Animated Solution for Chemistry - Coordination Compounds: Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour ? (At. no. of Cr = 24, Mn = 25, Fe = 26, Co = 27)

When we talk about the magnetic properties of coordination compounds, we are essentially looking at the number of unpaired electrons present in the central metal ion's d-orbitals. The paramagnetic behaviour of a complex is directly proportional to the number of unpaired electrons ($n$). The magnetic moment ($ \mu $) can be calculated using the spin-only formula:

Our goal is to find the complex with the lowest paramagnetic behaviour, which translates to finding the complex with the minimum number of unpaired electrons.

Oxidation State and Ligand Field

Let's look at the commonalities among the given options. All four complexes have the cyanide ion ($C{N}^{-}$) as the ligand. Cyanide is a well-known strong field ligand (SFL) according to the spectrochemical series. This means it causes a large crystal field splitting energy (${\Delta }_o>P$), forcing electrons to pair up in the lower energy $t_{2g}$ orbitals before occupying the higher energy $e_g$ orbitals.

Furthermore, all complexes have an overall charge of $-3$. Since each of the six cyanide ligands carries a $-1$ charge, we can easily calculate the oxidation state ($x$) of the central metal ion:

So, we are dealing with $C{o}^{3+}$, $F{e}^{3+}$, $M{n}^{3+}$, and $C{r}^{3+}$ ions in a strong octahedral field.

Let's evaluate the electronic configuration for each metal ion:

1. Cobalt Complex: $[Co(CN{)}_6{]}^{3-}$ Cobalt ($Z=27$) has a ground state configuration of $[Ar]3d^{7}4s^2$. The $C{o}^{3+}$ ion loses three electrons to become $3d^6$. In the presence of the strong $C{N}^{-}$ field, all six electrons pair up in the $t_{2g}$ level. Configuration: $t_{2g}^6{e}_g^0$. Unpaired electrons ($n$) = $0$. Magnetic moment ($\mu$) = $0$ BM (Diamagnetic).

2. Iron Complex: $[Fe(CN{)}_6{]}^{3-}$ Iron ($Z=26$) has a ground state configuration of $[Ar]3d^{6}4s^2$. The $F{e}^{3+}$ ion becomes $3d^5$. The strong field forces pairing, resulting in two pairs and one unpaired electron in the $t_{2g}$ level. Configuration: $t_{2g}^5{e}_g^0$. Unpaired electrons ($n$) = $1$. Magnetic moment ($\mu$) = $\sqrt{3}$ BM.

3. Manganese Complex: $[Mn(CN{)}_6{]}^{3-}$ Manganese ($Z=25$) has a ground state configuration of $[Ar]3d^{5}4s^2$. The $M{n}^{3+}$ ion becomes $3d^4$. The strong field causes pairing, leaving one pair and two unpaired electrons. Configuration: $t_{2g}^4{e}_g^0$. Unpaired electrons ($n$) = $2$. Magnetic moment ($\mu$) = $\sqrt{8}$ BM.

4. Chromium Complex: $[Cr(CN{)}_6{]}^{3-}$ Chromium ($Z=24$) has a ground state configuration of $[Ar]3d^{5}4s^1$. The $C{r}^{3+}$ ion becomes $3d^3$. According to Hund's rule, these three electrons will singly occupy the three degenerate $t_{2g}$ orbitals. Pairing only begins with the fourth electron, so the ligand strength doesn't affect the number of unpaired electrons here. Configuration: $t_{2g}^3{e}_g^0$. Unpaired electrons ($n$) = $3$. Magnetic moment ($\mu$) = $\sqrt{15}$ BM.

Comparing the number of unpaired electrons, we see that the cobalt complex, $[Co(CN{)}_6{]}^{3-}$, has $0$ unpaired electrons. Therefore, it exhibits the lowest paramagnetic behaviour (it is entirely diamagnetic).