Coordination Chemistry

Q1 (12)

(a) Since only 2 of 3 Cl⁻ are precipitated, 2 Cl⁻ are ionizable (outside coordination sphere) and 1 Cl⁻ is coordinated. Formula: $[\text{CoCl}(\text{NH}_3)_5]\text{Cl}_2$. (1) Name: pentaamminechloridocobalt(III) chloride. (2)

(b) Coordination number = 6 (5 NH₃ + 1 Cl inside sphere). Oxidation state of Co = +3. Primary valence (ionizable, = oxidation state) = 3; secondary valence (= CN) = 6. (3)

(c) Co³⁺ is $d^6$. With strong-field NH₃ (and Cl⁻ present but complex is low-spin as an amine complex), electrons pair: $t_{2g}^6 e_g^0$ → inner-orbital, $d^2sp^3$ hybridization. All electrons paired → $n=0$, $\mu = 0$ BM (diamagnetic). (3)

(d) EAN = $Z - \text{oxidation state} + 2\times(\text{CN})$ = $27 - 3 + 2(6) = 27 - 3 + 12 = 36$. Equals Kr → obeys EAN rule. (3)

Q2 (10)

(a) Both are $d^6$ (Fe²⁺: $26-2=24$ e⁻; $[\text{Ar}]3d^6$). (1)

• $[\text{Fe}(\text{H}_2\text{O})_6]^{2+}$: weak field → high-spin $t_{2g}^4 e_g^2$. (1)
• $[\text{Fe}(\text{CN})_6]^{4-}$: strong field → low-spin $t_{2g}^6 e_g^0$. (1)

(b) CFSE = $(-0.4\,n_{t2g} + 0.6\,n_{eg})\Delta_o + (\text{extra pairs})P$. Free $d^6$ ion has 1 pair.

• High-spin ($t_{2g}^4 e_g^2$): $(-0.4\times4 + 0.6\times2)\Delta_o = (-1.6+1.2) = \mathbf{-0.4\,\Delta_o}$ (no extra pairing). (2)
• Low-spin ($t_{2g}^6$): $(-0.4\times6)\Delta_o + 2P = \mathbf{-2.4\,\Delta_o + 2P}$ (2 extra pairs beyond free ion). (2)

(c) The intense colour arises from charge-transfer (CT) transitions (metal-to-ligand / ligand-to-metal), which are Laporte- and spin-allowed hence intense. d–d bands are governed by the Laporte (orbital) selection rule ($\Delta l = \pm1$; g→g forbidden) — d–d transitions are Laporte-forbidden and therefore weak. (Also spin selection rule $\Delta S=0$.) (3)

Q3 (10)

(a) Cu(II) = $d^9$: $t_{2g}^6 e_g^3$. (1) The $e_g$ orbitals ($d_{z^2}, d_{x^2-y^2}$) point directly at ligands; with 3 electrons the $e_g$ set is unequally/degenerately occupied (one orbital doubly, one singly filled). (2) This asymmetric occupation of $e_g$ removes degeneracy by elongating along z (Jahn–Teller theorem: any non-linear molecule in an orbitally degenerate ground state distorts to lower energy), giving 4 short + 2 long bonds. (1)

(b) $d^9$ (Cu²⁺) has degeneracy in the $e_g$ set → strong (large) J–T distortion. $d^3$ (Cr³⁺) is $t_{2g}^3 e_g^0$: the $t_{2g}$ set is symmetrically half-filled and $e_g$ empty → ground state orbitally non-degenerate, so essentially no J–T distortion. Hence Cu(II) shows the stronger distortion. (3)

(c) $d^9$ → 1 unpaired electron, $n=1$: $\mu = \sqrt{1(1+2)} = \sqrt{3} = \mathbf{1.73\ BM}$. (3)

Q4 (10)

(a) Ni²⁺ = $d^8$.

• $[\text{Ni}(\text{CN})_4]^{2-}$: diamagnetic → all paired; requires $dsp^2$ hybridization → square planar (one 3d orbital used, electrons paired into $t$-like set). (2)
• $[\text{NiCl}_4]^{2-}$: paramagnetic, $\mu \approx 2.83$ BM → $n=2$ unpaired → $sp^3$ hybridization → tetrahedral. (2)
• The two unpaired electrons (Cl weak field, no pairing forced) vs zero (CN strong field forces pairing) distinguish them magnetically. (1)

(b) en is bidentate; forming $[\text{Ni}(\text{en})_3]^{2+}$ releases more free ligand-solvent molecules than it consumes (3 chelate rings replace 6 monodentate), increasing translational disorder → $\Delta S > 0$. Since $\Delta G = \Delta H - T\Delta S$, the positive entropy makes $\Delta G$ more negative → larger stability constant than the comparable monodentate NH₃ complex. (3)

(c) en = bidentate (denticity 2). EDTA⁴⁻ = hexadentate (denticity 6). (2)

Q5 (8)

(a) Geometrical (cis–trans) isomerism of an octahedral $\text{MA}_4\text{B}_2$ type. (1) Number of geometrical isomers = 2 (cis and trans). (1) The cis isomer lacks a plane of symmetry and can (in principle) be optically active; the trans isomer has a symmetry plane and is optically inactive. (2)

(b) Linkage isomerism; caused by an ambidentate ligand ($\text{NO}_2^-$: N-bonded nitro vs O-bonded nitrito). (2)

(c) Geometrical (cis–trans) isomerism; Pt coordination number = 4, geometry = square planar. (2)

[
  {"claim":"EAN of Co in [CoCl(NH3)5]Cl2 = 36","code":"Z=27; ox=3; CN=6; EAN=Z-ox+2*CN; result=(EAN==36)"},
  {"claim":"High-spin d6 CFSE = -0.4 Delta_o","code":"cfse=-0.4*4+0.6*2; result=(cfse==-0.4)"},
  {"claim":"Low-spin d6 CFSE t2g coefficient = -2.4","code":"cfse=-0.4*6; result=(cfse==-2.4)"},
  {"claim":"mu for d9 (1 unpaired) = sqrt3 approx 1.73","code":"import sympy as sp; mu=sp.sqrt(1*(1+2)); result=(abs(float(mu)-1.732)<0.01)"},
  {"claim":"mu for NiCl4 2- (2 unpaired) approx 2.83","code":"import sympy as sp; mu=sp.sqrt(2*(2+2)); result=(abs(float(mu)-2.828)<0.01)"}
]