A stainless‑steel spoon of area 20 cm² is to be electro‑plated with silver to a thickness of 3 µm. Density of Ag = 10.5 g cm⁻³, molar mass = 107.87 g mol⁻¹. A constant current of 0.60 A is passed and the current efficiency is 92 %. For the reduction reaction Ag⁺ + e⁻ → Ag, calculate the time required (in seconds) to obtain the desired coating. Use F = 96485 C mol⁻¹.

Step-by-step solution

1. Convert thickness to centimetres: 3\,$\mu \text{m}$=3$\times 10^{-4}$\,$\text{cm}$.
2. Calculate the volume of Ag needed: V = area $\times$ thickness = 20\,${\text{cm}}^2$ $\times$ 3$\times 10^{-4}$\,$\text{cm}$=6$\times 10^{-3}$\,${\text{cm}}^3$ = 0.006\,${\text{cm}}^3$.
3. Find the mass: m = density $\times$ volume = 10.5\,${\text{g cm}}^{-3}\times 0$.006\,${\text{cm}}^3$ = 0.063\,$\text{g}$.
4. Convert mass to moles: $n_{Ag}$= m/M = 0.063\,$\text{g}$/107.87\,${\text{g mol}}^{-1}$=5.85$\times 10^{-4}$\,$\text{mol}$.
5. Electrons required (n=1 per Ag): $Q_{theoretical}=n_{Ag}\times$ F =5.85$\times 10^{-4}\times 96485$ = 56.4\,$\text{C}$.
6. Adjust for current efficiency: $Q_{actual}=Q_{theoretical}$/0.92 = 56.4/0.92 = 61.3\,$\text{C}$.
7. Time = $Q_{actual}$/I = 61.3\,$\text{C}$/0.60\,$\text{A}$=102\,$\text{s}$ $\approx$ 1.0$\times 10^2$\,$\text{s}$.

Concept tested: Electroplating charge‑time calculation

Published 16 September 2026 · How this solution was prepared and checked