Question

How many unpaired electrons are present in the tetrahedral ion \(\mathrm{FeCl}_{4}^{-} ?\)

Short answer

In the tetrahedral ion \(\mathrm{FeCl}_{4}^{-}\), the central iron (Fe) atom has an oxidation state of +3. The electron configuration of the Fe³⁺ ion is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{5}\), and in the 3d subshell, there are 5 unpaired electrons. Therefore, there are 5 unpaired electrons present in the tetrahedral ion \(\mathrm{FeCl}_{4}^{-}\).

Step-by-step solution

Identify the central atom and oxidation state

The central atom in the complex ion \(\mathrm{FeCl}_{4}^{-}\) is the iron (Fe) atom. To determine the oxidation state, we will use the fact that the total charge of the ion must equal the sum of the oxidation states of each element in it. Considering that a chlorine (Cl) atom has a charge of -1, we can set up the equation: IronOxidationState + 4 × ChlorineOxidationState = TotalCharge x + 4 × (-1) = -1 Solve for x: x = -1 + 4 = 3 Thus, the oxidation state of the Fe atom in the complex ion is +3.

Write the electron configuration

Now, we need to write down the electron configuration for Fe. In its neutral state, Fe has an atomic number of 26, which means it has 26 electrons. The electronic configuration of a neutral Fe atom is: Fe: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{6}\) However, in the complex ion \(\mathrm{FeCl}_{4}^{-}\), the Fe atom has an oxidation state of +3 (it is losing 3 electrons). Therefore, we need to modify the electron configuration for the Fe ion: Fe³⁺: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{5}\)

Determine the unpaired electrons

The electron configuration of the Fe³⁺ ion is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{5}\). The number of unpaired electrons can be found by checking the occupancy of the subshells in the configuration that contain unpaired electrons. In this case, the 3d subshell is the not fully occupied one: 3d: ↑↑↑↑↑ (5 unpaired electrons) Therefore, there are 5 unpaired electrons in the tetrahedral ion \(\mathrm{FeCl}_{4}^{-}\).