Coordination Compounds – JEE Main ChemistryPractice Questions & PYQs

The distribution of electrons in a $3d^4$ metal complex is governed by the relative magnitude of the crystal field splitting energy $\Delta_0$ compared to the pairing energy $P$. In the presence of a weak field ligand, the energy gap $\Delta_0$ is smaller than $P$, making it energetically favorable for the fourth electron to occupy the higher $e_g$ orbital rather than pairing up in the $t_{2g}$ set. This results in the $t_{2g}^3 e_g^1$ configuration, which maximizes the number of unpaired electrons and defines the system as a high spin complex.

Werner's coordination theory establishes that primary valency corresponds to the oxidation state of the central metal ion, while secondary valency refers to the coordination number defined by the total number of donor atoms directly bonded to it. For the complex $\mathrm{[Co(en)_2Cl_2]Cl}$, the cobalt ion possesses a +3 oxidation state and a coordination number of 6, which matches set (I). The complex $\mathrm{[Pt(NH_3)_2Cl(NO_2)]}$ involves a platinum center with a +2 oxidation state and a coordination number of 4, corresponding to set (IV), whereas $\mathrm{Hg[Co(SCN)_4]}$ displays a primary valency of 3 and a secondary valency of 4, pairing it with set (II). Finally, the $\mathrm{[Mg(EDTA)]^{2-}}$ complex features a magnesium ion with a +2 oxidation state and a hexadentate coordination resulting in a secondary valency of 6, aligning with set (III).

Diamagnetism in octahedral coordination complexes occurs when all electrons in the metal $d$-orbitals are paired, a state typically achieved in low-spin configurations where the crystal field splitting energy is sufficient to force electrons into the lower-energy $t_{2g}$ orbitals. In the case of $[\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}$, the central $\mathrm{Co}^{3+}$ ion possesses a $d^6$ configuration; the strong-field ammonia ligands ensure a low-spin arrangement with an electron distribution of $t_{2g}^6 e_g^0$, meaning all electrons are paired, rendering the complex diamagnetic. Similarly, $[\mathrm{Fe}(\mathrm{CN})_6]^{4-}$ contains an $\mathrm{Fe}^{2+}$ ion, which is also a $d^6$ system. Under the influence of strong-field cyanide ligands, it adopts the same $t_{2g}^6 e_g^0$ electron distribution, resulting in a completely paired state that exhibits diamagnetism.

In contrast, the remaining complexes possess unpaired electrons. $[\mathrm{Mn}(\mathrm{CN})_6]^{3-}$ involves a $\mathrm{Mn}^{3+}$ center with a $d^4$ configuration, resulting in a $t_{2g}^4 e_g^0$ filling that leaves unpaired electrons, while $[\mathrm{Co}(\mathrm{H}_2\mathrm{O})_3\mathrm{F}_3]$ features a $\mathrm{Co}^{3+}$ ion in a high-spin $t_{2g}^4 e_g^2$ arrangement, which also results in paramagnetic behavior.

The tris-oxalato complex $[\mathrm{Fe}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}$ is the most stable among the given options due to the chelate effect, which provides significantly greater thermodynamic stability than monodentate ligand complexes. The central $\mathrm{Fe}^{3+}$ ion possesses a $d^5$ electronic configuration, and in the presence of the oxalate ligand, it adopts a high-spin state with a $t_{2g}^3 e_g^2$ configuration, meaning $X = 3$. The vanadium oxide $\mathrm{V}_2\mathrm{O}_3$ is classified as amphoteric, as it exhibits the property of reacting with both acidic and basic reagents in specific chemical environments.

The energy gap between the split d-orbitals in an octahedral complex, denoted as $\Delta_o$, is inversely proportional to the wavelength of light absorbed, following the relationship $\Delta_o = \frac{hc}{\lambda}$. Stronger ligands induce a greater splitting of the d-orbitals, thereby increasing $\Delta_o$ and causing the complex to absorb light of a shorter wavelength. Based on the spectrochemical series, the field strength of the ligands involved follows the order $\text{Cl}^- < \text{H}_2\text{O} < \text{NH}_3 < \text{CN}^-$. Consequently, the magnitude of crystal field splitting for these complexes increases in the order $D < A < B < C$. Because wavelength is inversely related to this splitting energy, the final order for the wavelength of light absorbed becomes $D > A > B > C$.

The geometry and magnetic properties of coordination complexes are determined by the oxidation state of the metal center and the field strength of the surrounding ligands. $\mathrm{Ni}(\mathrm{CO})_4$ features neutral nickel ($3d^{10}$), which forms a tetrahedral geometry via $sp^3$ hybridization with all electrons paired, resulting in a magnetic moment of $0$ BM. The $[\mathrm{Ni}(\mathrm{CN})_4]^{2-}$ complex contains $\mathrm{Ni}^{2+}$ ($3d^8$), where the strong cyanide ligand forces electron pairing to produce a square planar geometry and a magnetic moment of $0$ BM. In contrast, $[\mathrm{NiCl}_4]^{2-}$ consists of $\mathrm{Ni}^{2+}$ ($3d^8$) paired with weak chloride ligands that do not induce pairing, leading to a tetrahedral geometry and a magnetic moment of $2.8$ BM from the two unpaired electrons. Lastly, $[\mathrm{MnBr}_4]^{2-}$ involves $\mathrm{Mn}^{2+}$ with a $3d^5$ configuration, where weak bromide ligands leave five unpaired electrons to generate a tetrahedral complex with a magnetic moment of $5.9$ BM.

The color of coordination complexes depends significantly on the identity of the ligands attached to the central metal ion, as ligand substitution modifies the d-orbital splitting and the corresponding light absorption characteristics. Initially, an aqueous nickel(II) solution exists as the green complex $[\mathrm{Ni}(\mathrm{H_2O})_{6}]^{2+}$, but as ethane-1,2-diamine is introduced, it undergoes stepwise ligand exchange that shifts the observable color. This process progresses from the initial green solution to the pale blue $[\mathrm{Ni}(\mathrm{H_2O})_4(\mathrm{en})]^{2+}$ complex, continues through the blue $[\mathrm{Ni}(\mathrm{H_2O})_2(\mathrm{en})_2]^{2+}$ species, and finally results in the formation of the violet $[\mathrm{Ni}(\mathrm{en})_3]^{2+}$ complex as the concentration of the ligand increases.

According to Werner's coordination theory, chloride ions positioned outside the coordination sphere ionize in water, whereas those inside the coordination sphere are covalently bonded to the central metal atom and do not dissociate. The precipitation of two moles of $\mathrm{AgCl}$ signifies that two chloride ions are counter-ions outside the coordination bracket, which implies that the remaining one chloride ion serves as a ligand within the sphere, coordinated alongside five $\mathrm{NH}_3$ molecules. This configuration, denoted as $[\mathrm{Co}(\mathrm{NH}_3)_5\mathrm{Cl}]\mathrm{Cl}_2$, undergoes electrolytic dissociation in water to produce a total of three ions, consisting of one complex cation $[\mathrm{Co}(\mathrm{NH}_3)_5\mathrm{Cl}]^{2+}$ and two chloride anions $\mathrm{Cl}^-$.

The coordination of nickel with dimethylglyoxime involves the formation of a stable chelate complex where the nickel ion is associated with two dimethylglyoxime ligands. Each individual dimethylglyoxime molecule, represented by the chemical formula $\mathrm{C}_4\mathrm{H}_8\mathrm{N}_2\mathrm{O}_2$, undergoes deprotonation at one of the oxime groups upon coordinating with the nickel center. This process results in the formation of the complex $[\mathrm{Ni}(\mathrm{C}_4\mathrm{H}_7\mathrm{N}_2\mathrm{O}_2)_2]$, where each ligand retains 7 hydrogen atoms after losing one proton. Multiplying these 7 hydrogen atoms by the two ligands present in the complex yields a total of 14 hydrogen atoms.

Determining hybridization involves calculating the electron distribution around the central atom, accounting for both valence bonding and the influence of ligand field strength in transition metal complexes. In $\mathrm{PF}_5$, phosphorus uses five valence electrons to bond with fluorine, resulting in $\mathrm{sp}^3\mathrm{d}$ hybridization, while sulfur in $\mathrm{SF}_6$ employs six bonding regions, leading to $\mathrm{sp}^3\mathrm{d}^2$ hybridization. For transition metal complexes, $\mathrm{Ni}(\mathrm{CO})_4$ contains strong-field ligands that force electron pairing to achieve $\mathrm{sp}^3$ hybridization, whereas the $[\mathrm{PtCl}_4]^{2-}$ complex exhibits $\mathrm{dsp}^2$ hybridization associated with its characteristic square planar structure.

To determine the properties of these complexes, note that in $[\mathrm{NiCl}_4]^{2-}$, the nickel ion exists in the $\mathrm{Ni}^{2+}$ state with a $3d^8$ configuration. Because chloride ions act as weak field ligands, no electron pairing occurs, leaving the complex paramagnetic and resulting in an $sp^3$ tetrahedral geometry. In contrast, the neutral $[\mathrm{Ni}(\mathrm{CO})_4]$ complex features nickel in the $\mathrm{Ni}^{0}$ oxidation state with a $3d^{10}$ configuration, where the ligands allow for an $sp^3$ hybridized, diamagnetic tetrahedral structure.

Determining the strongest oxidizing agent among the transition metal oxides $\mathrm{Mn}_2\mathrm{O}_3$, $\mathrm{TiO}$, and $\mathrm{VO}$ identifies $\mathrm{Mn}_2\mathrm{O}_3$ as the species of interest. In this compound, manganese exists in the $+3$ oxidation state with an electronic configuration of $[\mathrm{Ar}] 3d^4$, which contains four unpaired electrons. Applying the formula for the spin-only magnetic moment, $\mu = \sqrt{n(n+2)}$, yields $\mu = \sqrt{4(4+2)} = \sqrt{24}$, resulting in a value of approximately 4.89 B.M. Rounding this calculation to the nearest integer gives a final magnetic moment of 5 B.M.

Because $\mathrm{Cl}^{-}$ acts as a weak field ligand, it fails to induce electron pairing in the $\mathrm{Mn}^{3+}$ metal ion, which maintains a $3d^4$ configuration distributed as $t_{2g}^3 e_g^1$. This high-spin arrangement leaves 4 unpaired electrons in the $3d$ orbitals, necessitating the use of outer $d$ orbitals for bonding to form an $s p^3 d^2$ hybridized octahedral complex. Consequently, the presence of these 4 unpaired electrons makes the complex paramagnetic.

The crystal field splitting energy depends heavily on the oxidation state of the central metal ion, the coordination geometry, and the field strength of the ligands. Tetrahedral complexes exhibit significantly lower splitting than their octahedral counterparts, as defined by the relationship $\Delta_{t} = \frac{4}{9} \Delta_{o}$. Consequently, $[\mathrm{Co}(\mathrm{NH}_3)_4]^{2+}$ possesses the lowest stabilization energy among these complexes due to its tetrahedral geometry and the relatively lower charge on the $\mathrm{Co}^{2+}$ ion. Shifting to octahedral geometry, $[\mathrm{Co}(\mathrm{NH}_3)_6]^{2+}$ maintains the same $\mathrm{Co}^{2+}$ metal ion but benefits from the larger octahedral splitting energy, resulting in a higher value than the tetrahedral complex.

When considering $\mathrm{Co}^{3+}$ complexes, the increased positive charge on the central metal enhances the electrostatic interaction, significantly increasing the splitting energy compared to $\mathrm{Co}^{2+}$ species. Between the two $\mathrm{Co}^{3+}$ octahedral complexes, $[\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}$ and $[\mathrm{Co}(\mathrm{en})_3]^{3+}$, the chelating nature of the ethylenediamine ligands provides a stronger crystal field than the ammonia ligands. This difference in ligand strength ensures that $[\mathrm{Co}(\mathrm{en})_3]^{3+}$ exhibits the largest crystal field splitting energy, establishing a clear progression based on geometry, oxidation state, and ligand type.

Crystal Field Theory determines the magnetic behavior of a metal complex by describing how $d$-orbitals split into $t_{2g}$ and $e_g$ energy levels based on the strength of the coordinating ligands. For the cobalt complexes $[\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}$ and $[\mathrm{Co}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}$, the $\mathrm{Co}^{3+}$ ion ($d^6$) experiences strong field splitting, leading to a $t_{2g}^6 e_g^0$ configuration where all electrons are paired, making them diamagnetic. Conversely, $[\mathrm{MnCl}_6]^{3-}$ containing $\mathrm{Mn}^{3+}$ ($d^4$) with a weak-field ligand adopts a $t_{2g}^3 e_g^1$ arrangement, resulting in 4 unpaired electrons. Similarly, $[\mathrm{CoF}_6]^{3-}$ has a $\mathrm{Co}^{3+}$ center ($d^6$) in a weak-field environment, producing a $t_{2g}^4 e_g^2$ configuration with 4 unpaired electrons. The remaining species, $[\mathrm{Fe}(\mathrm{CN})_6]^{3-}$ ($\mathrm{Fe}^{3+}$, $d^5$), exhibits $t_{2g}^5 e_g^0$ with 1 unpaired electron, while $[\mathrm{FeF}_6]^{3-}$ ($\mathrm{Fe}^{3+}$, $d^5$) results in $t_{2g}^3 e_g^2$ with 5 unpaired electrons. Identifying the paramagnetic species with an identical number of unpaired electrons, only $[\mathrm{MnCl}_6]^{3-}$ and $[\mathrm{CoF}_6]^{3-}$ share a count of 4 unpaired electrons.

Facial-Meridional isomerism is a distinct form of geometric isomerism that occurs specifically in octahedral coordination complexes with the general formula $Ma_3b_3$, where $a$ and $b$ are monodentate ligands. Among the given choices, only the complex $[\mathrm{Co}(\mathrm{NH}_3)_3\mathrm{Cl}_3]$ adheres to this $Ma_3b_3$ pattern, containing three ammonia molecules and three chloride ions attached to the cobalt center. In this arrangement, the three identical ligands can either occupy the corners of one triangular face, resulting in the facial isomer, or lie along a meridian plane, resulting in the meridional isomer.

The classification of complexes as diamagnetic or paramagnetic relies on the presence or absence of unpaired electrons in the central metal ion's $d$-orbitals. In $\mathrm{K}_2[\mathrm{NiCl}_4]$, the $\mathrm{Ni}^{2+}$ ion features a $3d^8$ configuration, and its tetrahedral geometry with weak $\mathrm{Cl}^-$ ligands leaves unpaired electrons, resulting in paramagnetism. The complex $[\mathrm{Zn}(\mathrm{H}_2\mathrm{O})_6]\mathrm{Cl}_2$ involves $\mathrm{Zn}^{2+}$ with a completely filled $3d^{10}$ configuration, making it diamagnetic. Within $\mathrm{K}_3[\mathrm{Mn}(\mathrm{CN})_6]$, the $\mathrm{Mn}^{3+}$ ion with a $3d^4$ configuration is paramagnetic due to unpaired electrons, whereas the complex $[\mathrm{Cu}(\mathrm{PPh}_3)_3\mathrm{I}]$ contains $\mathrm{Cu}^{+}$ with a $3d^{10}$ configuration, rendering it diamagnetic. With exactly two diamagnetic species identified, the value of $n$ is $2$.

Zinc exhibits the lowest enthalpy of atomization among the listed metals because its $3d^{10}4s^2$ electronic configuration provides minimal contribution to metallic bonding compared to transition metals with partially filled $d$-shells. Determining the spin-only magnetic moment for the $\mathrm{Zn}^{2+}$ ion requires evaluating its unpaired electrons. Since $\mathrm{Zn}^{2+}$ retains a $3d^{10}$ configuration with zero unpaired electrons, the spin-only magnetic moment $\mu$ calculated as $\sqrt{0(0+2)}$ results in $0$.

Ionisation isomerism occurs when the counter ion of a coordination compound acts as a ligand and exchanges places with a ligand from the coordination sphere, resulting in different ionic species in solution. In the complex $[Co(NH_3)_5(Cl)(SO_4)]$, isomer A is $[Co(NH_3)_5(SO_4)]Cl$, which yields a precipitate with $\mathrm{AgNO}_3$ due to the presence of free $\mathrm{Cl}^-$, whereas isomer B is $[Co(NH_3)_5(Cl)]SO_4$, which yields a precipitate with $\mathrm{BaCl}_2$ due to the presence of free $\mathrm{SO}_4^{2-}$. Because the anion and ligand are swapped between the coordination sphere and the ionisation sphere, the compound exhibits ionisation isomerism.

Paramagnetism arises in chemical species that possess at least one unpaired electron, allowing them to be attracted by an external magnetic field. Evaluating the molecular orbital configurations reveals that $\mathrm{O}_2$ has two unpaired electrons, while $\mathrm{O}_2^{+}$ and $\mathrm{O}_2^{-}$ each contain one unpaired electron, making these three species paramagnetic. Furthermore, the odd-electron molecules $\mathrm{NO}$ and $\mathrm{NO}_2$ exhibit paramagnetic behavior, while $\mathrm{CO}$ is diamagnetic because all its electrons are paired. In terms of metal complexes, $\mathrm{K}_2 [ \mathrm{NiCl}_4 ]$ features $\mathrm{Ni}^{2+}$ in a tetrahedral geometry with weak-field ligands, leading to unpaired electrons, whereas both $[ \mathrm{Co} ( \mathrm{NH}_3 )_6 ] \mathrm{Cl}_3$ and $\mathrm{K}_2 [ \mathrm{Ni}( \mathrm{CN})_4 ]$ are diamagnetic due to the pairing of electrons induced by strong-field ligands, confirming a total of six paramagnetic species.

The central nickel ion (atomic number 28) in the $[\mathrm{Ni}(\mathrm{NH}_3)_6]^{2+}$ complex is in a $+2$ oxidation state, leading to a $3d^8$ electronic configuration. Because ammonia acts as a weak field ligand in this octahedral arrangement, two electrons remain unpaired in the $d$-orbitals, meaning $n=2$. Applying the spin-only formula $\mu = \sqrt{n(n+2)}$ yields $\mu = \sqrt{8}$, which is 2.82 BM. Converting this value into the specified form $28.2 \times 10^{-1}$ BM identifies the required numerical value as 28.