A solution contains 0.25\(M \mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}\) and 0.25\(M \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\) Can the metal ions be separated by slowly adding \(\mathrm{Na}_{2} \mathrm{CO}_{3} ?\) Assume that for successful separation 99\(\%\) of the metal ion must be precipitated before the other metal ion begins to precipitate, and assume no volume change on addition of \(\mathrm{Na}_{2} \mathrm{CO}_{3}.\)

When sodium carbonate is added, the precipitate of nickel carbonate and copper carbonate can form. The precipitation reactions are: 1) Ni²⁺(aq) + CO₃²⁻(aq) ⇌ NiCO₃(s) 2) Cu²⁺(aq) + CO₃²⁻(aq) ⇌ CuCO₃(s) Now, let's write the solubility product expressions for both reactions: For Nickel Carbonate: \(K_{sp1} = \mathrm{[Ni^{2+}][CO_3^{2-}]} \) For Copper Carbonate: \(K_{sp2} = \mathrm{[Cu^{2+}][CO_3^{2-}]} \)

From tabulated data, the solubility product constants (Ksp) for the nickel carbonate and copper carbonate are: \(K_{sp1} = \mathrm{1.3\times10^{-7}}\) (for Nickel Carbonate) \(K_{sp2} = \mathrm{2.5\times10^{-10}}\) (for Copper Carbonate)

We need to find the concentration of carbonate ions required to precipitate 99% of each metal ion. Let's calculate the CO₃²⁻ concentration required for each metal ion to reach 99% precipitation: For Nickel Carbonate: \[[\mathrm{CO_3^{2-}}] = \frac{K_{sp1}}{[\mathrm{Ni^{2+}} \times 0.01]} = \frac{1.3\times10^{-7}}{\mathrm{0.25M \times 0.01}} = 5.2\times10^{-7} M\] For Copper Carbonate: \[ [\mathrm{CO_3^{2-}}] = \frac{K_{sp2}}{[\mathrm{Cu^{2+}} \times 0.99]} = \frac{2.5\times10^{-10}}{\mathrm{0.25M \times 0.99}} = 1.01\times10^{-9} M\]

To achieve the successful separation of the metal ions, the carbonate concentration required for 99% precipitation of nickel should be lower than that for copper precipitation to begin. Comparing the calculated carbonate concentrations above: \[ 5.2\times10^{-7} M > 1.01\times10^{-9} M\] Since the carbonate concentration requirement for nickel precipitation (found in Step 3) is higher than that required for copper precipitation to begin, we can conclude that adding sodium carbonate slowly to the solution will not result in successful separation of 99% nickel ions before copper ions begin to precipitate. In summary, the metal ions cannot be separated by slowly adding sodium carbonate, as the requirement for successful separation i.e. 99% of nickel ions precipitation before copper ions start to precipitate is not met.