Animated Solution for Chemistry - Coordination Compounds: Match the electronic configurations in List-I with appropriate metal complex ions in List-II and choose the correct option. [Atomic Number: Fe = 26, Mn = 25, Co = 27]

To crack this, we need to determine three things for each complex: the oxidation state of the central metal ion, the geometry of the complex (octahedral or tetrahedral), and the strength of the ligand (strong or weak field).

Hexaamminecobalt(III) Let's start with $[Co(N{H}_3{)}_6{]}^{3+}$. The oxidation state of cobalt here is $+3$. Since the atomic number of cobalt is 27, removing three electrons leaves us with a $3d^6$ configuration.

Now, ammonia ($N{H}_3$) is a strong field ligand. This means the crystal field splitting energy (${\Delta }_o$) is greater than the pairing energy ($P$). As a result, all six electrons will pair up in the lower energy $t_{2g}$ orbitals, leaving the $e_g$ orbitals completely empty. The configuration is $t_{2g}^6{e}_g^0$, which perfectly matches option (P)!

Hexaaquamanganese(II) Next up is $[Mn(H_{2}O{)}_6{]}^{2+}$. Manganese is in a $+2$ oxidation state. With an atomic number of 25, $M{n}^{2+}$ has a $3d^5$ configuration.

Here, water ($H_{2}O$) acts as a weak field ligand. Therefore, the splitting energy is less than the pairing energy (${\Delta }_o<P$). The five electrons will singly occupy all five $d$ orbitals before any pairing occurs. We get three electrons in $t_{2g}$ and two in $e_g$. The configuration is $t_{2g}^3{e}_g^2$, matching option (Q).

Tetrachloroferrate(III) Now let's look at $[FeC{l}_4{]}^{-}$. Notice the coordination number is 4, which tells us this is a tetrahedral complex! Iron is in a $+3$ state, giving us a $3d^5$ configuration.

In a tetrahedral field, the splitting is inverted: the $e$ orbitals are lower in energy than the $t_2$ orbitals. Chloride ($C{l}^{-}$) is a weak field ligand, so the five electrons will singly occupy all orbitals. We get two electrons in $e$ and three in $t_2$. The configuration is $e^2{t}_2^3$, matching option (R).

Hexaaquairon(II) Finally, let's examine $[Fe(H_{2}O{)}_6{]}^{2+}$. Iron is in a $+2$ state, meaning it has a $3d^6$ configuration. The ligand is water, which is a weak field ligand.

Being an octahedral complex with a weak field ligand, the first five electrons will singly occupy all orbitals. The sixth electron will then pair up in the lowest energy $t_{2g}$ orbital. This gives us a configuration of $t_{2g}^4{e}_g^2$, matching option (S).

We have successfully matched all the configurations! - (P) maps to (3) - (Q) maps to (2) - (R) maps to (4) - (S) maps to (1)

Understanding ligand strength and geometry is the ultimate key to mastering Crystal Field Theory. Keep practicing, and these patterns will become second nature!