Final answer:
The volume of NH3 produced at 1.20 atm and 45 C when 6.20 liters of H2 react with 3.8 liters of nitrogen gas, based on stoichiometry and the provided molar ratios, will be 4.13 liters. This calculation assumes that hydrogen gas is the limiting reactant as it is present in less than the stoichiometrically required amount compared to nitrogen gas.
Step-by-step explanation:
The problem is based on stoichiometry and the gas laws which stipulate that, under the same conditions of temperature and pressure, gases react in volumes that are ratios of small whole numbers. This is derived from both Gay-Lussac's law of combining volumes and Avogadro's law. In this case, we are provided with the balanced reaction equation for the synthesis of ammonia (NH3), which is:
N2(g) + 3H2(g) → 2NH3(g)
The question asks what volume of NH3 can be produced at 1.20 atm and 45 C when 6.20 liters of H2 reacts with 3.8 liters of nitrogen gas at the same conditions. Given that the reaction of 4.20 mol of hydrogen with excess nitrogen produces 2.80 mol of ammonia, this corresponds to a stoichiometric ratio of 2 mols of NH3 for every 3 mols of H2 based on the balanced chemical equation.
For the volumes of gases at the same temperature and pressure, this stoichiometric ratio translates directly into volumes. Thus, since 3 volumes of H2 react to produce 2 volumes of NH3, the volume of NH3 produced would be 2/3 of the volume of H2 provided that there is sufficient nitrogen to react with all the hydrogen. Since we start with 6.20 liters of H2, we can calculate the expected volume of NH3 produced as: (2/3) × 6.20 liters = 4.13 liters of NH3, assuming complete reaction and no limiting reactants.
However, to determine which reactant is the limiting reactant, we must look at the stoichiometric relationship between N2 and H2. The balanced equation indicates that for every 1 volume of N2, 3 volumes of H2 are required. Therefore, if we have 3.8 liters N2, the required H2 would be 3 times that, which is 11.4 liters of H2. Given that we only have 6.20 liters of H2, the hydrogen gas is the limiting reactant in this scenario.
Because the hydrogen gas is the limiting reactant, the volume of NH3 produced will be 4.13 liters as calculated based on the stoichiometry of the reaction, and since we have less H2 than required by the ratio for the amount of N2 present. This assumes all of the hydrogen reacts and is based on the initial condition that the reaction takes place at 1.20 atm and 45 C.