A nickel plate of area 8 cm² is to be electrolytically plated with palladium to a thickness of 5 µm. The density of palladium is 12.0 g cm⁻³, its molar mass is 106.42 g mol⁻¹, and the current efficiency is 70 %. If a constant current of 1.5 A is passed, how long (in seconds) will it take to deposit the desired layer? Reaction: Pd²⁺ + 2e⁻ → Pd. Use F = 96485 C mol⁻¹.
Answer
≈ 83 s
The correct answer is ≈ 83 s — Time needed: t = Q / I = 124.3 C / 1.5 A = 82.9 s ≈ 83 s.
Step-by-step solution
- Compute volume of Pd deposited: V = area × thickness = 8 cm² × 5×10⁻⁴ cm = 0.004 cm³.
- Find mass: m = ρV = 12.0 g cm⁻³ × 0.004 cm³ = 0.048 g.
- Calculate moles of Pd: n = m / M = 0.048 g / 106.42 g mol⁻¹ = 4.51×10⁻⁴ mol.
- Ideal charge required (n=2 e⁻ per Pd): Q₀ = n × 2F = 4.51×10⁻⁴ mol × 2 × 96485 C mol⁻¹ = 87.0 C.
- Actual charge accounting for 70 % efficiency: Q = Q₀ / 0.70 = 124.3 C.
- Time needed: t = Q / I = 124.3 C / 1.5 A = 82.9 s ≈ 83 s.
Common mistake: Ignoring current efficiency in the calculation of required charge
Concept tested: Faraday's laws of electrolysis
Published · How this solution was prepared and checked
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