Question

A solution contains \(0.25 \mathrm{M} \mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}\) and \(0.25 \mathrm{M} \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\). 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 \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\)

Short answer

Yes, the metal ions can be separated by slowly adding Na2CO3, because the concentration of CO3²⁻ ions needed for 99% precipitation of Ni²⁺ (4.762 × 10⁻¹⁵) is less than the concentration of CO3²⁻ ions needed for Cu²⁺ precipitation (8.0 × 10⁻¹⁰).

Step-by-step solution

Write the precipitation equilibrium reactions

Precipitation reactions for Ni2+ and Cu2+ are given as follows, along with their solubility product constants (Ksp): \(NiCO_3 (s) \rightleftharpoons Ni^{2+} (aq) + CO_3^{2-} (aq)\) ; Ksp(NiCO3) = 1.3 × 10⁻¹⁶ \(CuCO_3 (s) \rightleftharpoons Cu^{2+} (aq) + CO_3^{2-} (aq)\) ; Ksp(CuCO3) = 2.0 × 10⁻¹₀

Calculate the CO32- concentration required for the precipitation of Ni2+

To calculate the CO3²⁻ concentration needed to initiate the precipitation of Ni²⁺ we need to use the solubility product constant (Ksp) for the NiCO3 reaction: \(Ksp = [Ni^{2+}][CO_3^{2-}]\) Given that the initial concentration of Ni2+ is 0.25 M: \([CO_3^{2-}] = \dfrac{Ksp(NiCO3)}{[Ni^{2+}]}\) Substitute values: \([CO_3^{2-}] = \dfrac{1.3 \times 10^{-16}}{0.25}\) \([CO_3^{2-}] = 5.2 \times 10^{-16}\)

Calculate the CO32- concentration required for the precipitation of Cu2+

To calculate the CO3²⁻ concentration needed to initiate the precipitation of Cu²⁺ we need to use the solubility product constant (Ksp) for the CuCO3 reaction: \(Ksp = [Cu^{2+}][CO_3^{2-}]\) Given that the initial concentration of Cu2+ is 0.25 M: \([CO_3^{2-}] = \dfrac{Ksp(CuCO3)}{[Cu^{2+}]}\) Substitute values: \([CO_3^{2-}] = \dfrac{2.0 \times 10^{-10}}{0.25}\) \([CO_3^{2-}] = 8.0 \times 10^{-10}\)

Determine if the two metals can be separated

To check if separation is possible, we need to calculate the minimum concentration of CO32- ions required to precipitate 99% of Ni²⁺, before Cu²⁺ starts to precipitate. Initial [Ni²⁺] = 0.25 M [CO32-] required for 99% precipitation of Ni²⁺ = (0.25 x 0.99) / [CO32-] calculated in Step 2 Substitute values: [CO3²⁻] required for 99% precipitation of Ni²⁺ = (0.25 x 0.99) / (5.2 x 10⁻¹⁶) = 4.762 × 10⁻¹⁵ Comparing the required concentration of CO32- ions for 99% precipitation of Ni²⁺ to that required for Cu²⁺ precipitation: 4.762 × 10⁻¹⁵ < 8.0 × 10⁻¹⁰ Since the concentration of CO3²⁻ ions needed for 99% precipitation of Ni²⁺ is less than the concentration of CO3²⁻ ions needed for Cu²⁺ precipitation: Yes, the metal ions can be separated by slowly adding Na2CO3.

Key concepts

Solubility Product Constant

The solubility product constant, often abbreviated as Ksp, is a crucial concept in understanding precipitation reactions. It quantifies the extent to which a solid will dissolve in water to form its ionic components. For a given salt, the Ksp value is determined by the equilibrium concentrations of the dissociated ions in a saturated solution. If the concentration of the ions in solution exceeds the Ksp, precipitation occurs. Conversely, if the ion product is below the Ksp, the solid remains dissolved.

For example, in the solution provided in the exercise, the precipitation of nickel carbonate, NiCO3, and copper carbonate, CuCO3, is governed by their respective solubility product constants. These values (Ksp(NiCO3) = 1.3 x 10⁻¹⁶ and Ksp(CuCO3) = 2.0 x 10⁻¹⁰) indicate the concentration thresholds needed for each compound to start forming a precipitate. Lower Ksp values mean that the salt is less soluble, thus precipitating more readily.

Understanding how Ksp values interact with concentration helps determine when a metal will precipitate from solution, key for any separation process that relies on precipitation.

Separation Techniques

Separation techniques in chemistry often involve exploiting differences in physical or chemical properties between substances. In the case of separating metal ions, precipitation is a widely used technique. This method takes advantage of the varying solubility of different ionic compounds in a solution.

To effectively separate metal ions using precipitation, a reagent is added that forms an insoluble compound with one of the ions while leaving the other in solution. In the provided exercise, sodium carbonate (Na2CO3) is used to separate Ni²⁺ and Cu²⁺ ions by precipitating them as carbonates. By carefully selecting the amount of Na2CO3 added, one can control which metal ion precipitates first, based on their solubility products. This is crucial for achieving a successful separation.

This kind of separation technique is beneficial due to its simplicity and efficiency, especially when dealing with mixtures of ions that have distinct solubility profiles. The right strategy ensures that one metal ions precipitates almost completely before the other begins to form a solid, enabling effective isolation.

Metal Ion Precipitation

Metal ion precipitation is a process used to remove ions from solutions as a solid product, commonly in the form of an insoluble salt. This reaction typically depends on the ionic product exceeding a specific solubility product constant (Ksp).

In the context of the given exercise, the task is to separate nickel (Ni²⁺) and copper (Cu²⁺) ions by adding carbonate ions from Na2CO3. Each metal ion has a unique solubility product with carbonate ions, signifying the concentration at which it begins to precipitate. By gradually adding Na2CO3, it is possible to reach the Ksp of one metal carbonate before affecting the other. This selective precipitation ensures that one metal ion forms a solid first, allowing for effective separation.

Precipitation reactions are widely used in industrial processes, wastewater treatment, and analytical chemistry to recover or eliminate metal ions. It is crucial to maintain precise control over reaction conditions to achieve the desired precipitate and successful ion separation.