The solubility product constant for magnesium hydroxide, \(\operatorname{Mg}(\mathrm{OH})_{2}\), in water is \(K_{s p}=1.2 \times 10^{-11}(\mathrm{kmol} / \mathrm{m})^{3}\). If \(5 \mathrm{~g}\) of magnesium hydroxide were put into \(50 \mathrm{ml}\) of water and allowed to dissolve to equilibrium, estimate the molar conductivity of the solution at \(298 \mathrm{~K}\). (The mobility and diffusivity of \(\mathrm{Mg}^{2+}\) are not given in the tables. However, data for \(\mathrm{Ca}^{2+}\) exist in Table 3.12 and data for the infinite dilution conductivity of a Mg-based and Ca-based solution exist in Table 3.11. Based on that information, what is your best estimate for the mobility and diffusivity of \(\mathrm{Mg}^{2+}\) ?)

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TABLE 3.12 Ionic Mobilities and Diffusivities at Infinite Dilution in Aqueous Solution (25C) Cation Mobility (m/s-V) Diffusivity (m/s) +H 36.30 x 10-8 9.31 10-9 Li+ 4.01 x 10-8 1.03 x 10-9 Na+ 5.19 10-8 1.33 x 10-9 K+ 7.62 10-8 1.96 10-9 Rb+ 7.92 10-8 2.07 10-9 NH+ 7.60 10-8 Ca2+ 6.16 10-8 La+ 7.21 10-8 Anion Mobility (m/s-V) OH- 20.50 10-8 1.96 10-9 0.79 10-9 0.62 x 10-9 Diffusivity (m/s) 5.28 x 10-9 F 5.70 10-8 1.47 10-9 CH- 7.91 10-8 2.03 x 10-9 Br 8.13 x 10-8 2.08 x 10-9 I- 7.95 x 10-8 2.05 10-9 CO- 7.46 10-8 0.92 10-9 SO 8.25 x 10-8 1.06 x 10-9 CH,CO; 4.23 x 10-8 1.09 10-9