Final answer:
To produce 45.0 g of lithium nitride, approximately 26.9 g of lithium are needed, based on stoichiometry calculations from the balanced chemical equation. None of the provided answer choices are correct.
Step-by-step explanation:
To determine how many grams of lithium are needed to produce 45.0 g of lithium nitride, Li₃N, according to the balanced chemical equation 6 Li(s) + N₂(g) → 2 Li₃N(s), we first need to calculate the molar mass of Li₃N and then use stoichiometry to find the mass of Li needed.
The molar mass of Li₃N is approximately 34.83 g/mol (3*6.94 g/mol + 14.01 g/mol). 45.0 g of Li₃N is about 1.292 mol (45.0 g / 34.83 g/mol). According to the stoichiometry of the balanced equation, 6 mol of Li is needed to produce 2 mol of Li₃N, so 1.292 mol of Li₃N would need 3.876 mol of Li (1.292 mol * (6 mol Li / 2 mol Li₃N)). The molar mass of Li is about 6.94 g/mol, so 3.876 mol of Li corresponds to 26.9 g (3.876 mol * 6.94 g/mol).
None of the answer choices provided (15.0 g, 45.0 g, 30.0 g, 90.0 g) are correct. The correct amount of lithium needed is approximately 26.9 g.