Final answer:
To determine the number of moles of nitrogen and hydrogen, we calculated using their masses and molar masses. With 3,000,000 moles of nitrogen and 14,851,485 moles of hydrogen, it was deduced that nitrogen is the limiting reactant because it has less than the required tripling amount compared to hydrogen for ammonia synthesis according to the stoichiometry of the reaction.
Step-by-step explanation:
Firstly, we need to calculate the number of moles of both nitrogen and hydrogen. The number of moles is given by the mass divided by the molar mass (molecular weight).
For nitrogen:
Molecular weight of N2 = 14.0 × 2
= 28.0 g/mol
Mass of nitrogen = 84,000,000 g (84 tonnes × 1,000,000 g/tonne)
Number of moles of nitrogen = Mass ÷ Molecular weight
= 84,000,000 g ÷ 28.0 g/mol
= 3,000,000 moles
For hydrogen:
Molecular weight of H2 = 1.01 × 2
= 2.02 g/mol
Mass of hydrogen = 30,000,000 g (30 tonnes × 1,000,000 g/tonne)
Number of moles of hydrogen = Mass ÷ Molecular weight
= 30,000,000 g ÷ 2.02 g/mol
= 14,851,485 moles
The balanced chemical equation for the formation of ammonia (NH3) is:
N2(g) + 3H2(g) → 2NH3(g)
To determine the limiting reactant, compare the mole ratio of the reactants to the stoichiometric ratio from the equation. From the calculated moles, the ratio of H2 to N2 is approximately 14,851,485 : 3,000,000, which simplifies to about 4.95 : 1.
This is higher than the necessary stoichiometric ratio of 3:1 (hydrogen to nitrogen), indicating that nitrogen is the limiting reactant since there is not enough of it to react with all the available hydrogen to produce ammonia.
In a chemical reaction, the limiting reactant is the substance that is totally consumed when the chemical reaction is complete. Since all of the nitrogen will react and there will be leftover hydrogen, nitrogen limits the amount of ammonia that can be produced.