Suggest how the cations in each of the following solution mixtures can be separated: (a) \(\mathrm{Na}^{+}\) and \(\mathrm{Cd}^{2+},(\mathbf{b}) \mathrm{Cu}^{2+}\) and \(\mathrm{Mg}^{2+},(\mathbf{c}) \mathrm{Pb}^{2+}\) and \(\mathrm{Al}^{3+},(\mathbf{d}) \mathrm{Ag}^{+}\) and \(\mathrm{Hg}^{2+}\) .

To separate Na+ and Cd2+ ions from the mixture, we can use the following steps: 1. Add an excess amount of \(\mathrm{H}_2\mathrm{S}\) gas into the solution. This will precipitate \(\mathrm{CdS}\) but leave \(\mathrm{Na}^+\) ions in the solution since \(\mathrm{Na}^+\) is not a precipitate with \(\mathrm{H}_2\mathrm{S}\). 2. Filter the solution to remove the \(\mathrm{CdS}\) precipitate and collect the filtrate containing \(\mathrm{Na}^+\) ions.

To separate Cu2+ and Mg2+ ions from the mixture, we can follow these steps: 1. Adjust the pH of the solution to around 10 by adding \(\mathrm{NH}_3\) or \(\mathrm{NaOH}\). This will precipitate \(\mathrm{Cu(OH)}_2\) while the \(\mathrm{Mg}^{2+}\) ions will remain in the solution. 2. Filter the solution to separate the \(\mathrm{Cu(OH)}_2\) precipitate from the solution containing \(\mathrm{Mg}^{2+}\) ions.

To separate Pb2+ and Al3+ ions from the mixture, follow these steps: 1. Add \(\mathrm{HCl}\) or \(\mathrm{NaCl}\) to the solution to form a precipitate of \(\mathrm{PbCl}_2\). The \(\mathrm{Al}^{3+}\) ions will not react, and hence will remain in the solution. 2. Filter the solution to separate the \(\mathrm{PbCl}_2\) precipitate and collect the supernatant containing \(\mathrm{Al}^{3+}\) ions.

To separate Ag+and Hg2+ ions from the mixture, follow this procedure: 1. Add \(\mathrm{HCl}\) or \(\mathrm{NaCl}\) to the solution. This will form a precipitate of \(\mathrm{AgCl}\) and \(\mathrm{Hg}_2\mathrm{Cl}_2\). 2. Filter the solution to separate the mixture of \(\mathrm{AgCl}\) and \(\mathrm{Hg}_2\mathrm{Cl}_2\) precipitates from the solution. 3. Rinse the mixture of precipitates with cold water to wash off any excess \(\mathrm{HCl}\) or \(\mathrm{NaCl}\). 4. Add a hot, concentrated solution of \(\mathrm{NH}_3\) to the mixture of precipitates. \(\mathrm{AgCl}\) will dissolve in \(\mathrm{NH}_3\) to form \(\mathrm{[Ag(NH}_3)_2]\mathrm{Cl}\) complex while \(\mathrm{Hg}_2\mathrm{Cl}_2\) will not dissolve since it is insoluble in \(\mathrm{NH}_3\). The resulting solution contains the \(\mathrm{Ag}+\) ions. 5. Filter the solution again to separate the supernatant containing the \(\mathrm{Ag}+\) ions from the undissolved \(\mathrm{Hg}_2\mathrm{Cl}_2\).