Question

Negatively charged monodentate strong field ligand \(X^-\) and weak field ligand \(Y^-\) form the complexes \[ [MnX_6]^{4-} \quad \text{and} \quad [MnY_6]^{4-} \] respectively. Under certain reaction conditions, let the crystal field splitting energies for \[ [MnX_6]^{4-} \quad \text{and} \quad [MnY_6]^{4-} \] be \(\Delta_{o1}\) and \(\Delta_{o2}\), respectively. Which of the following statements is/are correct?

• A. Electron pairing energy in \([MnX_6]^{4-}\) is smaller than \(\Delta_{o1}\).
• B. \([MnY_6]^{4-}\) is more stabilized than \([MnX_6]^{4-}\).
• C. The \(t_{2g}\) orbitals in \([MnX_6]^{4-}\) are stabilized by \(2\Delta_{o1}\) as compared to degenerate \(d\)-orbitals.
• D. \([MnY_6]^{4-}\) is more intense in colour as compared to \([MnX_6]^{4-}\).

Hint:

For octahedral \(d^5\) complexes: \[ \text{Weak field} \Rightarrow t_{2g}^{3}e_g^{2} \ (\text{high spin}) \] \[ \text{Strong field} \Rightarrow t_{2g}^{5}e_g^{0} \ (\text{low spin}) \] High-spin complexes usually have more unpaired electrons and often show more intense colour, while low-spin complexes possess greater crystal field stabilization energy.

Answer 1

The Correct Option is A, D

Concept: To determine the correct statements, we first identify the oxidation state and electronic configuration of manganese and then analyze the effect of strong field and weak field ligands using Crystal Field Theory (CFT). For an octahedral complex: \[ \text{CFSE} = (-0.4n_{t_{2g}}+0.6n_{e_g})\Delta_o \] A strong field ligand produces a larger crystal field splitting and may cause electron pairing, whereas a weak field ligand generally leads to a high-spin configuration.

Step 1: Determine the oxidation state of manganese. For \[ [MnX_6]^{4-} \] let the oxidation state of Mn be \(x\). Since each ligand carries charge \(-1\), \[ x+6(-1)=-4 \] \[ x-6=-4 \] \[ x=+2 \] Thus manganese is present as \[ Mn^{2+} \] whose electronic configuration is \[ [Ar]\,3d^5 \] Hence both complexes contain a \(d^5\) metal ion.

Step 2: Electronic configuration in the strong field complex. Since \(X^-\) is a strong field ligand, \[ \Delta_{o1}>P \] where \(P\) denotes pairing energy. Therefore electrons pair in the lower energy \(t_{2g}\) orbitals. The electronic arrangement becomes \[ t_{2g}^{5}e_g^{0} \] which corresponds to a low-spin \(d^5\) configuration. Since pairing occurs only when crystal field splitting exceeds pairing energy, \[ P<\Delta_{o1} \] Therefore statement (A) is correct.

Step 3: Electronic configuration in the weak field complex. Since \(Y^-\) is a weak field ligand, \[ \Delta_{o2}<P \] Therefore electrons occupy higher orbitals before pairing. The configuration becomes \[ t_{2g}^{3}e_g^{2} \] which is the high-spin \(d^5\) arrangement.

Step 4: Compare the stabilization energies. For low-spin \(d^5\): \[ CFSE = 5(-0.4\Delta_{o1}) \] \[ =-2\Delta_{o1} \] For high-spin \(d^5\): \[ CFSE = 3(-0.4\Delta_{o2}) +2(+0.6\Delta_{o2}) \] \[ =-1.2\Delta_{o2}+1.2\Delta_{o2} \] \[ =0 \] Thus the strong field complex possesses greater crystal field stabilization. Hence \[ [MnX_6]^{4-} \] is more stabilized than \[ [MnY_6]^{4-} \] Therefore statement (B) is incorrect.

Step 5: Examine stabilization of \(t_{2g}\) orbitals. In an octahedral field, each electron in a \(t_{2g}\) orbital is stabilized by \[ -\frac{2}{5}\Delta_o = -0.4\Delta_o \] and not by \[ 2\Delta_o. \] Therefore statement (C) is incorrect.

Step 6: Compare colour intensity. The weak field complex has more unpaired electrons and generally exhibits greater spin-allowed transitions. Consequently, absorption is stronger and the colour appears more intense. Hence \[ [MnY_6]^{4-} \] is more intensely coloured than \[ [MnX_6]^{4-}. \] Therefore statement (D) is correct.

Step 7: Final conclusion. The correct statements are \[ \boxed{(A)\ \text{and}\ (D)} \]