US05CCHE22

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INORGANIC CHEMISTRY

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Unit II

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CRYSTAL FIELD THEORY

Ionic : NaCl

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Covalent : NH₃

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Coordinate covalent : Complex

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M⁺ⁿ + Ligand → [ML₆]²⁺

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M_(s)²⁺ + excess H₂O → [M(H₂O)₆]²⁺

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Important features of CFT

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(i)The central metal atom/ion is surrounded by ligands which contain one or more pair of electron

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(ii) The ionic ligand (eg. Cl-, F-, CN- etc ) are regarded as negative point charge and

the neutral ligands is dipolar, its negative end oriented towards the metal cation.

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(iii)In CFT the electron does not enter into the metal orbitals , means the metal ion and ligands do not mix their orbitals or share ligand

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Crystal field theory

Assumptions

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1.Ligands are treated as point charge

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2. There is no interaction between metal orbitals and ligand orbitals

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3. The d orbital of the metal have same energy

i.e. degenerate in the free atom,

however when complex is formed ligand destroy the degeneracy of these orbital

i.e. the orbital now have different energy

T_2g Gerade

E_g Ungerade

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Structure of different d orbitals

Structure of different d orbital

In octahedral complexes the six ligands are arranged octahedraly around a central metal ion

i.e. the metal is at the centre of the octahedron and the ligands are at six corners. Figure 1

In t2g orbital i.e. dxy, dyz & dxz

their lobes are lie between the axis (Non Axial Orbital) . . experience less repulsion than eg orbital

acquire lower energy level

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In eg orbital i.e. dx²-y² & dz²

their lobes are along the axis (Axial Orbital)

experience more repulsion than t_2g orbital

acquire higher energy level

Thus under the influence of octahedral ligand field d orbital split into two groups of different energy.

The difference in energy between two d level is given by ∆o or 10 Dq.

The eg orbitals are 0.6 ∆o or 6Dq. above the average level and the t2g orbitals are 0.4∆o or 4Dq. below the average level

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Once again, whether a complex is high spin or low spin depends on two main factors:

1. the crystal field splitting energy and
2. the pairing energy. 

The electrons will take the path of least resistance

means the path that requires the least amount of energy.

If the paring energy is greater than Δ, then electrons will move to a higher energy orbital because it takes less energy.

If the pairing energy is less than Δ, then the electrons will pair up rather than moving singly to a higher energy orbital.

Below, tips and examples are given to help figure out whether a certain molecule is high spin or low spin.

CFSE = -(n₁)(2/5)(Δ_O) +(n₂)(3/5)(Δ_O)

Or

CFSE = -(n₁)(0.4)(Δ_O) +(n₂)(0.6Δ_O)

Distribution of dn electrons in t₂g & eg orbitals in Oh complexes

When the ligands are weak – HIGH SPIN COMPEXES - ∆o<P

Under the influence of weaker ligand the energy difference ∆o between the t₂g & eg sets is relatively small

hence in all the five d orbital's the distribution of d electrons in t₂g & eg sets take place according to Hund’s rule

(electrons will be paired up only when each of the 5d orbitals are atleast singlely filled).

[CoF₆]^-3 is a weaker ligand ,

for such complexes ∆o < P ; where P= Pairing Energy

∆o tend to force as many electrons to t₂g level &

P tends to prevent the electrons to paired in t₂g level

t₂g ^1,2,3 → eg ^4,5 → t₂g ^6,7,8 →eg^9,10

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When the ligands are strong or

In the influence of strong ligand field - LOW SPIN COMPEX

∆o>P

Under the influence of strong ligand or strong field ligand

the energy difference ∆o between the t₂g & eg sets is relatively large

Hence in all the five d orbital's the distribution of d electrons in t₂g & eg sets does not obey Hund’s rule

First 6 electrons will go to t₂g set and the remaining

4 electrons enter in the eg set

[Co(NH₃)₆]⁺³ is a stronger ligand or strong field ligand or Spin Pair complexes

t₂g^1,2,3,4,5,6 → eg ^7,8,9,10 ∆o>P

Pairing Energy: P: The energy to required to pair two electrons against electron - electron repulsion in the same orbital.

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LOW SPIN COMPLEXES

When the crystal field splitting energy ∆o is greater than the pairing energy, ∆o>P low spin complex is formed

Electrons will fill up all the lower energy orbitals first and then paired up with electrons before moving to the higher energy orbitals.

This complexes are also called Low spin Complexes

When stronger ligand attached to metal ion form this complexes ∆o>P

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HIGH SPIN COMPLEXES

When the crystal field splitting energy is less than the pairing energy, ∆o<P high spin complex is formed

Electrons will fill up singly in all the lower energy orbitals than to higher energy orbitals,after that paired up electrons in the orbitals.

This complexes are also called High spin Complexes

When weak ligand attached to metal ion form this complexes ∆o<P

In tetrahedral complexes the four ligands are arranged tetrahedraly around a central metal ion

i.e. the metal is at the centre of the tetrahedral and the ligands are at four corners. Figure 2

In t2 orbital i.e. dxy, dyz & dxz their lobes are lie between the axis

experience more repulsion than eg orbital

acquire higher energy level

In e orbital i.e. dx²-y² & dz² their lobes are along the axis

experience less repulsion than t2g orbital

acquire lower energy level

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Thus under the influence of tetrahedral ligand field d orbital split into two groups of different energy.

The difference in energy between two d level is given by ∆t or 10 Dq.

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The t2g orbitals are 0.4∆o (2/5) or 4Dq. above the average level and the e orbitals are 0.6∆o (3/5) or 6Dq. below the average level

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Factors affecting the magnitude of Δ_O (A)Geometry of the complex ion

If we consider the complex ions having the same central metal ion and the same ligands but having different geometry , than the value of Δ_O depends on the geometry of the complex ion

Δ_sp > Δ_O > Δ_t

1.3 ΔO > Δ_O > 0.45Δ_t

In octahedral complexes, the splitting of d-orbitals is more than twice as strong as in tetrahedral complexes.

The difference in the value of Δ_{sp ,}Δ_O and Δ_t is due to two factors.

(i) In octahedral complexes six ligands are involved while in tetrahedral complexes only four ligands are involved, thus 33% decrease in the field strength.

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(ii) In octahedral complexes the ligands are situated directly in the path of d_z² and d_x²_-y² orbitals while in tetrahedral complexes the ligands are not in the path of axis.

In square planner complexes the degree of splitting is much more than in tetrahedral complexes

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(B) Nature of Ligands: Weaker/stronger ligands : The Spectrochemical series

In complex ions having the same central metal ion and the same geometry but different ligands arranged according to splitting strength.

It is possible to arrange ligands into a series that reflects their ability to split the d-orbitals, this series is called as Spectro chemical Series

The series is as follows :

I^-< Br^- < Cl^- < SCN^-< NO₃^- < F^- < OH- < H₂O < NCS^-< gly < py < NH₃ < en <NO₂^- < PPh₃ < CN^- < CO

Weak field ligands 🡨--------------------🡪Strong field ligands

Small Δ-splitting Large Δ-splitting

In crystal field theory, the difference in energy between the d orbitals (Δ) called the ligand-field splitting parameter

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Ligands arranged on the left end of this spectrochemical series are generally regarded as weaker ligands

ligands lying at the right end are stronger ligands

[NiBr₆]^-4, [NiCl₆]^-4, [Ni(H₂O)₆]⁺²,[Ni(NH₃)₆]⁺², [Ni(en)₃]⁺²,

Δcm^-1 7000 < 7200 < 8500 < 10800 < 11500

[Co(H₂O)₆]⁺³ ,[Co(NH₃)₆]⁺³ , [Co(en)₃]⁺³

Δcm^-1 18200 < 23000 < 23200

(C)Nature of central metal ion

(i) The Δ value increases as we move from first transition series to second transition series and then to the third transition series.

The Δ value increases as we move from the central metal ion with 3d configuration to 4d, for the same ligand, again 4d configuration to 5d. Thus Δ value increases with the value of principal quantum number

[Co(NH₃)₆]⁺³ ,[Rh(NH₃)₆]⁺³ ,[Ir(NH₃)₆]⁺³

Δcm^-1 23000 < 34000 < 41000

[Co(en)₃]⁺³ , [Rh(en)₃]⁺³ , [Ir(en)₃]⁺³

Δcm^-1 24000 < 35000 < 41000

Due to their large size 4d and 5d orbitals are likely to interact with the ligand orbitals more effectively than 3d orbitals.

(ii) Central metal ions of the same metal having different oxidation state

The Δ value of the complex ions have the same ligand, same geometry and same metal ion with different oxidation state increases with the increase with oxidation state.

[Mn(H₂O)₆]⁺² [Mn(H₂O)₆]⁺³

Δcm^-1 8500 < 21000

Oxidation state +2 +3

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The Δ value increases due to substantial increase of σ bonding , which is because of the decrease in the radius of the metal ion having higher positive charge.

(iii) Central metal ions of the different metal having different oxidation state

The Δ value of the complex ions have the same ligand, same geometry but different metal ion with different oxidation state increases with the increase with oxidation state.

[V(H₂O)₆]⁺² [Cr(H₂O)₆]⁺³

Δcm^-1 12400 < 17400

Oxidation state +2 +3

The Spectrochemical series

A spectrochemical series is a list of ligands ordered on ligand strength.

It is possible to arrange ligands into a series that reflects their ability to split the d-orbitals.

This series is as follows :

I- < Br- < Cl- < SCN- < NO₃ ^- < F^- < OH- < H2O < NCS- < gly < py < NH₃ < en . <NO₂ - < PPh₃ < CN^- < CO  

Weak field ligands _______________Strong field ligands

Small Δ-splitting Large Δ-splitting

In crystal field theory, ligands modify the difference in energy between the d orbitals (Δ) called the ligand-field splitting parameter

Ligands arranged on the left end of this spectrochemical series are generally regarded as weaker ligands

thus form outer orbital octahedral complexes that are high spin. 

ligands lying at the right end are stronger ligands

thus form inner orbital octahedral complexes that are low spin. 

X weak field < O middle < N strong field < C very strong

Variations are due to σ-donating and Π-accepting properties of the ligand.

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CFSE = -(n₁)(2/5)(Δ_O) +(n₂)(3/5)(Δ_O)

Or

CFSE = -(n₁)(0.4)(Δ_O) +(n₂)(0.6Δ_O)

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CFSE = -(1)(0.4)(Δ_O) +(0)(0.6Δ_O)

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= -0.4 Δ_O

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CFSE = -(2)(0.4)(Δ_O) +(0)(0.6Δ_O)

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= -0.8Δ_O

d²

d¹

CFSE = -(n₁)(2/5)(Δ_O) +(n₂)(3/5)(Δ_O)

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= -(3)(2/5)(Δ_O) +(0)(3/5)(Δ_O) +2P

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=-1.2 Δ_O

Eg

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t_2g

Eg

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t_2g

CFSE = -(n₁)(2/5)(Δ_O) +(n₂)(3/5)(Δ_O)

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= -(6)(2/5)(Δ_O) +(3)(3/5)(Δ_O) +2P

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=-0.6 Δ_O +4P

d⁹

d⁴ High spin

eg

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t_2g

CFSE = -(n₁)(2/5)(Δ_O) +(n₂)(3/5)(Δ_O)

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= -(3)(2/5)(Δ_O) +(1)(3/5)(Δ_O) +2P

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=-0.6 Δ_O

CFSE = -(n₁)(2/5)(Δ_O) +(n₂)(3/5)(Δ_O)

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= -(4)(2/5)(Δ_O) +(0)(3/5)(Δ_O) +P

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=-01.6 Δ_O +P

d⁴ Low spin

CFSE = -(n₁)(2/5)(Δ_O) +(n₂)(3/5)(Δ_O)

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= -(5)(2/5)(Δ_O) +(0)(3/5)(Δ_O) +2P

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=-2.0 Δ_O +2P

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CFSE = -(n₁)(2/5)(Δ_O) +(n₂)(3/5)(Δ_O)

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= -(6)(2/5)(Δ_O) +(0)(3/5)(Δ_O) +2P

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=-2.4 Δ_O +3P

eg

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t_2g

High Spin

CFSE = -(n₁)(2/5)(Δ_O) +(n₂)(3/5)(Δ_O)

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= -(6)(2/5)(Δ_O) +(1)(3/5)(Δ_O) +2P

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=-1.8 Δ_O +3P

d⁷ Low spin

d¹

d²

CFSE = -(n₁)(3/5)(Δ_t) +(n₂)(2/5)(Δ_t)

Or

CFSE = -(n₁)(0.6)(Δ_t) +(n₂)(0.4Δ_t)

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CFSE = -(1)(0.6)(Δ_t) +(0)(0.4Δ_t)

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= -0.6 Δ_t

Δ_o = -0.6 Δ_t x 0.45

CFSE = -0.27 Δ_o

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_=0.

CFSE = -(2)(0.6)(Δ_t) +(0)(0.4Δ_t)

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= -1.2 Δ_t

Δ_o = -1.2 Δ_t x 0.45

CFSE = -0.0.54 Δ_o

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t₂

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e

t₂

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e

CFSE = -(n₁)(3/5)(Δ_t) +(n₂)(2/5)(Δ_t)

Or

CFSE = -(n₁)(0.6)(Δ_t) +(n₂)(0.4Δ_t)

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CFSE = -(2)(0.6)(Δ_t) +(1)(0.4Δ_t)

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= -0.8 Δ_t

CFSE Δ_o= -1.8 Δ_t x.45 = 0.36

CFSE = -(2)(0.6)(Δ_t) +(2)(0.4Δ_t)

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= -0.4Δ_t

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CFSE Δ_o= -0.4 Δ_t x0.45 = -0.18

d⁴

d³

t₂

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e

t₂

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e

CFSE = -(n₁)(3/5)(Δ_t) +(n₂)(2/5)(Δ_t)

Or

CFSE = -(n₁)(0.6)(Δ_t) +(n₂)(0.4Δ_t)

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CFSE = -(3)(0.6)(Δ_t) +(3)(0.4Δ_t)

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= -0.6 Δ_t

CFSE Δ_o= -0.6 Δ_t x.45 = 0.27 

CFSE = -(4)(0.6)(Δ_t) +(4)(0.4Δ_t)

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= -0.8Δ_t

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CFSE Δ_o= -0.8 Δ_t x0.45 = -0.36

d⁸

d⁶

t₂

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e

t₂

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e

MOLECULAR ORBITAL THEORY

In MOT of complexes, the AO of central metal ion and ligand combine to form σ or π MO orbitals.

These set of MO have equal number of bonding(having lower energy) and antibonding (having higher energy) orbitals.

The non-participating AO of central metal ion is called as nonbonding MO and their energy remains unchanged.

Steps involved in σ MO orbitals in octahedral complexes

1. Selection of metal ion orbitals which are suitable to overlap with ligand pσ orbitals.

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(ii) To determine the ligand pσ orbitals which may combine with suitable metal ion orbitals to give σ MO orbitals.

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(iii)The combination of metal ion orbitals and ligands orbitals of same symmetry to form σ bonding molecular orbitals-BMO and σ antibonding molecular orbitals-ABMO

Metal ion orbitals , Symmetry symbols and shape

T_2g Gerade

E_g Ungerade

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Formation of a_1g BMO σ^bs and a*_1g ABMO σ*s

Formation of two e_g BMO σ^be_g and two t*e_g ABMO σ*e_g

Formation of three t_1u BMO σ^bp and three t*_1u ABMO σ*p

MO Diagram –Octahedral Complexes

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Mo diagram showing sigma bonding in MX₆ Complexes

The diagram shows that the six electron pairs donated by ligand can be accommodated in the six sigma bonding molecular orbitals of the complex resulting in the formation of six sigma bonds .

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From the MO diagram , it is cleared that the MO theory also supports the splitting of d orbitals in the t2g and eg orbital as indicated by the CFT

Metal Obitals

Ligand Orbitals

X + 6(-1) = -3

X= -3 +6 =+3

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Co⁺³ = [Ar] 3d⁶

The distribution of 18 electrons can be written as

(a_1g)² (t_1g)⁶ (e_g)⁴ Bonding MO

(t_2g)⁴ or [(3d_xy)² (3d_yz)¹ (3d_xz)¹] Non bonding MO

(e_g*)² or [(σ*d_z²)¹, (σ*d_x²_-y²)¹] Antiboning MO

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The total 4 unpaired electron present in (non bonding) t_2g & (anti bonding) e_g* is 2+2=4.

Thus [CoF₆]^-3 is paramagnetic. Since n=4 , S= 4/2 =2

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The energy difference ∆o between (non bonding) t_2g & (anti bonding) e_g* is 13000cm^-1, which is less than the pairing energy (P=19000cm^-1).

Therefore instead of paired up in (t_2g) orbitals electron preferred to occupy in Antiboning (e_g*)

X + 6(-1) = -3

X= -3 +6 =+3

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Co⁺³ = [Ar] 3d⁶

The distribution of 18 electrons can be written as

(a_1g)² (t_1g)⁶ (e_g)⁴ Bonding MO

(t_2g)⁶ or [(3d_xy)² (3d_yz)² (3d_xz)²] Non bonding MO

(e_g*)⁰ or [(σ*d_z²)⁰, (σ*d_x²_-y²)⁰] Antiboning MO

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All the electron present in bonding MO and nonbonding MO (t_2g orbitals) are paired up.

Thus [Co(NH₃)₆]⁺³ is dimagnetic. Since n=0 , S= 0

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The energy difference (∆o) between (non bonding) t_2g & (anti bonding) e_g* is 23000cm^-1, which is larger than the pairing energy (P=19000cm^-1).

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Therefore electrons are paired up in (t_2g) orbitals .

ASSIGNMENT

SQ

1. Draw eg and t₂g orbitals? What is the main difference between them?

2. What is degenerate orbitals? When it is found?

3. What is ∆o?

4. What is pairing energy?

5. Write the equation to calculate CFSE. Calculate CFSE for Cr⁺²,Co^+2, Ni⁺²

6. Write the difference between high spin and low spin complexes.

7. Write the relation between ∆o and ∆t?

8. List the factors affecting ∆o.

9. What is Spectrochemical series?

10. Write assumptions of CFT.

LQ

1. Explain splitting of d orbitals in octahedral field.

2. Explain splitting of d orbitals in tetrahedral field.

3. Discuss the factors affecting the magnitude of Δ_O .

4. Discuss the important features of CFT.

5. Explain MOT for [Co(H₂O)₆]⁺³ & [CoF₆]⁺³

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