A-Level The mole and reacting-quantity calculations: worked solution

Question

One way to apply this method is to power the electrolysis with renewable electricity and make ammonia directly at a farm for immediate use. A typical UK farm covers 130 acres and needs 0.0770 tonnes of ammonia per acre each year. Assuming the lithium hydroxide is not recovered afterwards, work out the total mass of lithium, in tonnes, that must be made to supply one year's worth of ammonia for such a farm. [1 tonne = 1000 kg]

Ammonia needed per farm per year = 130 acres x 0.0770 tonne/acre = 10.01 tonnes NH3. The lithium route fixes nitrogen as Li3N (6Li + N2 -> 2Li3N), then Li3N + 3H2O -> NH3 + 3LiOH. Since the lithium hydroxide is not recovered, 3 mol of Li are consumed per mol of NH3. Mass ratio Li:NH3 = (3 x 6.9)/17.0 = 20.7/17.0 = 1.218. Mass of Li = 10.01 x 1.218 = 12.2 tonnes.