Chapter 5: Coordination Compounds (Inorganic Chemistry)

• (i) $[\mathrm{Co}(\mathrm{NH}{}_3){}_4(\mathrm{H}{}_2\mathrm{O}){}_2]\mathrm{Cl}{}_3$
• (ii) $\mathrm{K}{}_2[\mathrm{Ni}(\mathrm{CN}){}_4]$
• (iii) $[\mathrm{Cr}(\mathrm{en}){}_3]\mathrm{Cl}{}_3$
• (iv) $[\mathrm{Pt}(\mathrm{NH}{}_3)\mathrm{BrCl}(\mathrm{NO}{}_2)]{}^{-}$
• (v) $[\mathrm{PtCl}{}_2(\mathrm{en}){}_2](\mathrm{NO}{}_3){}_2$
• (vi) $\mathrm{Fe}{}_4[\mathrm{Fe}(\mathrm{CN}){}_6]{}_3$

As listed above.

• (i) Hexaamminecobalt(III) chloride
• (ii) Pentaamminechloridocobalt(III) chloride
• (iii) Potassium hexacyanidoferrate(III)
• (iv) Potassium trioxalatoferrate(III)
• (v) Potassium tetrachloridopalladate(II)
• (vi) Diamminechlorido(methanamine)platinum(II) chloride

As listed above.

(i) Octahedral, two didentate oxalates and two water molecules. Geometrical: cis (the two $\mathrm{H}{}_2\mathrm{O}$ at 90°) and trans (at 180°). The cis form has no plane of symmetry, so it also shows optical isomerism (d and l forms). The trans form is optically inactive.

(ii) Three didentate en ligands round the octahedron, arranged like a propeller: optical isomerism, two non-superimposable mirror images (d and l).

(iii) Linkage isomerism (nitrito-N, $-\mathrm{NO}{}_2$, or nitrito-O, $-\mathrm{ONO}$) and ionisation isomerism (e.g. $[\mathrm{Co}(\mathrm{NH}{}_3){}_5(\mathrm{NO}{}_3)](\mathrm{NO}{}_2)(\mathrm{NO}{}_3)$, exchanging the ion inside and outside the bracket). (The NCERT answer key notes that, counting all combinations, ten isomers are possible.)

(iv) Square planar $[\mathrm{MA}{}_2\mathrm{BC}]$ type: geometrical isomerism, cis (two Cl at 90°) and trans (two Cl opposite).

(i) Geometrical (cis/trans); cis is optically active. (ii) Optical (d and l). (iii) Linkage and ionisation. (iv) Geometrical (cis/trans).

They give different ions in water:

• $[\mathrm{Co}(\mathrm{NH}{}_3){}_5\mathrm{Cl}]\mathrm{SO}{}_4$ gives $\mathrm{SO}{}_4{}^{2-}$ ions: its solution gives a white precipitate with $\mathrm{BaCl}{}_2$ but none with $\mathrm{AgNO}{}_3$ (Cl is inside the bracket).
• $[\mathrm{Co}(\mathrm{NH}{}_3){}_5(\mathrm{SO}{}_4)]\mathrm{Cl}$ gives $\mathrm{Cl}{}^{-}$ ions: its solution gives a white precipitate with $\mathrm{AgNO}{}_3$ (AgCl) but none with $\mathrm{BaCl}{}_2$.

Same formula, different ions in solution: they are ionisation isomers.

The first precipitates BaSO₄ with BaCl₂ (free SO₄²⁻); the second precipitates AgCl with AgNO₃ (free Cl⁻).

$\mathrm{Ni}{}^{2+}$ is $3d^8$: in the free ion, two 3d electrons are unpaired.

• $[\mathrm{Ni}(\mathrm{CN}){}_4]{}^{2-}$: $\mathrm{CN}{}^{-}$ is a strong ligand. It forces the two unpaired electrons to pair, leaving one 3d orbital empty. That 3d, the 4s and two 4p orbitals form $ds{p}^2$ hybrids: square planar, no unpaired electrons, diamagnetic.
• $[\mathrm{NiCl}{}_4]{}^{2-}$: $\mathrm{Cl}{}^{-}$ is a weak ligand and causes no pairing. The 4s and three 4p orbitals form $s{p}^3$ hybrids: tetrahedral, with two unpaired electrons, paramagnetic.

CN⁻ pairs the d electrons (dsp², square planar, diamagnetic); Cl⁻ does not (sp³, tetrahedral, 2 unpaired, paramagnetic).

• In $[\mathrm{NiCl}{}_4]{}^{2-}$, nickel is $\mathrm{Ni}{}^{2+}$ ($3d^8$). The weak ligand $\mathrm{Cl}{}^{-}$ leaves two unpaired electrons; $s{p}^3$ hybridisation: paramagnetic.
• In $[\mathrm{Ni}(\mathrm{CO}){}_4]$, nickel is Ni(0) ($3d^{8}4s^2$). The strong ligand CO pushes the 4s electrons into 3d, giving $3d^{10}$ with all electrons paired; the empty 4s and 4p orbitals form $s{p}^3$ hybrids: diamagnetic.

[NiCl₄]²⁻ has Ni²⁺ with 2 unpaired electrons; in [Ni(CO)₄], Ni(0) becomes 3d¹⁰ with all electrons paired.

Both contain $\mathrm{Fe}{}^{3+}$ ($3d^5$).

• $\mathrm{H}{}_2\mathrm{O}$ is a weak ligand: no pairing, five unpaired electrons, outer-orbital $s{p}^3{d}^2$ complex: strongly paramagnetic.
• $\mathrm{CN}{}^{-}$ is a strong ligand: the electrons pair up in three 3d orbitals, leaving one unpaired electron; inner-orbital $d^{2}s{p}^3$ complex: weakly paramagnetic.

H₂O leaves 5 unpaired electrons (sp³d²); CN⁻ pairs them, leaving only 1 (d²sp³).

• $\mathrm{Co}{}^{3+}$ is $3d^6$. With $\mathrm{NH}{}_3$ the six electrons pair up in three 3d orbitals, freeing two inner 3d orbitals: $d^{2}s{p}^3$ hybridisation, an inner orbital complex (diamagnetic).
• $\mathrm{Ni}{}^{2+}$ is $3d^8$. Even if electrons pair, at most one 3d orbital could be emptied, so two inner d orbitals cannot be made free. The outer 4d orbitals are used: $s{p}^3{d}^2$ hybridisation, an outer orbital complex (two unpaired electrons).

Co³⁺ (d⁶) can free two 3d orbitals (d²sp³, inner); Ni²⁺ (d⁸) cannot, so it uses 4d orbitals (sp³d², outer).

$\mathrm{Pt}{}^{2+}$ is $5d^8$. In a square planar ($ds{p}^2$) complex with the strong ligand $\mathrm{CN}{}^{-}$, the eight electrons pair up in four 5d orbitals. So there are zero unpaired electrons.

Zero.

$\mathrm{Mn}{}^{2+}$ is $3d^5$.

• $\mathrm{H}{}_2\mathrm{O}$ is a weak-field ligand: ${\Delta }_o$ is smaller than the pairing energy, so electrons occupy all five d orbitals singly: $t_{2g}^3{e}_g^2$, five unpaired (high spin).
• $\mathrm{CN}{}^{-}$ is a strong-field ligand: ${\Delta }_o$ is larger than the pairing energy, so all five electrons go into the lower $t_{2g}$ set: $t_{2g}^5{e}_g^0$, one unpaired (low spin).

Weak-field H₂O gives t₂g³e_g² (5 unpaired); strong-field CN⁻ gives t₂g⁵ (1 unpaired).

• A metal shows two kinds of valence: primary (ionisable) and secondary (non-ionisable).
• Primary valences correspond to the oxidation state; they are satisfied by negative ions.
• Secondary valences equal the coordination number; they are satisfied by neutral molecules or negative ions (ligands) and are fixed for a metal.
• The groups attached by secondary valences are directed in space, giving definite geometries (octahedral, tetrahedral, square planar).

Example: $\mathrm{CoCl}{}_3\cdot 6\mathrm{NH}{}_3$ is $[\mathrm{Co}(\mathrm{NH}{}_3){}_6]\mathrm{Cl}{}_3$: six $\mathrm{NH}{}_3$ satisfy the secondary valence (coordination number 6, octahedral), and three $\mathrm{Cl}{}^{-}$ satisfy the primary valence (all three precipitate with $\mathrm{AgNO}{}_3$).

Primary (ionisable, = oxidation state) and secondary (non-ionisable, = coordination number, spatially directed) valences, e.g. [Co(NH₃)₆]Cl₃.

$\mathrm{FeSO}{}_4$ and $(\mathrm{NH}{}_4){}_2\mathrm{SO}{}_4$ form Mohr's salt, $\mathrm{FeSO}{}_4\cdot (\mathrm{NH}{}_4){}_2\mathrm{SO}{}_4\cdot 6\mathrm{H}{}_2\mathrm{O}$, a double salt, which dissociates completely in water into simple ions, including $\mathrm{Fe}{}^{2+}$.

$\mathrm{CuSO}{}_4$ and 4 $\mathrm{NH}{}_3$ form the complex ion $[\mathrm{Cu}(\mathrm{NH}{}_3){}_4]{}^{2+}$, which stays intact in solution; free $\mathrm{Cu}{}^{2+}$ ions are hardly present, so the test fails.

The first is a double salt that releases Fe²⁺; the second forms the stable complex [Cu(NH₃)₄]²⁺, which does not release Cu²⁺.

• Coordination entity: a central metal atom or ion bonded to a fixed number of ions or molecules, e.g. $[\mathrm{CoCl}{}_3(\mathrm{NH}{}_3){}_3]$, $[\mathrm{Ni}(\mathrm{CO}){}_4]$, $[\mathrm{Fe}(\mathrm{CN}){}_6]{}^{4-}$.
• Ligand: an ion or molecule bound to the central atom through a donor atom, e.g. $\mathrm{Cl}{}^{-}$, $\mathrm{NH}{}_3$, $\mathrm{H}{}_2\mathrm{O}$, $\mathrm{CN}{}^{-}$.
• Coordination number: the number of donor atoms directly bonded to the metal, e.g. 6 in $[\mathrm{PtCl}{}_6]{}^{2-}$, 4 in $[\mathrm{Ni}(\mathrm{NH}{}_3){}_4]{}^{2+}$.
• Coordination polyhedron: the spatial arrangement of the donor atoms round the metal, e.g. octahedral $[\mathrm{Co}(\mathrm{NH}{}_3){}_6]{}^{3+}$, tetrahedral $[\mathrm{Ni}(\mathrm{CO}){}_4]$, square planar $[\mathrm{PtCl}{}_4]{}^{2-}$.
• Homoleptic: all ligands are the same, e.g. $[\mathrm{Co}(\mathrm{NH}{}_3){}_6]{}^{3+}$, $[\mathrm{Ni}(\mathrm{CO}){}_4]$.
• Heteroleptic: more than one kind of ligand, e.g. $[\mathrm{Co}(\mathrm{NH}{}_3){}_4\mathrm{Cl}{}_2]{}^{+}$, $[\mathrm{Pt}(\mathrm{NH}{}_3){}_2\mathrm{Cl}{}_2]$.

See the definitions and examples above.

• Unidentate: binds through one donor atom, e.g. $\mathrm{Cl}{}^{-}$, $\mathrm{NH}{}_3$, $\mathrm{H}{}_2\mathrm{O}$.
• Didentate: binds through two donor atoms, e.g. ethane-1,2-diamine ($\mathrm{H}{}_2\mathrm{NCH}{}_2\mathrm{CH}{}_2\mathrm{NH}{}_2$, en), oxalate ($\mathrm{C}{}_2\mathrm{O}{}_4{}^{2-}$).
• Ambidentate: can bind through either of two different atoms, e.g. $\mathrm{NO}{}_2{}^{-}$ (through N or O), $\mathrm{SCN}{}^{-}$ (through S or N).

Unidentate: Cl⁻, NH₃. Didentate: en, oxalate. Ambidentate: NO₂⁻, SCN⁻.

• (i) $x+0+(-1)+0=+2$: +3
• (ii) $x+2(-1)+0=+1$: +3
• (iii) $x+4(-1)=-2$: +2
• (iv) $[\mathrm{Fe}(\mathrm{CN}){}_6{]}^{3-}$: $x-6=-3$: +3
• (v) $x+0+3(-1)=0$: +3

(i) +3, (ii) +3, (iii) +2, (iv) +3, (v) +3.

• (i) $[\mathrm{Zn}(\mathrm{OH}){}_4]{}^{2-}$
• (ii) $\mathrm{K}{}_2[\mathrm{PdCl}{}_4]$
• (iii) $[\mathrm{Pt}(\mathrm{NH}{}_3){}_2\mathrm{Cl}{}_2]$
• (iv) $\mathrm{K}{}_2[\mathrm{Ni}(\mathrm{CN}){}_4]$
• (v) $[\mathrm{Co}(\mathrm{NH}{}_3){}_5(\mathrm{ONO})]{}^{2+}$
• (vi) $[\mathrm{Co}(\mathrm{NH}{}_3){}_6]{}_2(\mathrm{SO}{}_4){}_3$
• (vii) $\mathrm{K}{}_3[\mathrm{Cr}(\mathrm{C}{}_2\mathrm{O}{}_4){}_3]$
• (viii) $[\mathrm{Pt}(\mathrm{NH}{}_3){}_6]{}^{4+}$
• (ix) $[\mathrm{CuBr}{}_4]{}^{2-}$
• (x) $[\mathrm{Co}(\mathrm{NH}{}_3){}_5(\mathrm{NO}{}_2)]{}^{2+}$

As listed above.

• (i) Hexaamminecobalt(III) chloride
• (ii) Diamminechlorido(methanamine)platinum(II) chloride
• (iii) Hexaaquatitanium(III) ion
• (iv) Tetraamminechloridonitrito-N-cobalt(III) chloride
• (v) Hexaaquamanganese(II) ion
• (vi) Tetrachloridonickelate(II) ion
• (vii) Hexaamminenickel(II) chloride
• (viii) Tris(ethane-1,2-diamine)cobalt(III) ion
• (ix) Tetracarbonylnickel(0)

As listed above.

Stereoisomerism

• Geometrical: cis- and trans-$[\mathrm{Pt}(\mathrm{NH}{}_3){}_2\mathrm{Cl}{}_2]$
• Optical: d- and l-$[\mathrm{Co}(\mathrm{en}){}_3]{}^{3+}$

Structural isomerism

• Linkage: $[\mathrm{Co}(\mathrm{NH}{}_3){}_5(\mathrm{NO}{}_2)]\mathrm{Cl}{}_2$ and $[\mathrm{Co}(\mathrm{NH}{}_3){}_5(\mathrm{ONO})]\mathrm{Cl}{}_2$
• Coordination: $[\mathrm{Co}(\mathrm{NH}{}_3){}_6][\mathrm{Cr}(\mathrm{CN}){}_6]$ and $[\mathrm{Cr}(\mathrm{NH}{}_3){}_6][\mathrm{Co}(\mathrm{CN}){}_6]$
• Ionisation: $[\mathrm{Co}(\mathrm{NH}{}_3){}_5(\mathrm{SO}{}_4)]\mathrm{Br}$ and $[\mathrm{Co}(\mathrm{NH}{}_3){}_5\mathrm{Br}]\mathrm{SO}{}_4$
• Solvate (hydrate): $[\mathrm{Cr}(\mathrm{H}{}_2\mathrm{O}){}_6]\mathrm{Cl}{}_3$ (violet) and $[\mathrm{Cr}(\mathrm{H}{}_2\mathrm{O}){}_5\mathrm{Cl}]\mathrm{Cl}{}_2\cdot \mathrm{H}{}_2\mathrm{O}$ (grey-green)

Geometrical, optical, linkage, coordination, ionisation and solvate isomerism, with the examples above.

(i) None. With three identical didentate ligands, all arrangements are the same geometrically (it shows only optical isomerism).

(ii) Two: fac (the three Cl on one face of the octahedron) and mer (the three Cl in a line round the meridian).

(i) 0. (ii) 2 (fac and mer).

(i) The three oxalate rings span the octahedron like a propeller; the left-handed and right-handed propellers are mirror images that cannot be superimposed: the d and l forms.

(ii) Only the cis isomer (two Cl at 90°) is optically active: its two en rings and two Cl form a pair of non-superimposable mirror images (d and l). The trans isomer has a plane of symmetry and is inactive.

(iii) The isomer in which the two $\mathrm{NH}{}_3$ are cis and the two Cl are cis (each Cl opposite one end of en) has no plane of symmetry; it exists as a d and l pair. The isomers with the two Cl trans or the two $\mathrm{NH}{}_3$ trans are optically inactive.

(i) d and l propellers; (ii) d and l forms of the cis isomer; (iii) d and l forms of the isomer with both NH₃ cis and both Cl cis.

(i) Three isomers: trans (two Cl opposite; has a plane of symmetry, inactive) and cis (two Cl at 90°), which exists as a d and l pair.

(ii) Three isomers: trans ($\mathrm{NH}{}_3$ opposite Cl; inactive) and cis ($\mathrm{NH}{}_3$ and Cl adjacent), which exists as a d and l pair.

(iii) Four isomers:

• the two Cl trans (the $\mathrm{NH}{}_3$ cis): inactive
• the two $\mathrm{NH}{}_3$ trans (the Cl cis): inactive
• both $\mathrm{NH}{}_3$ cis and both Cl cis: chiral, giving a d and l pair

(i) trans + cis (d, l): 3. (ii) trans + cis (d, l): 3. (iii) two inactive geometrical isomers plus a chiral cis–cis pair (d, l): 4.

Square planar $[\mathrm{Mabcd}]$ gives three geometrical isomers, depending on which ligand is trans to $\mathrm{NH}{}_3$:

• $\mathrm{NH}{}_3$ trans to Br (Cl trans to py)
• $\mathrm{NH}{}_3$ trans to Cl (Br trans to py)
• $\mathrm{NH}{}_3$ trans to py (Br trans to Cl)

None of them shows optical isomerism: a square planar complex lies in a plane, which is a plane of symmetry.

Three geometrical isomers; none is optically active.

Copper sulphate in water contains the blue $[\mathrm{Cu}(\mathrm{H}{}_2\mathrm{O}){}_4]{}^{2+}$ ion. The water ligands are replaced by halide ions:

• (i) $[\mathrm{Cu}(\mathrm{H}{}_2\mathrm{O}){}_4]{}^{2+}+4\mathrm{F}{}^{-}\to [\mathrm{CuF}{}_4]{}^{2-}+4\mathrm{H}{}_2\mathrm{O}$ (green)
• (ii) $[\mathrm{Cu}(\mathrm{H}{}_2\mathrm{O}){}_4]{}^{2+}+4\mathrm{Cl}{}^{-}\to [\mathrm{CuCl}{}_4]{}^{2-}+4\mathrm{H}{}_2\mathrm{O}$ (bright green)

The new ligands change the crystal field splitting, so the colour changes.

F⁻ and Cl⁻ replace the water ligands, forming green [CuF₄]²⁻ and bright green [CuCl₄]²⁻.

A very stable cyanido complex forms. The NCERT answer writes it as

$$[\mathrm{Cu}(\mathrm{H}{}_2\mathrm{O}){}_4]{}^{2+}+4\mathrm{CN}{}^{-}\to [\mathrm{Cu}(\mathrm{CN}){}_4]{}^{2-}+4\mathrm{H}{}_2\mathrm{O}$$

(in practice, excess cyanide first reduces $\mathrm{Cu}{}^{2+}$, and the complex is $[\mathrm{Cu}(\mathrm{CN}){}_4]{}^{3-}$).

$\mathrm{CN}{}^{-}$ is a strong ligand and the complex is so stable that almost no free copper ions remain in solution. The tiny concentration of copper ions cannot reach the solubility product of CuS, so no precipitate forms with $\mathrm{H}{}_2\mathrm{S}$.

A very stable tetracyanidocuprate complex forms; it leaves too few free copper ions for CuS to precipitate.

• (i) $[\mathrm{Fe}(\mathrm{CN}){}_6]{}^{4-}$: $\mathrm{Fe}{}^{2+}$ ($3d^6$). Strong $\mathrm{CN}{}^{-}$ pairs the electrons in three 3d orbitals, leaving two 3d free: $d^{2}s{p}^3$, inner orbital, octahedral, diamagnetic.
• (ii) $[\mathrm{FeF}{}_6]{}^{3-}$: $\mathrm{Fe}{}^{3+}$ ($3d^5$). Weak $\mathrm{F}{}^{-}$ causes no pairing; 4s, 4p and 4d are used: $s{p}^3{d}^2$, outer orbital, octahedral, 5 unpaired electrons.
• (iii) $[\mathrm{Co}(\mathrm{C}{}_2\mathrm{O}{}_4){}_3]{}^{3-}$: $\mathrm{Co}{}^{3+}$ ($3d^6$). Oxalate pairs the electrons (low spin): $d^{2}s{p}^3$, inner orbital, octahedral, diamagnetic.
• (iv) $[\mathrm{CoF}{}_6]{}^{3-}$: $\mathrm{Co}{}^{3+}$ ($3d^6$). Weak $\mathrm{F}{}^{-}$, no pairing: $s{p}^3{d}^2$, outer orbital, octahedral, 4 unpaired electrons.

(i) d²sp³, diamagnetic. (ii) sp³d², 5 unpaired. (iii) d²sp³, diamagnetic. (iv) sp³d², 4 unpaired.

In an octahedral field the ligands approach along the x, y and z axes. The $d_{x^2-y^2}$ and $d_{z^2}$ orbitals, which point along the axes, are repelled more and rise in energy (the $e_g$ set, $+0.6{\Delta }_o$). The $d_{xy}$, $d_{yz}$ and $d_{xz}$ orbitals, which point between the axes, are lowered (the $t_{2g}$ set, $-0.4{\Delta }_o$). The energy gap is the crystal field splitting ${\Delta }_o$.

The five d orbitals split into a lower t₂g set (d_xy, d_yz, d_xz; −0.4Δ_o) and a higher e_g set (d_x²−y², d_z²; +0.6Δ_o).

The spectrochemical series lists ligands in order of increasing crystal field splitting they produce (found from absorption spectra):

I⁻ < Br⁻ < SCN⁻ < Cl⁻ < S²⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < edta⁴⁻ < NH₃ < en < CN⁻ < CO

• A weak field ligand (e.g. I⁻, Cl⁻, F⁻, H₂O) causes a small splitting, ${\Delta }_o<P$ (pairing energy). Electrons stay unpaired and enter the $e_g$ orbitals: high-spin complexes.
• A strong field ligand (e.g. CN⁻, CO, en) causes a large splitting, ${\Delta }_o>P$. Electrons pair up in the $t_{2g}$ orbitals: low-spin complexes.

The order of ligands by the splitting they cause; weak field ligands give small Δ_o (high spin), strong field ligands give large Δ_o (low spin).

Crystal field splitting energy (${\Delta }_o$ for octahedral complexes) is the energy difference between the two sets of d orbitals ($t_{2g}$ and $e_g$) after they split in the field of the ligands.

For $d^1$–$d^3$ the electrons simply go into $t_{2g}$. From $d^4$ onwards there is a choice, decided by comparing ${\Delta }_o$ with the pairing energy $P$:

• If ${\Delta }_o<P$ (weak field): the fourth electron goes into $e_g$: $t_{2g}^3{e}_g^1$, high spin.
• If ${\Delta }_o>P$ (strong field): the fourth electron pairs in $t_{2g}$: $t_{2g}^4{e}_g^0$, low spin.

It is the t₂g–e_g energy gap; if Δ_o < P the complex is high spin (e.g. t₂g³e_g¹), if Δ_o > P it is low spin (t₂g⁴).

• $[\mathrm{Cr}(\mathrm{NH}{}_3){}_6]{}^{3+}$: $\mathrm{Cr}{}^{3+}$ is $3d^3$. The three electrons occupy the $t_{2g}$ orbitals singly ($d^{2}s{p}^3$ uses the two empty 3d orbitals), so there are three unpaired electrons: paramagnetic.
• $[\mathrm{Ni}(\mathrm{CN}){}_4]{}^{2-}$: $\mathrm{Ni}{}^{2+}$ is $3d^8$. The strong ligand $\mathrm{CN}{}^{-}$ pairs all the electrons ($ds{p}^2$, square planar): no unpaired electrons, diamagnetic.

Cr³⁺ (d³) has 3 unpaired electrons; in [Ni(CN)₄]²⁻ all 8 d electrons are paired (dsp²).

• In $[\mathrm{Ni}(\mathrm{H}{}_2\mathrm{O}){}_6]{}^{2+}$, $\mathrm{Ni}{}^{2+}$ ($3d^8$) has two unpaired electrons in a weak field. A d–d transition absorbs red light from the visible region, and the complementary green colour is seen.
• In $[\mathrm{Ni}(\mathrm{CN}){}_4]{}^{2-}$, the strong field of $\mathrm{CN}{}^{-}$ pairs all the electrons and the splitting is large, so no absorption takes place in the visible region (the NCERT answer: no unpaired electrons, no d–d transition in the visible). The solution is colourless.

[Ni(H₂O)₆]²⁺ has unpaired electrons and absorbs red light (looks green); in [Ni(CN)₄]²⁻ all electrons are paired and no visible light is absorbed.

Both contain $\mathrm{Fe}{}^{2+}$, but the ligands differ. $\mathrm{CN}{}^{-}$ is a strong field ligand (large ${\Delta }_o$, low spin) and $\mathrm{H}{}_2\mathrm{O}$ is a weak field ligand (small ${\Delta }_o$, high spin). Different splitting energies mean light of different wavelengths is absorbed in the d–d transitions, so the complementary colours seen are different.

Different ligands give different Δ_o, so different wavelengths are absorbed.

The metal–carbon bond in carbonyls has both σ and π character:

• σ bond: the carbon of CO donates its lone pair into an empty orbital of the metal (M ← CO).
• π back bond: a filled d orbital of the metal donates electrons into the empty antibonding π* orbital of CO (M → CO).

This synergic bonding strengthens the M–C bond (each part strengthens the other) and weakens the C–O bond slightly. Examples: $\mathrm{Ni}(\mathrm{CO}){}_4$ (tetrahedral), $\mathrm{Fe}(\mathrm{CO}){}_5$ (trigonal bipyramidal), $\mathrm{Cr}(\mathrm{CO}){}_6$ (octahedral).

A σ bond from CO's lone pair to the metal plus π back-bonding from metal d orbitals into CO's π* orbital (synergic bonding).

• (i) Co +3; $3d^6$ ($t_{2g}^6$, low spin); coordination number 6
• (ii) Cr +3; $3d^3$ ($t_{2g}^3$); coordination number 6
• (iii) Co +2; $3d^7$ (tetrahedral, $e^4{t}_2^3$); coordination number 4
• (iv) Mn +2; $3d^5$ ($t_{2g}^3{e}_g^2$, high spin); coordination number 6

(i) +3, d⁶, 6. (ii) +3, d³, 6. (iii) +2, d⁷, 4. (iv) +2, d⁵, 6.

(i) Potassium diaquadioxalatochromate(III) trihydrate. Cr +3, $3d^3$, CN 6, octahedral; shows cis/trans isomerism (cis is optically active). 3 unpaired: $\mu =3.87$ BM.

(ii) Pentaamminechloridocobalt(III) chloride. Co +3, $3d^6$ (low spin, $t_{2g}^6$), CN 6, octahedral. No unpaired electrons: $\mu =0$ (diamagnetic).

(iii) Trichloridotripyridinechromium(III). Cr +3, $3d^3$, CN 6, octahedral; fac and mer isomers. $\mu =3.87$ BM.

(iv) Caesium tetrachloridoferrate(III). Fe +3, $3d^5$, CN 4, tetrahedral ($s{p}^3$). 5 unpaired: $\mu =5.92$ BM.

(v) Potassium hexacyanidomanganate(II). Mn +2, $3d^5$ (low spin, $t_{2g}^5$), CN 6, octahedral ($d^{2}s{p}^3$). 1 unpaired: $\mu =1.73$ BM.

See each complex above (names, oxidation states, d configurations, coordination numbers, shapes and moments).

$\mathrm{Ti}{}^{3+}$ is $3d^1$. In the octahedral field of six water molecules, the single electron is in the lower $t_{2g}$ set. When white light falls on the complex, the electron absorbs light of about 498 nm (blue-green) and jumps to the $e_g$ set (a d–d transition, $t_{2g}^1\to e_g^1$). The light that remains, the complementary colour, is violet.

The d¹ electron absorbs blue-green light (≈ 498 nm) in a t₂g → e_g transition; the transmitted complementary colour is violet.

When a didentate or polydentate ligand binds a metal through two or more donor atoms, it forms a ring (a chelate). Such complexes are more stable than similar complexes with unidentate ligands; this extra stability is the chelate effect. Example: $[\mathrm{Ni}(\mathrm{en}){}_3]{}^{2+}$ is much more stable than $[\mathrm{Ni}(\mathrm{NH}{}_3){}_6]{}^{2+}$, although both have six Ni–N bonds.

Chelate complexes (ring-forming ligands) are more stable than similar complexes of unidentate ligands, e.g. [Ni(en)₃]²⁺ vs [Ni(NH₃)₆]²⁺.

• (i) Biological systems: chlorophyll (Mg complex) for photosynthesis; haemoglobin (Fe complex) carries oxygen; vitamin B12 (cyanocobalamin) is a Co complex.
• (ii) Medicinal chemistry: cis-platin, $[\mathrm{Pt}(\mathrm{NH}{}_3){}_2\mathrm{Cl}{}_2]$, is an anticancer drug; EDTA is used to remove lead from the body in lead poisoning.
• (iii) Analytical chemistry: hardness of water is estimated by titration with EDTA ($\mathrm{Ca}{}^{2+}$ and $\mathrm{Mg}{}^{2+}$ complexes); $\mathrm{Ni}{}^{2+}$ is detected with dimethylglyoxime (red complex).
• (iv) Extraction of metals: silver and gold are extracted as the cyanide complexes $[\mathrm{Ag}(\mathrm{CN}){}_2]{}^{-}$ and $[\mathrm{Au}(\mathrm{CN}){}_2]{}^{-}$; nickel is purified through $[\mathrm{Ni}(\mathrm{CO}){}_4]$ (Mond process).

(i) Chlorophyll, haemoglobin, B12. (ii) Cis-platin, EDTA for lead poisoning. (iii) EDTA titrations, DMG test for Ni. (iv) Cyanide extraction of Ag and Au; Mond process for Ni.

$[\mathrm{Co}(\mathrm{NH}{}_3){}_6]\mathrm{Cl}{}_2\to [\mathrm{Co}(\mathrm{NH}{}_3){}_6]{}^{2+}+2\mathrm{Cl}{}^{-}$: three ions.

(iii) 3

• $\mathrm{Cr}{}^{3+}$ ($3d^3$): 3 unpaired, 3.87 BM
• $\mathrm{Fe}{}^{2+}$ ($3d^6$, high spin with water): 4 unpaired, 4.90 BM
• $\mathrm{Zn}{}^{2+}$ ($3d^{10}$): 0 unpaired

(ii) [Fe(H₂O)₆]²⁺

Oxalate is a didentate (chelating) ligand, so $[\mathrm{Fe}(\mathrm{C}{}_2\mathrm{O}{}_4){}_3]{}^{3-}$ is the most stable (chelate effect).

(iii) [Fe(C₂O₄)₃]³⁻

Ligand field strength: $\mathrm{NO}{}_2{}^{-}>\mathrm{NH}{}_3>\mathrm{H}{}_2\mathrm{O}$, so ${\Delta }_o$ decreases in this order. A larger ${\Delta }_o$ means higher-energy (shorter wavelength) light is absorbed. Wavelength of absorption:

$$[\mathrm{Ni}(\mathrm{H}{}_2\mathrm{O}){}_6]{}^{2+}>[\mathrm{Ni}(\mathrm{NH}{}_3){}_6]{}^{2+}>[\mathrm{Ni}(\mathrm{NO}{}_2){}_6]{}^{4-}$$

[Ni(H₂O)₆]²⁺ > [Ni(NH₃)₆]²⁺ > [Ni(NO₂)₆]⁴⁻ (longest to shortest wavelength).