Physics · Electricity and magnetism · Grade 8

Electrolysis, Faraday's laws

How can a spoon be plated with copper, and how much current does it need?

The situation

In a workshop they want to coat an old steel spoon with a handsome layer of copper. The spoon is dipped into a solution of copper sulfate (CuSO₄) and connected to the “−” terminal of the source, while a copper plate is connected to the “+” terminal. After a few minutes the spoon takes on a reddish colour. What moves in the solution, what does the amount of copper deposited depend on, and how can the charge of the electron be found from this experiment?

Topic

Electric current in liquids, electrolysis. Copper-plating a spoon and Faraday's laws

Key ideas

Electrolytic dissociation
Faraday's laws
Electroplating

Formulas

{CuSO}_{4} \to {Cu}^{2 +} + {SO}_{4}^{2 -}

Electrolytic dissociation: a salt splits into ions in water even when there is no current.

m = k I t = k q

Faraday's first law: the mass of substance liberated is proportional to the charge passed; $k$ is the electrochemical equivalent.

k = \frac{1}{F} \cdot \frac{M}{n}

Faraday's second law: $M$ is the molar mass, $n$ is the ion's valency. For copper $k \approx 0.329$ mg/C.

F = e N_{A} \approx 96 485 C/mol, e = \frac{F}{N_{A}}

The Faraday constant is the charge of one mole of electrons; the charge of the electron is found from it.

v = u E

Drift speed of an ion: $u$ is the mobility (for Cu²⁺ ≈ $5.6 \cdot 10^{- 8}$ m²/(V·s)).

Theory

Electrolytes and dissociation

Aqueous solutions of salts, acids and alkalis are electrolytes. Water molecules are polar: they surround the ions and weaken the attraction between them by a factor of about 80, so the crystal breaks up into ions (dissociation). The ions are there even when there is no current — they just move at random. The blue colour of the solution comes from Cu²⁺ ions surrounded by water molecules. The “Drop in a crystal” button shows a crystal dissolving and splitting into pairs of ions.

Current in a liquid: ion mobility

A field $E$ is set up between the electrodes and the ions begin to drift in an orderly way: positive ions (cations) towards the cathode, negative ions (anions) towards the anode. The speed is $v = u E$ ; the mobility $u$ is very small, so the ions move only a few micrometres per second (the value in the HUD). Both kinds of ion carry the current together. Unlike in metals, if an electrolyte is heated its resistance decreases: the viscosity falls and the ions speed up. In the scene the motion of the ions is speeded up about 4000 times.

Electrolysis: what happens at the electrodes?

At the cathode (the spoon), copper ions pick up two electrons and become metal: ${Cu}^{2 +} + 2 e^{-} \to Cu$ . From the anode, the same number of copper ions pass into the solution: $Cu - 2 e^{-} \to {Cu}^{2 +}$ — the colour of the solution hardly changes, while the anode gets thinner. In the external wires the electrons travel from the anode through the source to the cathode. This process, in which a substance is liberated at the electrodes, is electrolysis.

Faraday's laws

First law: the mass of substance liberated is proportional to the charge, $m = k I t$ — on the graph $m (t)$ is a straight line. Second law: $k = M / (n F)$ . One ion brings a charge $n e$ , and one mole of ions needs a charge $n F$ . So the same charge liberates masses proportional to $M / n$ in different baths — compare copper and silver in the “Two baths” mode: $m_{A g} / m_{C u} = 107.9 / (63.5 / 2) \approx 3.4$ . $F = e N_{A}$ — electrolysis was one of the first pieces of evidence that charge is discrete (a multiple of the electron's charge).

Lab: the electrochemical equivalent of copper

With no current, weigh the dry spoon ( $m_{1}$ ). Connect the circuit, keep the current constant ( $I$ ) and record the time ( $t$ ). Switch off the current and weigh the spoon again ( $m_{2}$ ). Then $k = (m_{2} - m_{1}) / (I t)$ , $F = M / (n k)$ and $e = F / N_{A}$ . Sources of error: fluctuation of the current, washing and drying the spoon, the accuracy of the balance (here 1 mg). For an even coating the current density should be about 1–3 A/dm²; with too large a current the layer is porous and dark.

In everyday life and technology

Electroplating — coating objects with nickel, chromium, silver or gold (protection from rust and decoration). Electrotyping — making an exact metal copy of an object (B. Jacobi, 1838). Refining copper: the crude copper anode dissolves, 99.99 % pure copper is deposited on the cathode, and the precious metals remain in the anode sludge. Aluminium is obtained by electrolysis of alumina in molten cryolite at ≈ 950 °C — about 13–14 kW·h of energy per kg. Charging a battery is also electrolysis. Model: the current efficiency is 100 %, the bath resistance is approximate ( $κ \approx 3$ S/m), and the solution is kept uniform. For more on chemical sources of current, see the “Power sources, EMF, internal resistance” experiment.

Did you know?

Michael Faraday published the laws of electrolysis in 1833–1834; he also introduced the terms “electrode”, “anode”, “cathode” and “ion” into science, in consultation with William Whewell.
The method of obtaining aluminium by electrolysis of alumina in molten cryolite was discovered in 1886, independently of each other, by the American Charles Hall and the Frenchman Paul Héroult.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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