Coordination Compounds – JEE Main ChemistryPractice Questions & PYQs

To determine the number of unpaired electrons in $\mathrm{K}_3[\mathrm{Cr}(\mathrm{C}_2\mathrm{O}_4)_3]$, first find the oxidation state of the chromium atom. Given that potassium carries a $+1$ charge and the oxalate ligand carries a $-2$ charge, the charge balance equation $+3 + x + 3(-2) = 0$ yields an oxidation state of $+3$ for chromium. The electronic configuration for a neutral chromium atom is $3d^{5} 4s^{1}$, so removing three electrons to form the $\mathrm{Cr}^{3+}$ ion results in the $3d^{3} 4s^{0}$ configuration. With three electrons occupying three separate $d$-orbitals, the total number of unpaired electrons is 3.

Mohr's salt, defined by the formula $(\mathrm{NH}_4)_2\mathrm{Fe}(\mathrm{SO}_4)_2 \cdot 6\mathrm{H}_2\mathrm{O}$, contains 6 water molecules, while potash alum, defined by $\mathrm{K}_2\mathrm{SO}_4 \cdot \mathrm{Al}_2(\mathrm{SO}_4)_3 \cdot 24\mathrm{H}_2\mathrm{O}$, contains 24. Dividing the number of water molecules in Mohr's salt by those in potash alum yields the ratio $\frac{6}{24}$, which simplifies to $\frac{1}{4}$ or 0.25. This value is equivalent to $2.5 \times 10^{-1}$.

The intensity of color in coordination complexes is primarily governed by selection rules for electronic transitions, where non-centrosymmetric geometries such as the tetrahedral $\mathrm{[NiCl_4]^{2-}}$ allow Laporte transitions, resulting in significantly higher color intensity. Conversely, both the octahedral $\mathrm{[Ni(H_2O)_6]^{2+}}$ and square planar $\mathrm{[Ni(CN)_4]^{2-}}$ complexes possess a center of inversion, which renders their $d-d$ transitions Laporte forbidden and inherently less intense. Consequently, because the square planar configuration exhibits the greatest splitting energy and thus the lowest relative absorption intensity among these specific examples, the observed order of intensity follows the trend $\mathrm{[NiCl_4]^{2-}} > \mathrm{[Ni(H_2O)_6]^{2+}} > \mathrm{[Ni(CN)_4]^{2-}}$.

The stability of coordination complexes is primarily determined by the chelate effect, which dictates that complexes featuring a higher number of chelate rings are thermodynamically more stable than those with fewer or no such rings. In this series, $[{Co}({NH}_{3})_{6}] {Cl}_{2}$ contains zero chelate rings, whereas $[{Co}({en})({NH}_{3})_{4}] {Cl}_{2}$, $[{Co}({en})_{2}({NH}_{3})_{2}] {Cl}_{2}$, and $[{Co}({en})_{3}] {Cl}_{2}$ contain one, two, and three chelate rings, respectively. Since stability increases with the number of chelate rings present, $[{Co}({en})_{3}] {Cl}_{2}$ is the most stable complex among the options provided.

The bonding in $[Ni(CO)_4]$ is best interpreted through Molecular Orbital Theory because it successfully accounts for the intricate synergic interactions between the metal center and the carbonyl ligands. This model uniquely addresses the observed magnetic properties and explains the simultaneous decrease in Ni-C bond length alongside the increase in C-O bond length resulting from back-bonding. By considering the overlap of specific metal and ligand orbitals, this theory provides the necessary depth to interpret the electronic structure that other models lack.

The magnetic moment of a transition metal complex is determined by the number of unpaired electrons, which is dictated by the electronic configuration of the metal ion and the strength of the surrounding ligands. For $\mathrm{Ni(CO)_4}$, $\mathrm{Na_2[Ni(CN)_4]}$, and $\mathrm{PdCl_2(PPh_3)_2}$, the presence of strong-field ligands or significant crystal field splitting causes all $d$-electrons to pair up, resulting in a spin-only magnetic moment of 0 B.M. In contrast, $\mathrm{[Ni(H_2O)_6]Cl_2}$ contains the $\mathrm{Ni^{2+}}$ ion coordinated by weak-field water ligands, which allows for two unpaired electrons and leads to a magnetic moment of 2.8 B.M.

The number of coordination sites is determined by the denticity of a ligand, which represents the total count of donor atoms that bind to a central metal ion. Since ethylenediaminetetraacetate ($EDTA^{4-}$) acts as a hexadentate ligand, it utilizes two nitrogen atoms and four oxygen atoms to establish 6 simultaneous coordination bonds.

The spin-only magnetic moment formula $\mu = \sqrt{n(n+2)}\,\mathrm{BM}$ indicates that a value of $5.9\,\mathrm{BM}$ requires $n=5$ unpaired electrons, as $\sqrt{5(5+2)} = \sqrt{35} \approx 5.92\,\mathrm{BM}$. Among the given species, $[\mathrm{MnBr}_4]^{2-}$ contains $\mathrm{Mn}^{2+}$ in a $d^5$ configuration, where the weak-field ligand $\mathrm{Br}^-$ in a tetrahedral geometry ensures that all five electrons remain unpaired. In contrast, $\mathrm{Ni}(\mathrm{CO})_4$ has $\mathrm{Ni}(0)$ with a $d^{10}$ configuration ($n=0$), $[\mathrm{NiCl}_4]^{2-}$ features $\mathrm{Ni}^{2+}$ with two unpaired electrons ($n=2$), and the strong-field ligand $\mathrm{CN}^-$ in $[\mathrm{Ni}(\mathrm{CN})_4]^{2-}$ forces a paired, diamagnetic $d^8$ square planar structure ($n=0$).

A spin-only magnetic moment of 4.90 BM indicates the presence of 4 unpaired electrons, which is identified using the expression $\mu = \sqrt{n(n+2)}$. In a tetrahedral crystal field, the $d^6$ configuration occupies the split $d$-orbitals in an $e^3 t_2^3$ arrangement, consistently providing 4 unpaired electrons. The resulting crystal field stabilization energy for this tetrahedral geometry is calculated by the sum $(-0.6 \Delta_t) \times 3 + (+0.4 \Delta_t) \times 3$, which simplifies to $-0.6 \Delta_t$.

The observed spin-only magnetic moment of 3.83 BM signifies the presence of three unpaired electrons, confirming the chromium ion exists in the +3 oxidation state. Based on this, the complex must accommodate three chloride ions, as seen in the formula $Cr(H_2O)_6Cl_3$, which leads us to evaluate its hydrate isomers for their specific chemical behavior. The isomer $[Cr(H_2O)_4Cl_2]Cl \cdot 2H_2O$ is unique among these as it provides an ionizable chloride atom that precipitates silver chloride when mixed with $AgNO_3$ and possesses the appropriate ligand configuration to exhibit geometric isomerism. Following standard IUPAC conventions to name this structure, we identify the ligands and metal center to arrive at Tetraaquadichlorido chromium (III) chloride dihydrate.

Determining oxidation states relies on the principle that the sum of the oxidation numbers of all constituent atoms in a neutral molecule must be zero. For the first compound, $\mathrm{Na}_{4}[\mathrm{Fe}(\mathrm{CN})_{5}(\mathrm{NOS})]$, accounting for four sodium ions at $+1$ each, five cyanide ligands at $-1$ each, and the $\mathrm{NOS}$ ligand at $-1$, the iron state $x$ satisfies
$4(+1) + x + 5(-1) + (-1) = 0$
which identifies $x$ as $+2$. In the second compound, $\mathrm{Na}_{4}[\mathrm{FeO}_{4}]$, the charge balance for $y$ using four oxygen atoms at $-2$ each is given by
$4(+1) + y + 4(-2) = 0$
yielding $y = +4$. Finally, in the neutral complex $\mathrm{Fe}_{2}(\mathrm{CO})_{9}$, the carbonyl ligands are neutral, so the iron state $z$ follows the relation
$2z + 9(0) = 0$
which gives $z = 0$, making the final sum of the oxidation states $x + y + z = 2 + 4 + 0 = 6$.

Whether a coordination complex exhibits optical activity depends fundamentally on the absence of internal symmetry elements, specifically a plane of symmetry. In the $trans-[Co(en)_2Cl_2]^+$ isomer, the geometric arrangement of the ligands creates a plane of symmetry that renders the molecule superimposable on its mirror image, ensuring that it remains optically inactive. Conversely, the $cis-[Co(en)_2Cl_2]^+$ isomer lacks this internal plane of symmetry, resulting in a chiral structure that is capable of being optically active.

When distributing four electrons into the octahedral crystal field orbitals, one must evaluate whether the splitting energy $\Delta_o$ is smaller than the pairing energy $P$. Because $\Delta_o < P$, it is energetically cheaper to promote an electron to the higher energy $e_g$ orbital than to force it to pair within the lower energy $t_{2g}$ orbital. Consequently, the electrons occupy the orbitals singly to minimize the overall energy of the $d^4$ system, resulting in the configuration $t_{2g}^3 e_g^1$.

The spin-only magnetic moment of a complex is determined by the number of unpaired electrons $n$ present in the $d$-orbitals of the central metal ion, calculated using the relationship $\mu = \sqrt{n(n+2)}$ B.M. In $\mathrm{[Cr(H_2O)_6]Br_2}$, the $\mathrm{Cr}^{2+}$ ion has a $d^4$ configuration with weak field ligands, which prevents pairing and results in four unpaired electrons for a magnetic moment of $\sqrt{24}$ B.M. The complex $\mathrm{Na_4[Fe(CN)_6]}$ contains $\mathrm{Fe}^{2+}$ with a $d^6$ configuration coordinated to strong field $\mathrm{CN^-}$ ligands, forcing all electrons to pair up and leaving zero unpaired electrons. For $\mathrm{Na_3[Fe(C_2O_4)_3]}$, the $\mathrm{Fe}^{3+}$ ion has a $d^5$ configuration in a strong field environment ($\Delta_0 > P$), which leads to electron pairing and leaves one unpaired electron, yielding a magnetic moment of $\sqrt{3}$ B.M. Finally, $\mathrm{(Et_4N)_2[CoCl_4]}$ features $\mathrm{Co}^{2+}$ with a $d^7$ configuration and weak field $\mathrm{Cl^-}$ ligands, which results in three unpaired electrons and a magnetic moment of $\sqrt{15}$ B.M. Comparing these values, $\sqrt{24} > \sqrt{15} > \sqrt{3} > 0$, which establishes the descending order as (I) > (IV) > (III) > (II).

The wavelength of maximum absorption for a transition metal complex is inversely related to the crystal field splitting energy, a property directly dictated by the strength of the ligands involved. According to the spectrochemical series, the order of ligand field strength is $\mathrm{F}^- < \mathrm{NCS}^- < \mathrm{NH}_3$, which results in an inverse order for the absorption wavelengths of $\lambda_{\text{max}}(\mathrm{F}^-) > \lambda_{\text{max}}(\mathrm{NCS}^-) > \lambda_{\text{max}}(\mathrm{NH}_3)$. Consequently, the complex with the strongest ligand, $[\mathrm{M}(\mathrm{NH}_3)_6]$, exhibits the smallest absorption wavelength $A$, while the complex with the weakest ligand, $[\mathrm{MF}_6]$, corresponds to the largest absorption wavelength $C$, placing the intermediate $[\mathrm{M}(\mathrm{NCS})_6]$ complex at wavelength $B$.

Optical activity in coordination complexes occurs only in chiral molecules that lack both a plane of symmetry and a center of inversion. While octahedral complexes of the form $[MA_2B_4]$ and the trans-isomer of $[CrCl_2(ox)_2]^{3-}$ possess symmetry elements that render them achiral, the cis-$[CrCl_2(ox)_2]^{3-}$ isomer lacks these elements, allowing it to exist as non-superimposable mirror images.

The titanium center in the complex $[\mathrm{Ti}(\mathrm{H}_2\mathrm{O})_6]^{3+}$ possesses a d1 electronic configuration, where the single electron occupies the t2g orbital in an octahedral field, resulting in a stabilization energy given by the formula $\text{CFSE} = 0.4 \Delta_0$. The electronic spectrum peak at 20,300 cm-1 corresponds to the octahedral splitting energy, $\Delta_0$.

To calculate the stabilization energy in kJ mol-1, divide the splitting value of 20,300 by 83.7 to obtain 242.5 kJ mol-1. Multiplying this figure by 0.4 yields a final stabilization energy of 97 kJ mol-1.

The spin-only magnetic moment of a transition metal complex is determined by the number of unpaired electrons present in the central metal ion, which can be calculated using the relationship $\mu = \sqrt{n(n+2)}$ Bohr magnetons. In the $[\mathrm{Cr}(\mathrm{H}_2\mathrm{O})_6]^{2+}$ complex, chromium exists in the $+2$ oxidation state with a $3d^4$ electronic configuration, which leaves 4 unpaired electrons. Similarly, in the $[\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_6]^{2+}$ complex, the iron ion is in the $+2$ oxidation state with a $3d^6$ configuration, and because water is a weak field ligand, it does not force electron pairing, which results in 4 unpaired electrons. Since both complexes contain an identical number of unpaired electrons, they necessarily exhibit the same magnetic moment.

The magnetic state of a transition metal complex depends on whether the crystal field splitting energy exceeds the electron pairing energy. Mn(II), a $d^5$ ion, possesses five unpaired electrons in weak ligand fields, while strong field environments force these electrons to pair, resulting in a low spin configuration. Similarly, tetrahedral Ni(II) complexes, representing $d^8$ systems, typically exist as high spin species in the presence of weak field ligands, and they very rarely exhibit low spin behavior because strong field ligands instead favor square planar geometries. Finally, the characteristic color of aqueous Mn(II) ions is pink, which invalidates the claim that they appear yellow.

Geometrical isomerism in octahedral complexes like $[Co(NH_3)_4Cl_2]$ is determined by the relative spatial arrangement of the two chlorine atoms around the central metal ion. In the cis isomer, the chlorine ligands occupy adjacent positions, resulting in a Cl-Co-Cl bond angle of 90 degrees. In contrast, the trans isomer places these ligands in opposite positions across the metal center, creating a 180 degree bond angle, which confirms that only the cis configuration satisfies the specific angular requirement.