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Answer :
Final answer:
To determine the time needed to electroplate 175 g of nickel using a 10.0 A current, we calculate the moles of nickel, determine the total charge required using Faraday's Law, and then convert the charge to time. The required time is 16.0 hours. C. 16.0 hr
Explanation:
To calculate the time needed to plate out 175 g of nickel from a Ni²⁺ solution when a current of 10.0 A is applied, the first step is to determine the amount (in moles) of Ni that corresponds to 175 g. The molar mass of nickel is approximately 58.69 g/mol.
To find the moles of nickel, divide the mass of nickel by its molar mass:
Moles of Ni = 175 g ÷ 58.69 g/mol = 2.98 mol
The next step is to use Faraday's Law of Electrolysis, which states that the amount of substance liberated at an electrode is directly proportional to the quantity of electricity that flows through the cell. Since nickel is a divalent metal (Ni²⁺), each mole of nickel requires 2 moles of electrons to be reduced and deposited.
Total moles of electrons needed = 2.98 mol Ni × 2 mol e⁺/mol Ni = 5.96 mol e⁺
Since 1 mole of electrons is equivalent to 1 Faraday (approximately 96485 coulombs), the total charge needed to deposit 175 g of nickel is:
Charge = 5.96 mol e⁺ × 96485 Coulombs/mol e⁺ = 575110 Coulombs
To find the time, we divide the total charge by the current:
Time = 575110 Coulombs ÷ 10.0 A = 57511 seconds
Since there are 3600 seconds in an hour, convert seconds to hours:
Time in hours = 57511 s ÷ (1 hour/3600 s) = 15.975 hours
Therefore, the time needed to plate out 175 g of nickel is 16.0 hours, which corresponds to answer choice C.
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