexico, promoting the growth of algae and edging out other aquatic life. Corn farmers typically use 5000 kg of ammonium nitrate per square kilometer of cornfield per year. Ammonium nitrate can be prepared by the following reaction NH₃ + HNO₃ = NH₄NO₃.

The ammonium ions can be converted into NO₃⁻ by bacterial action. If 10% of the ammonium component of 5000 kg of fertilizer ends up as nitrate, how much oxygen would be consumed in the reaction NH₄⁺ + 2O₂ = NO₃⁻ + H₂O + 2H⁺?

Answer 1

In the oxidation of ammonium to nitrate by bacteria, 500 kg of the ammonium component of fertilizer would consume 400 kg of oxygen, based on stoichiometric calculations.

Step-by-step explanation:

The question involves calculating the amount of oxygen consumed in the reaction where ammonium ions are converted to nitrates in an agricultural context. Given that corn farmers use 5000 kg of ammonium nitrate per square kilometer and that 10% of this ammonium ends up as nitrate, first, we calculate the mass of the ammonium component which is 500 kg (10% of 5000 kg). Next, we apply the stoichiometry of the reaction NH4+ + 2O2 = NO3− + H2O + 2H+ to determine the amount of oxygen needed.

From the reaction equation, we see that one mole of NH4+ requires two moles of O2. The molar mass of NH4NO3 (ammonium nitrate) is approximately 80 g/mol, so 500 kg of NH4NO3 is equivalent to 6250 mol. Thus, the oxygen needed is twice this amount, which is 12500 mol of O2. Since the molar mass of O2 is about 32 g/mol, the mass of oxygen consumed is 12500 mol × 32 g/mol = 400000 g or 400 kg.