A beaker of water at contains calcium chloride (

PHYSICS · Subjective · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Condensed Matter, Materials & Soft Matter · Electrostatic fields and potential

Soft Matter at the Thermal Scale, Ch Forces between colloids and the stability of a dispersion

Problem

A beaker of water at

298\,\mathrm{K}

contains calcium chloride (

\mathrm{CaCl_2}

, a 2:1 salt that dissociates into

\mathrm{Ca^{2+}}

ions of concentration

c

and

\mathrm{Cl^-}

ions of concentration

2c

) at

c = 5\,\mathrm{mM}

. Calculate the Debye screening length, given that the linearisation of Poisson's equation sums the contribution of every ion species as

\kappa^2 \propto \sum_i n_i^\infty z_i^2

, so that the formula

\lambda_{\rm D} = 0.304\,\mathrm{nm}/\sqrt{c/\mathrm{M}}

for a 1:1 salt generalises to

\lambda_{\rm D} = 0.304\,\mathrm{nm}/\sqrt{I/\mathrm{M}}

, with the ionic strength

I = \tfrac12\sum_i c_i z_i^2

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