How many unpaired electrons are there in the following transition metal ions in their hexacyano-complex ions?

Fe^3+, Pd^2+,CO^2+

To determine the number of unpaired electrons in transition metal ions in their hexacyano-complex ions, we need to consider the electron configuration of each ion.

Let's start with Fe^3+:
- Fe is a transition metal with the atomic number 26. To determine the electron configuration of Fe^3+, we need to remove three electrons from Fe.
- The electron configuration of Fe is [Ar] 3d^6 4s^2.
- Removing three electrons gives us [Ar] 3d^3.

In the hexacyano-complex ion, the cyanide (CN^-) ligands will form coordination bonds by donating their lone pairs of electrons to the central metal ion. The coordination number of Fe^3+ in the hexacyano-complex ion is 6.

According to Hund's rule, when electrons occupy degenerate orbitals (orbitals of the same energy level), they first occupy different orbitals with parallel spins before pairing up. This means that each of the three 3d orbitals in Fe^3+ will have one unpaired electron.

Next, let's consider Pd^2+:
- Pd is also a transition metal, with the atomic number 46. To determine the electron configuration of Pd^2+, we need to remove two electrons from Pd.
- The electron configuration of Pd is [Kr] 4d^10.
- Removing two electrons gives us [Kr] 4d^8.

In the hexacyano-complex ion, Pd^2+ will form coordination bonds with the CN^- ligands. The coordination number of Pd^2+ in the hexacyano-complex ion is also 6.

According to Hund's rule, each of the five 4d orbitals in Pd^2+ will have one unpaired electron, resulting in a total of five unpaired electrons.

Lastly, let's consider CO^2+:
- CO^2+ consists of a cobalt (Co) ion coordinated with two cyanide (CN^-) ligands.
- To determine the electron configuration of CO^2+, we need to consider the electron configuration of Co.
- The electron configuration of Co is [Ar] 3d^7 4s^2.
- Since CO^2+ has a charge of +2, two electrons will be removed from Co to form the ion.
- Removing two electrons gives us [Ar] 3d^7.

In the hexacyano-complex ion, Co will form coordination bonds with the CN^- ligands. The coordination number of CO^2+ is 6.

According to Hund's rule, each of the three 3d orbitals in Co^2+ will have one unpaired electron, resulting in a total of three unpaired electrons.

To summarize:
- Fe^3+ has 3 unpaired electrons.
- Pd^2+ has 5 unpaired electrons.
- CO^2+ has 3 unpaired electrons.