Why does a small anode with a large cathode corrode so fast, and how does overvoltage affect corrosion?

In one line

Corrosion is intense when the anodic area is small compared with the cathodic area, and it is slower when the hydrogen overvoltage on the metal is high.

Explained simply

Area effect: the cathode "demands" electrons in proportion to its area. If the cathode is huge and the anode tiny, that tiny anode must supply all the electrons, so it dissolves very fast, like one cashier serving a crowd of customers.

Overvoltage: hydrogen gas does not form easily on every metal surface. Some metals need an extra voltage (overvoltage) before H₂ is released. If that barrier is high, the cathode reaction is slow and the whole corrosion cell slows down.

How it works

1. In a corrosion cell, electrons released at the anode = electrons consumed at the cathode.
2. Current density at anode = I / A_anode. If A_cathode ≫ A_anode, the cathodic reaction can proceed fast, total current I is large, and it is concentrated on a small anodic area. Hence rate ∝ A_cathode/A_anode.
3. For overvoltage: the cathodic reaction 2H⁺ + 2e⁻ → H₂ needs a potential more negative than the theoretical value. The extra required is the hydrogen overvoltage, which depends on the metal surface.
4. High overvoltage → slow H₂ evolution → slow corrosion. Lowering overvoltage speeds corrosion.

Key formula

\( \text{Rate of anodic corrosion} \propto \dfrac{\text{Cathodic area}}{\text{Anodic area}} \)

Quick example

• Area: copper plates fastened with steel rivets → small steel anodes and a large copper cathode → rivets corrode rapidly. Steel plates with copper rivets → large anode, small cathode → slow, spread-out corrosion. Similarly, a small break in a cathodic coating like tin on iron leads to deep pitting of the exposed iron.
• Overvoltage: pure zinc in dilute H₂SO₄ corrodes slowly because hydrogen overvoltage on zinc is high. Add a few drops of CuSO₄: copper deposits on zinc, H₂ now evolves on copper where overvoltage is low, and zinc corrodes much faster.

Common mistakes

• Reversing the area rule (large anode + small cathode is the safer combination).
• Defining overvoltage as the cell voltage. It is the excess voltage needed over the theoretical value for gas evolution at an electrode.
• Painting only the anodic metal in a dissimilar-metal joint; a scratch then creates a tiny anode next to a big bare cathode. If only one is painted, paint the cathode (or both).

How MU asks it

"Explain the effect of relative areas of anode and cathode on corrosion with example" (3 marks), "Explain the role of hydrogen overvoltage in corrosion" (3 marks), or as part of a factors question (5–6 marks). For full marks: the principle in one line, the reason in terms of electron demand, and the rivet or Zn/CuSO₄ example.