 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/4/d/iii/solution

The Stern layer is the compact near-surface layer of specifically adsorbed or closely associated ions. The diffuse layer is the more extended, thermally distributed excess of counterions that screens the surface charge.

For water near

2 5^{\circ} C

, the Debye length can be written

λ_{D} ≃ \frac{0.304 nm}{I / ( mol L ^{- 1} )}, I = \frac{1}{2} \sum_{i} c_{i} z_{i}^{2} .

For

0.01

M KCl,

I = 0.01

M and $λ_{D} ≃ 3.0$ nm. For a fully dissociated 2:2 electrolyte at the same formula-unit concentration,

I = 4 c = 0.04

M, giving $λ_{D} ≃ 1.5$ nm, half as large. These are linear-screening estimates, not sharp boundaries of the diffuse layer.

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