1. Determine the Half-Reaction and Faraday's Constant
* Half-reaction: The relevant half-reaction is the reduction of bismuth(III) ions:
Bi³⁺(aq) + 3e⁻ → Bi(s)
* Faraday's Constant (F): This constant represents the charge carried by one mole of electrons, approximately 96,485 C/mol.
2. Calculate the Moles of Bismuth
* Molar mass of Bi: 208.98 g/mol
* Moles of Bi: (10.0 g Bi) / (208.98 g/mol) = 0.0478 mol Bi
3. Calculate the Total Charge Required
* Electrons per mole of Bi: From the half-reaction, 3 moles of electrons are required to produce 1 mole of Bi.
* Total charge (Q): (0.0478 mol Bi) * (3 mol e⁻/mol Bi) * (96,485 C/mol e⁻) = 13,850 C
4. Calculate the Time
* Current (I): 25.0 A (amps)
* Time (t): Q/I = (13,850 C) / (25.0 A) = 554 seconds
5. Convert to Minutes (Optional)
* Time (t): (554 seconds) / (60 seconds/minute) = 9.23 minutes
Therefore, it would take approximately 9.23 minutes to produce 10.0 g of bismuth using a current of 25.0 amps.
