For the octahedral complexes of Fe3+ in SCN- (thiocyanato-S) and in CN- ligand environments, the dif

Q: Why is the oxidation state of Iron +3 in both complexes?

Both $\text{CN}^{-}$ and $\text{SCN}^{-}$ are monoanionic ligands with a charge of -1. Since there are 6 ligands and the overall complex charge is -3, the math is $x + 6(-1) = -3$, which gives $x = +3$.

Q: How do we know if a ligand is strong or weak field?

This is determined by the Spectrochemical Series. Carbon-donor ligands like $\text{CN}^{-}$ are typically strong field, while halogen and sulfur-donor ligands like $\text{SCN}^{-}$ are weak field.

Q: Why do electrons pair up in the cyanide complex?

Because $\text{CN}^{-}$ is a strong field ligand, the crystal field splitting energy ($\Delta_o$) is greater than the pairing energy ($P$). It requires less energy for electrons to pair up in the lower $t_{2g}$ orbitals than to jump to the higher $e_g$ orbitals.

Q: What is the formula for spin-only magnetic moment?

The formula is $\mu = \sqrt{n(n+2)}$ Bohr Magnetons (B.M.), where $n$ is the number of unpaired electrons.

Q: Why do we approximate the final answer?

The question explicitly asks to approximate the difference to the nearest integer. The exact difference is $5.92 - 1.73 = 4.19$, which rounds to 4.

Question

For the octahedral complexes of $	ext{Fe}^{3+}$ in $	ext{SCN}^{-}$ (thiocyanato-S) and in $	ext{CN}^{-}$ ligand environments, the difference between the spin only magnetic moments in Bohr magnetons (when approximated to the nearest integer) is
[Atomic number of $	ext{Fe} = 26$]

Sigma Percentile · Accepted Answer

### Analyzing the Setup
Imagine you are a molecular detective, and your suspects are two octahedral complexes of Iron: $[	ext{Fe}(	ext{CN})_6]^{3-}$ and $[	ext{Fe}(	ext{SCN})_6]^{3-}$. Our mission is to uncover the difference in their spin-only magnetic moments.

First, we need to strip away the disguise and find the true state of the central Iron atom. Both cyanide ($	ext{CN}^{-}$) and thiocyanate ($	ext{SCN}^{-}$) are monoanionic ligands, meaning they each carry a $-1$ charge. Since the overall charge of the complex is $-3$, the Iron atom must be in a $+3$ oxidation state to balance the scales.

With an atomic number of 26, neutral Iron has the configuration $[	ext{Ar}] 4s^2 3d^6$. Removing three electrons (two from the $4s$ and one from the $3d$) leaves us with $	ext{Fe}^{3+}$ having a $3d^5$ configuration. We have exactly five d-electrons ready to play the game of crystal field theory.

### The Battle of the Ligands
Here is where the plot thickens. The behavior of these five electrons depends entirely on the environment created by the surrounding ligands.

Cyanide ($	ext{CN}^{-}$) is a notorious **Strong Field Ligand (SFL)**. It pushes the d-orbitals apart with immense force, creating a large energy gap ($\Delta_o$) between the lower $t_{2g}$ and upper $e_g$ orbitals. This gap is so large that it exceeds the pairing energy ($P$).

On the flip side, thiocyanate ($	ext{SCN}^{-}$) is a **Weak Field Ligand (WFL)**. It creates a much gentler environment, resulting in a small energy gap ($\Delta_o < P$).

### Crystal Field Splitting in Action
Let's see how the electrons settle into their new homes. In the cyanide complex, the large energy gap forces the electrons to take the path of least resistance: pairing up in the lower energy level. All five electrons crowd into the $t_{2g}$ orbitals, resulting in a $t_{2g}^5 e_g^0$ configuration. This leaves us with just **one unpaired electron** ($n = 1$).

In the thiocyanate complex, the small energy gap allows the electrons to spread out comfortably. They occupy both the $t_{2g}$ and $e_g$ orbitals before any pairing occurs. This gives us a $t_{2g}^3 e_g^2$ configuration, leaving all **five electrons unpaired** ($n = 5$).

### Calculating the Magnetic Moments
Now, we bring in our master equation for the spin-only magnetic moment:
$$ \mu = \sqrt{n(n+2)} 	ext{ B.M.} $$

For the strong field cyanide complex ($n = 1$):
$$ \mu_{	ext{SFL}} = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 	ext{ B.M.} $$

For the weak field thiocyanate complex ($n = 5$):
$$ \mu_{	ext{WFL}} = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 	ext{ B.M.} $$

### Final Calculation
We are at the finish line. The question asks for the difference between these two magnetic moments, approximated to the nearest integer. Let's do the math:
$$ 	ext{Difference} = 5.92 - 1.73 = 4.19 $$

Rounding $4.19$ to the nearest integer gives us **4**. The elegance of crystal field theory perfectly predicts the magnetic behavior of these complexes!

Enter Numerical Value:

Visualized Solution

$Visual Anchor$

$Oxidation State$

$Ligand Field Strength$

$SFL Splitting$

$SFL Magnetic Moment$

$WFL Splitting$

$WFL Magnetic Moment$

$Final Calculation$

The Sigma Insight: Bonding and Crystal field

Analyzing the Setup Imagine you are a molecular detective, and your suspects are two octahedral complexes of Iron: $[Fe (CN)_{6}]^{3 -}$ and $[Fe (SCN)_{6}]^{3 -}$

The Battle of the Ligands Here is where the plot thickens

Crystal Field Splitting in Action Let's see how the electrons settle into their new homes

Calculating the Magnetic Moments

Final Calculation We are at the finish line

Similar Questions

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Enter Numerical Value:

Visualized Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Visual Anchor

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Oxidation State

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Ligand Field Strength

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } SFL Splitting

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } SFL Magnetic Moment

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } WFL Splitting

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } WFL Magnetic Moment

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Final Calculation