Problem 143 - A Complete Resource Book in Chemistry for JEE Main

Question

When excess of \(\mathrm{KCN}\) is added to aqueous solution of copper sulphate a co-ordination compound \(\mathrm{K}_{\mathrm{x}}\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]\) is formed. The value of \(\mathrm{x}\) is ____ .

Step-by-Step Solution

Answer

The value of \(x\) is 2.

Step 1: Understand the Reaction

When an excess of potassium cyanide (\(\mathrm{KCN}\)) is added to a solution of copper sulfate (\(\mathrm{CuSO}_{4}\)), a coordination complex is formed. This complex is denoted as \(\mathrm{K}_{x}\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]\). The complex formation is due to the ligand exchange reaction where \(\mathrm{CN}^{-}\) ions replace the water molecules bonded to the \(\mathrm{Cu}^{2+}\) ions.

Step 2: Determine the Charge on the Coordination Complex

To find the value of \(x\), we need to first determine the charge of the complex ion \(\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]\). The cyanide ions, \(\mathrm{CN}^{-}\), each have a charge of -1. With 4 cyanide ions, the total negative charge is -4. Copper in the complex is in the +2 oxidation state initially, so its charge after forming \(\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]\) must balance the total charge of \(+2 - 4 = -2\). Thus, the coordination complex \(\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]\) carries a charge of \(-2\).

Step 3: Determine the Number of Potassium Ions Required for Neutrality

Potassium ions (\(\mathrm{K}^+\)) have a charge of +1. Since the coordination complex has a charge of \(-2\), we need two \(\mathrm{K}^+\) ions to balance out this negative charge and achieve an electrically neutral compound. Therefore, \(x = 2\).

Key Concepts

Ligand Exchange Reaction

A ligand exchange reaction is a process in which one or more ligands in a coordination compound are replaced by other ligands. In our example, the initial reaction involves an aqueous solution of copper sulfate (\(\text{CuSO}_4\)). When potassium cyanide (\(\text{KCN}\)) is introduced to this solution, the cyanide ions (\(\text{CN}^-\)) act as ligands that replace the water molecules initially bonded to the \(\text{Cu}^{2+}\) ions. The driving force for this ligand exchange can be:

• Stability of the newly formed complex
• The strength of the new ligands binding to the central metal ion versus the old

Cyanide is a particularly strong ligand and forms a more stable complex than water, making it easier for \(\text{CN}^-\) to replace water molecules in the coordination sphere around copper.

Charge Balance in Coordination Complexes

Charge balance is crucial in coordination complexes as it determines the neutrality of the entire compound. Each component of a coordination complex - the central metal ion and its surrounding ligands - contributes to the overall charge.In \(\left[\text{Cu}(\text{CN})_4\right]\), the copper is in the oxidation state of \(+2\), while each of the four cyanide ligands carries a \(-1\) charge. Together, the ligands contribute \(-4\) to the charge, making the total charge of the complex \(+2 - 4 = -2\).For an electrically neutral compound, this negative charge needs counterbalancing by cations. Here, two potassium ions, each with a \(+1\) charge, are added to achieve electrical neutrality:

• This results in the compound: \(\text{K}_2\left[\text{Cu}(\text{CN})_4\right]\)

Balancing charges in coordination complexes ensures stability and neutrality of compounds formed during ligand exchange reactions.

Oxidation States in Coordination Compounds

Oxidation states in coordination compounds refer to the formal charge that an atom appears to have when electrons are assigned according to certain rules. Understanding oxidation states is critical for describing electron distribution and predicting reactions.In our copper cyanide complex, \(\left[\text{Cu}(\text{CN})_4\right]\), copper starts in the oxidation state of \(+2\). This indicates that as per these conventions, copper has effectively 'lost' two electrons within this complex.

• The oxidation state helps identify the electronic interactions and bonding nature.
• In ligand exchange, determining the oxidation state informs us how the central metal will interact with new ligands.

Thus, the oxidation state is not only critical for balance but also helps in understanding chemical behavior and reactivity in coordination chemistry. It provides insight into the compound's electronic composition.