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Limiting molar conductivity of $\mathrm{Mg}^{2+}$ and $\mathrm{Cl}^{-}$ ions in water is 106.0 and $76.3 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. The limiting molar conductivity of magnesium chloride (in $\mathrm{S} \mathrm{cm}^2 \mathrm{~mol}^{-1}$ ) in water is
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The correct answer is:
258.6
Molar conductivity of
$$
\mathrm{Mg}^{2+}\left(\Lambda_{\mathrm{mg}^{2+}}\right)=106 \mathrm{Scm}^2 / \mathrm{mol}
$$
Molar conductivity of $\mathrm{Cl}^{\ominus}$ ion $\left(\Lambda^{\circ}{ }_{\mathrm{Cl}}{ }^{-}\right)$
$$
=76.3 \mathrm{~S} \mathrm{~cm}^2 / \mathrm{mol}
$$
Molar conductivity of $\mathrm{MgCl}_2=\Lambda^{\circ}{ }_m$ of $\mathrm{Mg}^{2+}+2 \Lambda^{\circ} \mathrm{m}$ of $\mathrm{Cl}^{-}=(106+2 \times 76.3) \mathrm{S} \mathrm{cm}^2 / \mathrm{mol}$
$$
=258.6 \mathrm{~S} \mathrm{~cm}^2 / \mathrm{mol}
$$
$$
\mathrm{Mg}^{2+}\left(\Lambda_{\mathrm{mg}^{2+}}\right)=106 \mathrm{Scm}^2 / \mathrm{mol}
$$
Molar conductivity of $\mathrm{Cl}^{\ominus}$ ion $\left(\Lambda^{\circ}{ }_{\mathrm{Cl}}{ }^{-}\right)$
$$
=76.3 \mathrm{~S} \mathrm{~cm}^2 / \mathrm{mol}
$$
Molar conductivity of $\mathrm{MgCl}_2=\Lambda^{\circ}{ }_m$ of $\mathrm{Mg}^{2+}+2 \Lambda^{\circ} \mathrm{m}$ of $\mathrm{Cl}^{-}=(106+2 \times 76.3) \mathrm{S} \mathrm{cm}^2 / \mathrm{mol}$
$$
=258.6 \mathrm{~S} \mathrm{~cm}^2 / \mathrm{mol}
$$
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