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

Short answer

The value of \(x\) is 3.

Step-by-step solution

Understand the Reaction

When excess \(\text{KCN}\) is added to \(\text{CuSO}_4\), complex ion \(\left[\text{Cu(CN)}_4\right]^{3-}\) is formed, paired with \(\text{K}^+\) ions. This means copper changes its state from \(\text{Cu}^{2+}\) in \(\text{CuSO}_4\) to \(\text{Cu}^+\) in the coordination compound. The cyanide ion \(\text{CN}^-\) acts as a ligand.

Determine the Charge of the Coordination Compound

Determine the charge of the complex ion \(\left[\text{Cu(CN)}_4\right]^{3-}\). Each \(\text{CN}^-\) ion contributes a \(-1\) charge, and since there are four \(\text{CN}^-\) ions, they contribute a total \(-4\) charge. Copper is in the \(+1\) oxidation state, so the total charge on \(\left[\text{Cu(CN)}_4\right]\) is \(-3\) (\(+1 + (-4) = -3\)).

Balance the Charges with Potassium Ions

Since the complex ion has a \(-3\) charge, three potassium ions \(\text{K}^+\) are needed to balance this negative charge. This means that the coordination compound formula should be \(\text{K}_3\left[\text{Cu(CN)}_4\right]\).

Identify the Value of \(x\)

In the formula \(\text{K}_x\left[\text{Cu(CN)}_4\right]\), \(x\) represents the number of \(\text{K}^+\) ions needed for charge balance. Since we calculated that 3 \(\text{K}^+\) ions are required, \(x = 3\).

Key concepts

Coordination Compounds

Coordination compounds are fascinating chemical entities formed by the combination of central metal atoms or ions with surrounding molecules or ions known as ligands. These ligands form coordinate covalent bonds with the metal center. In our example, copper from copper sulfate acts as the central metal, bonding with cyanide ligands to form a new coordination compound. Coordination compounds are essential in chemistry because they expand the range of possible chemical behaviors and interactions. They are found in various applications, such as catalysis, medicine, and materials science.

Oxidation States

Oxidation states, also known as oxidation numbers, help us understand the electron distribution in atoms during chemical reactions. In our coordination compound example, the copper in copper sulfate (\(\text{CuSO}_4\)) originally has an oxidation state of \(+2\). However, when it forms a complex with cyanide ions (\(\text{CN}^-\)), the oxidation state changes to \(+1\). This change results from the transfer of electrons between copper and the ligands. Understanding oxidation states is crucial for predicting the chemical behavior and reactions of compounds.

Ligands

Ligands are ions or molecules that bind to central metal atoms within coordination compounds. They play a crucial role in determining the structure and properties of the compound. In the example we are considering, cyanide ions \(\text{CN}^-\) serve as ligands, coordinating with a copper ion. Ligands are important because they affect the geometry and electronic properties of the metal center in the compound. There are many types of ligands, including monodentate (binding through a single atom) and polydentate (binding through multiple atoms) types. Their ability to donate electron pairs to the a metal is what characterizes them as ligands.

Charge Balance

Achieving charge balance is a key concept when studying coordination compounds. This ensures that compounds remain neutral overall. In our exercise, the complex ion \(\left[\text{Cu(CN)}_4\right]^{3-}\) carries a \(-3\) charge. To balance this negative charge, three potassium ions \(\text{K}^+\), having a positive charge each, are required. Thus, the formula for the complete coordination compound becomes \(\text{K}_3\left[\text{Cu(CN)}_4\right]\). Charge balance is fundamental to correctly writing chemical formulas for coordination compounds, as it helps to maintain neutrality and stability in the compound.