Question

Experiments can measure not only whether a compound is paramagnetic but also the number of unpaired electrons. It is found that the octahedral complex ion ${\mathbf{\left[}\mathbf{\text{Fe}}{\mathbf{\left(}\mathbf{\text{CN}}\mathbf{\right)}}_{\mathbf{\text{6}}}\mathbf{\right]}}^{\mathbf{\text{3-}}}$has fewer unpaired electrons than the octahedral complex ion ${\mathbf{\left[}\mathbf{F}\mathbf{e}{\mathbf{\left(}\mathbf{O}{\mathbf{H}}_{\mathbf{2}}\mathbf{\right)}}_{\mathbf{6}}\mathbf{\right]}}^{\mathbf{3}\mathbf{+}}$. How many unpaired electrons are present in each species? Explain. In each case, express the CFSE in terms ofDo.

Short answer

The number of unpaired electrons in Hexacyanoferrate (+3) is one, and CFSE is -2 Do. The number of unpaired electrons in Hexaaquaferrate (+3) is five, and CFSE is 0.

Step-by-step solution

Hexacyanoferrate (3+).

Ferrous has the atomic number 26, and its electronic configuration is,

${}_{26}Fe=\left(Ar\right)3d^{6}4s^2$

Here ferrous has the +3 oxidation number, and the electronic configuration of the Fe (3+) ion is,

$F{e}^{3+}=\left(Ar\right)3d^{5}4s^0$

CFSE of Hexacyanoferrate (3+).

Cyanide is a strong field ligand, so the pairing of electrons can be done into the t2g orbital, and the, eg, orbital remains vacant. There is only one unpaired electron.

The crystal field splitting energy of hexacyanoferrate (+3) is calculated below.

$\begin{array}{l}=-0.4\times n\left(t_{2}g\right)+0.6\times n\left(eg\right){\Delta }_0\\ =-0.4\times 5+0.6\times 0\\ =-0.4\times 5\\ =-2Do\end{array}$

n = no. of electrons present in respected orbitals.

Hexaaquaferrate (3+).

Ferrous has the atomic number 26, and its electronic configuration is,

${}_{26}Fe=\left(Ar\right)3d^{6}4s^2$

Here ferrous has the +3 oxidation number, and the electronic configuration of the Fe (3+) ion is,

$F{e}^{3+}=\left(Ar\right)3d^{5}4s^0$

CFSE of hexaaquaferrate (+3).

Water or aqua is a weak field ligand, so the pairing of electrons does not occur. Among the five electrons, three go into the t2g orbital, and the remaining two go into the, eg, orbital. There are five unpaired electrons.

The crystal field splitting energy of hexaaquaferrate (+3) is calculated below.

$\begin{array}{l}=-0.4\times n\left(t_{2}g\right)+0.6\times n\left(eg\right){\Delta }_0\\ =-0.4\times 3+0.6\times 2\\ =-1.2+1.2\\ =0Do\end{array}$

n = no. of electrons present in respected orbitals.