Question

The oxidation state of \(\mathrm{Fe}\) in \(\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) is (a) \(+2\) (b) \(+3\) (c) \(+4\) (d) \(+6\)

Short answer

+2

Step-by-step solution

Understand Oxidation States

The oxidation state or oxidation number is an indicator of the degree of oxidation of an atom in a chemical compound. The sum of the oxidation states of all atoms in a molecule or polyatomic ion must equal the total charge of the molecule or ion.

Assign Oxidation States to Known Atoms

In the complex \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})_{6}]\), we know that potassium \(\mathrm{K}\) has an oxidation state of +1. Cyanide, \(\mathrm{CN}\), is a polyatomic ion with a charge of -1. Since there are 6 cyanide ions, their total charge will be -6.

Determine the Total Charge of the Complex Ion

The complex ion \(\mathrm{Fe}(\mathrm{CN})_{6}\) has a charge that equals the charge of 4 potassium ions, which is +4 since each \(\mathrm{K}\) ion has a charge of +1.

Calculate the Oxidation State of Iron (Fe)

The sum of the oxidation states in the complex ion must equal the charge of the complex ion. Since the total charge must be +4 and the total charge provided by the cyanide ions is -6, the oxidation state of iron must be such that when added to -6, the result is +4. This gives us \(\mathrm{Fe}\)'s oxidation state as +2.

Key concepts

Oxidation number in coordination compounds

Understanding the oxidation number, also known as oxidation state, in coordination compounds is fundamental in the realm of inorganic chemistry. It represents the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. Coordination compounds, which consist of complex ions and ligands, often present a challenge when determining oxidation states since they involve metal ions surrounded by various numbers of ligands.

When dealing with coordination compounds like \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})_{6}]\), it's critical to keep in mind that the total oxidation state of the compound must equate to the overall charge. In general, the oxidation states of the ligands and the central metal ion add up to zero for neutral compounds, or to the charge of the complex for charged species. Ligands have well-established oxidation states, typically the charge of the anion or neutral molecule they are derived from. Coordination numbers and the geometry of the complex may further influence the apparent oxidation state of the central metal. Breaking down the oxidation states within coordination complexes like this allows for a systematic approach to identifying the oxidation state of an individual atom within the compound.

Potassium cyanide complex

The potassium cyanide complex component of \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})_{6}]\) is a vivid example of the intertwining of cations and the more complex cyanide ligands. Specifically, potassium ions serve as counterions to the complex anion. In this compound, cyanide (CN) acts as a ligand, which is a molecule that donates a pair of electrons to the metal ion to form a coordination bond.

Each CN ligand in a complex brings with it a specific charge, usually negative, as cyanide is a negatively charged monodentate ligand with a charge of -1. The number of cyanide ions will therefore contribute a measurable negative charge to the overall complex, helping to balance out the positive charge of the metal ion at the center of the complex. Understanding the role of cyanide ligands in the complex is crucial because it allows us to deduce the charge balance and therefore the oxidation state of the central metal ion.

Determining oxidation state of iron

Determining the oxidation state of iron in coordination compounds involves a systematic process. In the instance of the compound \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})_{6}]\), this process begins by identifying known oxidation states of other atoms or ions within the compound. For example, potassium (K) typically has an oxidation state of +1, and as mentioned earlier, each cyanide (CN) ligand carries a charge of -1.

To find the oxidation state of iron, balance the equation by considering the total charge of the complex ion must equal the aggregate charge contributed by the counterions. With this balance in mind and acknowledging the total charge contributed by the cyanide ligands, one can deduce the unknown oxidation state of iron. It's a bit like solving a puzzle: you have some pieces with known positions, and you must figure out where the remaining piece fits to complete the picture—in this case, Fe's oxidation state fitting into our compound's balanced charge equation.