Final answer:
To calculate the mass of Ni²⁺ produced, we can use Faraday's law of electrolysis and stoichiometry. The mass of Ni²⁺ produced is approximately 0.45 g.
Step-by-step explanation:
To determine the mass of Ni²⁺ produced in solution, we need to calculate the number of moles of electrons passed through the cell. Given that a current of 67.0 A was passed for 13.0 hours, we can multiply the current by the time to get the total charge passed through the cell: 67.0 A * 13.0 h = 871 C. Since the cell is 85.0% efficient, the actual charge that participates in the reaction is 85.0% of 871 C, which is 740.35 C. Now, we can use the Faraday's law of electrolysis to determine the number of moles of electrons: 1 mole of electrons = 96,500 C (Faraday's constant). Therefore, the number of moles of electrons is 740.35 C / 96,500 C/mol = 0.007658 mol. Finally, using stoichiometry, we can calculate the mass of Ni²⁺ produced: 0.007658 mol * 58.7 g/mol (molar mass of Ni²⁺) = 0.45 g (rounded to two decimal places).