= Solution
A $0.10\ \mathrm M$ formula-unit <concentration> of fully dissociated $\mathrm{AlCl_3}$ gives $0.10\ \mathrm M$ trivalent cations and $0.30\ \mathrm M$ chloride:
$$
I=\frac12[0.10(3)^2+0.30(1)^2]=0.60\ \mathrm M.
$$
At unchanged <temperature> and <permittivity>, the <Debye–Hückel screening length> scales as $I^{-1/2}$, giving \b[$\kappa^{-1}=0.96/\sqrt6\simeq0.39\ \mathrm{nm}$]. It falls by a factor $\sqrt6$, not by three. This is a formal screening estimate: at this <ionic strength>, trivalent-ion activity, finite <ion> size, hydrolysis and specific <adsorption> make the ideal dilute model quantitatively limited.
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