Silver Electroplating: Efficiency or Silver Ion Depletion?
A technician electroplates steel teaspoons with silver using a silver anode and a silver nitrate electrolyte. The current is 0.500 A and the plating time is 30.0 min. The specification requires a silver coating of 0.900 g per spoon. The technician calculates the theoretical mass using Faraday's laws and obtains about 1.01 g, but the actual mass gain is 0.860 g. The bath contains 0.200 mol L−1 Ag+ and the cathode is a spoon of surface area 12.0 cm2. A rival supplier claims the low mass is because the Ag+ has been 'used up', and suggests increasing the silver nitrate concentration. The technician must decide whether the current efficiency, the anode reaction, or the Ag+ concentration is the real issue. Faraday constant = 96 485 C mol−1; M(Ag) = 107.9 g mol−1.
1. Calculate the theoretical mass of silver deposited from 0.500 A for 30.0 min. Compare it with the specification and the actual mass gain.
Read the worked answer
Q = I × t = 0.500 A × (30.0 × 60 s) = 900 C. n(e−) = Q/F = 900 C / 96 485 C mol−1 = 9.33 × 10−3 mol. Ag+ + e− → Ag, so n(Ag) = n(e−) = 9.33 × 10−3 mol. m(theoretical) = n × M = 9.33 × 10−3 mol × 107.9 g mol−1 = 1.01 g. The specification needs 0.900 g, and the theoretical amount is enough. The actual gain is 0.860 g, which is just below the specification. The shortfall is not because the theoretical calculation is too low; it is because not all the current produced silver.
2. Calculate the current efficiency. Explain why the actual mass is lower than the theoretical mass and why the Ag+ concentration is not the main problem.
Read the worked answer
Current efficiency = (actual mass / theoretical mass) × 100 = (0.860/1.01) × 100 = 85.1%. The missing current is used in side reactions, such as reduction of water or dissolved oxygen at the cathode, or in non-faradaic processes. Some silver may also be deposited as a non-adherent powder that falls off. The Ag+ concentration is not the main problem: 0.200 mol L−1 is a large reservoir, and the silver anode dissolves to replenish Ag+ as Ag → Ag+ + e−. Increasing silver nitrate concentration would not fix a current-efficiency problem and could waste chemicals; better control of current density, stirring and cathode surface preparation is needed.
3. The standard reduction potentials are Ag+/Ag = +0.80 V and Fe2+/Fe = −0.44 V. Calculate E°cell for Ag+(aq) + Fe(s) → Ag(s) + Fe2+(aq). Explain why electroplating is used instead of simply dipping the spoon in silver nitrate.
Read the worked answer
E°cell = E°(cathode) − E°(anode) = +0.80 − (−0.44) = +1.24 V. Positive E°cell means ΔG° is negative, so the reaction is spontaneous. If a clean iron surface were dipped in AgNO3, silver would tend to deposit while iron dissolves. However, uncontrolled spontaneous deposition gives a loose, powdery, non-adherent coating and etches the steel; the reaction also consumes Ag+ near the surface. Electroplating controls the rate and thickness by applying an external current, and the electrolyte and current density can be adjusted for an adherent coating. The spoon may also have an oxide layer that slows spontaneous deposition. Electroplating is therefore used for control and coating quality, not because the reaction is non-spontaneous.