Final answer:
The mass of cobalt metal that will be deposited from a solution containing Co²⁺ ions by applying a current of 1.08 A for 38.9 minutes is 1.361 grams.
Step-by-step explanation:
To calculate the mass of cobalt metal deposited from a solution containing Co²⁺ ions by electrolysis, we use the equation:
mass = (ItM)/(nF)
where I is the current in amperes, t is the time in seconds, M is the molar mass of cobalt, n is the number of moles of electrons required for the reduction of one mole of Co²⁺ to cobalt metal, and F is Faraday's constant (approximately 96,485 C/mol). Let's calculate the mass using the given values:
- I = 1.08 A (current)
- t = 38.9 minutes × 60 seconds/minute = 2334 seconds (convert minutes to seconds)
- M = 58.93 g/mol (molar mass of cobalt)
- n = 2 (cobalt is reduced from Co²⁺, thus requires 2 moles of electrons)
- F = 96,485 C/mol (Faraday’s constant)
mass = (1.08 A × 2334 s × 58.93 g/mol) / (2 × 96,485 C/mol)
mass = 1.361 grams of cobalt (rounded to three significant figures)
Therefore, 1.361 grams of cobalt will be deposited.