Question

Given below are two statements :
Statement I : Crystal Field Stabilization Energy (CFSE) of \( [Cr(H_2O)_6]^{2}+ \) is greater than that of \( [Mn(H_2O)_6]^{2+} \).
Statement II : Potassium ferricyanide has a greater spin-only magnetic moment than sodium ferrocyanide.
In the light of the above statements, choose the correct answer from the options given below :}

• A. Statement I is true but Statement II is false
• B. Statement I is false but Statement II is true
• C. Both Statement I and Statement II are true
• D. Both Statement I and Statement II are false

Hint:

Strong field ligands (\( CN^-, CO \)) favor pairing, while weak field ligands (\( H_2O, F^- \)) favor high spin configurations.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
CFSE is calculated based on the distribution of d-electrons in \( t_{2g} \) and \( e_g \) orbitals.
Magnetic moment is determined by the number of unpaired electrons (\( n \)) using the spin-only formula.

Step 2: Key Formula or Approach:
Octahedral CFSE \( = [-0.4 \times n(t_{2g}) + 0.6 \times n(e_g)] \Delta_o \).
Magnetic moment \( \mu = \sqrt{n(n+2)} \text{ BM} \).

Step 3: Detailed Explanation:
Statement I:
In \( [Cr(H_2O)_6]^{2+} \), \( Cr^{2+} \) is a \( d^4 \) ion. \( H_2O \) is a weak field ligand (high spin).
Configuration: \( t_{2g}^3 e_g^1 \). CFSE \( = [3(-0.4) + 1(0.6)] \Delta_o = -0.6 \Delta_o \).
In \( [Mn(H_2O)_6]^{2+} \), \( Mn^{2+} \) is a \( d^5 \) ion. \( H_2O \) is a weak field ligand (high spin).
Configuration: \( t_{2g}^3 e_g^2 \). CFSE \( = [3(-0.4) + 2(0.6)] \Delta_o = 0 \).
The magnitude of CFSE for \( Cr^{2+} \) (0.6) is greater than for \( Mn^{2+} \) (0). Statement I is true.
Statement II:
Potassium ferricyanide is \( K_3[Fe(CN)_6] \). \( Fe \) is in \( +3 \) state (\( d^5 \)).
\( CN^- \) is a strong field ligand (low spin). Configuration: \( t_{2g}^5 e_g^0 \). Unpaired electrons, \( n = 1 \).
Sodium ferrocyanide is \( Na_4[Fe(CN)_6] \). \( Fe \) is in \( +2 \) state (\( d^6 \)).
\( CN^- \) is a strong field ligand. Configuration: \( t_{2g}^6 e_g^0 \). Unpaired electrons, \( n = 0 \).
Since \( n=1>n=0 \), ferricyanide has a greater magnetic moment. Statement II is true.

Step 4: Final Answer:
Both statements I and II are true.