Question

Give the number of \(d\) electrons associated with the central metal ion in each of the following complexes: (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), (b) \(\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2}\), (c) \(\mathrm{Na}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]\) (d) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{ClO}_{4}\), (e) \([\mathrm{Sr}(\mathrm{EDTA})]^{2-}\)

Short answer

The number of \(d\) electrons associated with the central metal ion in each complex is: (a) \(\mathrm{Fe}^{3+}\): 5 \(d\) electrons (b) \(\mathrm{Mn}^{2+}\): 5 \(d\) electrons (c) \(\mathrm{Ag}^{1+}\): 10 \(d\) electrons (d) \(\mathrm{Cr}^{3+}\): 3 \(d\) electrons (e) \(\mathrm{Sr}^{2+}\): 0 \(d\) electrons

Step-by-step solution

Identifying the central metal ion in each complex

For each complex, the central metal ion is the atom which forms the coordination bonds with the ligands. (a) In \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), the central metal ion is Iron (Fe). (b) In \(\left[\mathrm{Mn}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2}\), the central metal ion is Manganese (Mn). (c) In \(\mathrm{Na}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]\), the central metal ion is Silver (Ag). (d) In \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{ClO}_{4}\), the central metal ion is Chromium (Cr). (e) In \([\mathrm{Sr}(\mathrm{EDTA})]^{2-}\), the central metal ion is Strontium (Sr).

Determine the oxidation state of the central metal ion

To find the oxidation state of the central metal ion, we must balance the charges of the complex ions and their respective ligands. (a) Iron: In \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), the overall charge of the complex is 0, so: \(3(+1) + [\mathrm{Fe} + 6(-1)] = 0\). Thus, \({\rm Fe} = +3\). (b) Manganese: In \(\left[\mathrm{Mn}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]\left(\mathrm{NO}_{3}\right)_{2}\), the overall charge of the complex is 0, so: \(\mathrm{Mn} + 2(-1) = 0\). Thus, \({\rm Mn} = +2\). (c) Silver: In \(\mathrm{Na}\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]\), the overall charge of the complex is 0, so: \(+1 + [\mathrm{Ag} + 2(-1)] = 0\). Thus, \({\rm Ag} = +1\). (d) Chromium: In \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{ClO}_{4}\), the overall charge of the complex is +1, so: \(\mathrm{Cr} + 2(-1) = +1\). Thus, \({\rm Cr} = +3\). (e) Strontium: In \([\mathrm{Sr}(\mathrm{EDTA})]^{2-}\), the overall charge of the complex is -2, so: \(\mathrm{Sr} = -2\). Thus, \({\rm Sr} = +2\).

Calculating the number of \(d\) electrons for each central metal ion

Now that we know the oxidation state of each central metal ion, we can determine the number of \(d\) electrons associated with them by looking at their electronic configuration. (a) \(\mathrm{Fe}^{3+}\): The electronic configuration of Fe is [Ar] \(3d^6 4s^2\), so \(\mathrm{Fe^{3+}}\) has 5 \(d\) electrons. (b) \(\mathrm{Mn}^{2+}\): The electronic configuration of Mn is [Ar] \(3d^5 4s^2\), so \(\mathrm{Mn^{2+}}\) has 5 \(d\) electrons. (c) \(\mathrm{Ag}^{1+}\): The electronic configuration of Ag is [Kr] \(4d^{10}5s^1\), so \(\mathrm{Ag^{1+}}\) has 10 \(d\) electrons. (d) \(\mathrm{Cr}^{3+}\): The electronic configuration of Cr is [Ar] \(3d^5 4s^1\), so \(\mathrm{Cr^{3+}}\) has 3 \(d\) electrons. (e) \(\mathrm{Sr}^{2+}\): The electronic configuration of Sr is [Kr] \(5s^2\), and as Sr is in the 2nd group, it does not have any \(d\) electrons. The number of \(d\) electrons associated with the central metal ion in each complex is as follows: (a) \(\mathrm{Fe}^{3+}\): 5 \(d\) electrons (b) \(\mathrm{Mn}^{2+}\): 5 \(d\) electrons (c) \(\mathrm{Ag}^{1+}\): 10 \(d\) electrons (d) \(\mathrm{Cr}^{3+}\): 3 \(d\) electrons (e) \(\mathrm{Sr}^{2+}\): 0 \(d\) electrons

Key concepts

Oxidation State

The oxidation state of a metal in a coordination complex is crucial for understanding its behavior and properties. It is a number that reflects the total number of electrons an atom gains or loses when forming bonds.
- To determine the oxidation state, we need to balance the charges of all atoms in a compound.- Ligands contribute their own charges, which are typically known.- For example, in \( \mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\), the potassium ion has a +1 charge while each cyanide ion has a -1 charge. Given that the compound is neutral overall, solving \(3(+1) + \mathrm{Fe} + 6(-1) = 0\), gives the iron a +3 oxidation state.
Understanding the oxidation state helps us predict the chemical reactivity and magnetic properties of the metal ion in the complex.

Electronic Configuration

Electronic configuration describes the distribution of electrons in an atom's available shell and subshell orbitals. It is vital to understanding chemical bonding and properties. The electronic configuration tells us precisely where electrons reside in a neutral atom or ion.
- For elements in transition, the filling of the electron subshells can be unexpected as electrons may populate the d-orbital before fully filling the s-orbital.- Consider iron, which has the configuration [Ar] \(3d^6 4s^2\). When it becomes \(\mathrm{Fe}^{3+}\), it loses three electrons, resulting in [Ar] \(3d^5\), signifying that electron removal happens first from the s-orbital before d-orbital.- The order of filling is impacted by the relative energies of the orbitals, affected by electron-electron repulsions and the shape of orbitals.

d Electrons

In coordination chemistry, the number of d electrons is important, as d electrons primarily influence the chemistry of transition metals.
- d electrons participate in the formation of coordinate bonds with ligands.- They can be involved in unusual bonding scenarios not seen in s- and p-block elements.- For instance, manganese with five d electrons [Ar] \(3d^5 4s^2\), when ionized to \(\mathrm{Mn}^{2+}\), ends up with five d electrons.
These d electrons can affect the geometrical shape and electron pairing, impacting magnetic and color properties of the metal complex. Therefore, knowing the number of d electrons aids in predicting the characteristics of the complexes.

Central Metal Ion

The central metal ion in a complex is vital as it acts as the focus around which the entire coordination complex is built.
- This ion typically belongs to the transition metals, known for their ability to form multiple bonds with surrounding ligands.- In a coordination complex such as \([\mathrm{Mn}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\), manganese is the central metal ion bonding with six water molecules as ligands.
The nature and identity of the central metal ion determine the overall stability, reaction mechanisms, and bonding patterns of the complex. It accepts electrons from the ligands, enabling the formation of a structured coordination complex.Understanding the central metal ion deepens insights into the physical and chemical properties of complexes, enabling predictions about behavior in chemical reactions.