Question

Without performing detailed calculations, indicate whether either of the following compounds is appreciably soluble in \(\mathrm{NH}_{3}(\mathrm{aq}):(\mathrm{a}) \mathrm{CuS}, K_{\mathrm{sp}}=6.3 \times 10^{-36},\)(b) \(\mathrm{CuCO}_{3}, K_{\mathrm{sp}}=1.4 \times 10^{-10} .\) Also use the fact that \(K_{\mathrm{f}}\) for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is \(1.1 \times 10^{13}\).

Short answer

Both CuS and CuCO3 are appreciably soluble in NH3(aq), given the fact that their Kf for [Cu(NH3)4]2+ complex formation is significantly greater than their Ksp.

Step-by-step solution

Understand the Problem

When the compound containing copper, either CuS or CuCO3, is dissolved in an aqueous solution of ammonia, the copper ions react with the NH3 to form a complex ion, [Cu(NH3)4]2+. This process is accompanied by a significant increase in solubility if the equilibrium constant for the formation of the complex ion (Kf) is much greater than the solubility constant (Ksp) of the compound.

Solubility of CuS in NH3(aq)

First, for CuS, the Ksp given is \(6.3 \times 10^{-36}\). This value is very small, indicating that the compound is barely soluble. However, the Kf for formation of the complex ion is \(1.1 \times 10^{13}\), a very large number. If the Kf is much greater than the Ksp, it indicates that CuS is appreciably soluble in an aqueous solution of ammonia as the reaction will be pushed towards the formation of the complex ion.

Solubility of CuCO3 in NH3(aq)

Next, for CuCO3, the Ksp given is \(1.4 \times 10^{-10}\), also very small, indicating the compound is barely soluble. However, similarly to CuS, the large Kf value suggests that CuCO3 may also be appreciably soluble in NH3(aq) since the formation of the complex ion is favored.

Key concepts

Ksp (Solubility Product Constant)

The solubility product constant, or Ksp, is a key factor in determining how soluble a compound is in a given solution. It represents the equilibrium constant for the dissolution of a sparingly soluble compound. A smaller Ksp value indicates a lower solubility of the compound in water.

• CuS has a Ksp of \(6.3 \times 10^{-36}\), which is extremely small.
• CuCO3 has a Ksp of \(1.4 \times 10^{-10}\), also indicating low solubility.

These values tell us that both CuS and CuCO3 are barely soluble in water. However, the presence of certain ions or molecules in a solution can affect this solubility. This concept becomes critical when considering complex ion formation, especially in solutions like ammonia (NH3), which can cause complex ions to form and increase a compound's solubility.

Complex Ion Formation

Complex ion formation can significantly affect the solubility of certain compounds. In an aqueous solution, metal ions can react with molecules or ions to form complex ions, which are more stable and often more soluble.
For instance, both CuS and CuCO3 contain copper ions that can interact with ammonia (NH3) present in the solution to form the complex ion \([\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+}\).

• This transformation is because the copper ion forms a stable complex with four ammonia molecules.
• The stability of this complex ion can increase the copper compound's apparent solubility in aqueous solutions containing ammonia.

Thus, even for compounds with low Ksp values, the formation of complex ions can push the equilibrium towards the dissolution side, thus enhancing solubility when a compound like NH3 is added.

Equilibrium Constant (Kf)

The Equilibrium Constant for the formation of a complex ion, denoted as Kf, quantifies how easily a metal ion forms a complex in solution. This value is exceptionally large for copper-ammonia complexes, reaching \(1.1 \times 10^{13}\).

• This high Kf signifies that the reaction heavily favors the formation of the complex ion \([\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+}\).
• When Kf is significantly larger than Ksp, as in the case of CuS and CuCO3 with NH3, it indicates that these compounds can dissolve more readily due to the formation of such stable complexes.

Thus, even though CuS and CuCO3 are nearly insoluble in pure water, the large Kf compared to the Ksp indicates an appreciable solubility in ammonia solution due to complex ion formation.