Octahedral Complex Unpaired Electrons Calculation
In octahedral complexes, the d-orbitals split into a lower energy set ($t_{2g}$) and a higher energy set ($e_g$). The number of unpaired electrons depends on the total number of d-electrons (the $\text{d}^{n}$ configuration) and the spin state, determined by ligand field strength.
Calculating Unpaired Electrons for Each System
We calculate the unpaired electrons for each specified configuration:
1. $\text{d}^{3}$ System
- Configuration in octahedral field: $t_{2g}^3$.
- Electrons fill the $t_{2g}$ orbitals singly as per Hund's rule.
- Number of unpaired electrons = 3.
2. $\text{d}^{4}$ (low spin) System
- Low spin indicates strong ligand field, favouring pairing.
- Configuration: $t_{2g}^4$.
- The first 3 electrons fill $t_{2g}$ singly. The 4th electron pairs up in a $t_{2g}$ orbital.
- Number of unpaired electrons = 2.
3. $\text{d}^{5}$ (high spin) System
- High spin indicates weak ligand field, favouring maximum unpaired electrons.
- Configuration: $t_{2g}^3 e_g^2$.
- All 5 electrons occupy orbitals singly.
- Number of unpaired electrons = 5.
4. $\text{d}^{6}$ (high spin) System
- High spin configuration.
- Configuration: $t_{2g}^4 e_g^2$.
- In $t_{2g}^4$, there are 2 unpaired electrons (3 singles + 1 pair).
- In $e_g^2$, there are 2 unpaired electrons.
- Total unpaired electrons = 2 + 2 = 4.
5. $\text{d}^{7}$ (low spin) System
- Low spin configuration.
- Configuration: $t_{2g}^6 e_g^1$.
- The $t_{2g}$ orbitals are fully paired ($t_{2g}^6$), contributing 0 unpaired electrons.
- The $e_g$ orbitals have 1 electron ($e_g^1$).
- Total unpaired electrons = 0 + 1 = 1.
Total Unpaired Electrons Summation
To find the total number of unpaired electrons, we sum the values calculated for each system:
Total = (Unpaired $\text{d}^{3}$) + (Unpaired $\text{d}^{4}$ low spin) + (Unpaired $\text{d}^{5}$ high spin) + (Unpaired $\text{d}^{6}$ high spin) + (Unpaired $\text{d}^{7}$ low spin)
Total = $3 + 2 + 5 + 4 + 1 = 15$.
Thus, the total number of unpaired electrons is 15.
Similar Questions
- A chromium complex with a formula $\text{CrCl}_3\cdot 6\text{H}_2\text{O}$ has a spin only magnetic moment value of $3.87 \text{ BM}$ and its solution conductivity corresponds to $1 : 2$ electrolyte. $2.75 \text{ g}$ of the complex solution was initially passed through a cation exchanger. The solution obtained after the process was reacted with excess of $\text{AgNO}_3$. The amount of $\text{AgCl}$ formed in the above process is _____ g. (Nearest integer)
[Given: Molar mass in $\text{g mol}^{-1}$ $\text{Cr} : 52; \text{Cl}: 35.5, \text{Ag}: 108, \text{O}: 16, \text{H}: 1$] - Consider the following reactions :
$\text{NaCl} + \text{K}_2\text{Cr}_2\text{O}_7 + \text{H}_2\text{SO}_4 \rightarrow \text{A} + \text{KHSO}_4 + \text{NaHSO}_4 + \text{H}_2\text{O}$
$\text{A} + \text{NaOH} \rightarrow \text{B} + \text{NaCl} + \text{H}_2\text{O}$
$\text{B} + \text{H}_2\text{SO}_4 + \text{H}_2\text{O}_2 \rightarrow \text{C} + \text{Na}_2\text{SO}_4 + \text{H}_2\text{O}$
In the product 'C', 'X' is the number of $\text{O}_2^{2-}$ units, 'Y' is the total number oxygen atoms present and 'Z' is the oxidation state of Cr. The value of X + Y + Z is ____________. - Identify the metal ions among $\text{Co}^{2+}, \text{Ni}^{2+}, \text{Fe}^{2+}, \text{V}^{3+}$ and $\text{Ti}^{2+}$ having a spin-only magnetic moment value more than $3.0\text{ BM}$. The sum of unpaired electrons present in the high spin octahedral complexes formed by those metal ions is __________.
The crystal field splitting energy of $[\text{Co(oxalate)}_3]^{3-}$ complex is '$n$' times that of the $[\text{Cr(oxalate)}_3]^{3-}$ complex. Here '$n$' is ___________. (Assume $\Delta_o >> P$)
- A metal complex with a formula $MCl_4.3NH_3$ is involved in $sp^3d^2$ hybridisation. It upon reaction with excess of $AgNO_3$ solution gives 'x' moles of AgCl. Consider 'x' is equal to the number of lone pairs of electron present in central atom of $BrF_5$. Then the number of geometrical isomers exhibited by the complex is ______
- Consider the molecules / ions given below
$XeO_3$, $BF_4^-$, $I_3^-$, $SF_6$, $PCl_5$
The ratio of number of molecules having $sp^3d$ hybridisation to those having $sp^3$ hybridisation is ________ - In the leaching method, bauxite ore is digested with a concentrated solution of NaOH that produces 'X'. When $CO_2$ gas is passed through the aqueous solution of 'X', a hydrated compound 'Y' is precipitated. 'X' and 'Y' respectively are :-
- The total number of possible isomers for square- planar $[Pt(Cl)(NO_2)(NO_3)(SCN)]^{2–}$ is :-
- In $KO_2$, the nature of oxygen species and the oxidation state of oxygen atom are, respectively
The correct order of spin-only magnetic moments among the following is :
(Atomic number : Mn = 25, Co = 27, Ni= 28, Zn = 30)
Important Questions from Inorganic Chemistry
- A chromium complex with a formula $\text{CrCl}_3\cdot 6\text{H}_2\text{O}$ has a spin only magnetic moment value of $3.87 \text{ BM}$ and its solution conductivity corresponds to $1 : 2$ electrolyte. $2.75 \text{ g}$ of the complex solution was initially passed through a cation exchanger. The solution obtained after the process was reacted with excess of $\text{AgNO}_3$. The amount of $\text{AgCl}$ formed in the above process is _____ g. (Nearest integer)
[Given: Molar mass in $\text{g mol}^{-1}$ $\text{Cr} : 52; \text{Cl}: 35.5, \text{Ag}: 108, \text{O}: 16, \text{H}: 1$] - Consider the following reactions :
$\text{NaCl} + \text{K}_2\text{Cr}_2\text{O}_7 + \text{H}_2\text{SO}_4 \rightarrow \text{A} + \text{KHSO}_4 + \text{NaHSO}_4 + \text{H}_2\text{O}$
$\text{A} + \text{NaOH} \rightarrow \text{B} + \text{NaCl} + \text{H}_2\text{O}$
$\text{B} + \text{H}_2\text{SO}_4 + \text{H}_2\text{O}_2 \rightarrow \text{C} + \text{Na}_2\text{SO}_4 + \text{H}_2\text{O}$
In the product 'C', 'X' is the number of $\text{O}_2^{2-}$ units, 'Y' is the total number oxygen atoms present and 'Z' is the oxidation state of Cr. The value of X + Y + Z is ____________. - Identify the metal ions among $\text{Co}^{2+}, \text{Ni}^{2+}, \text{Fe}^{2+}, \text{V}^{3+}$ and $\text{Ti}^{2+}$ having a spin-only magnetic moment value more than $3.0\text{ BM}$. The sum of unpaired electrons present in the high spin octahedral complexes formed by those metal ions is __________.
The crystal field splitting energy of $[\text{Co(oxalate)}_3]^{3-}$ complex is '$n$' times that of the $[\text{Cr(oxalate)}_3]^{3-}$ complex. Here '$n$' is ___________. (Assume $\Delta_o >> P$)
- Which of the following is the structure of pyrosulphuric acid?
