Coordination Compounds – JEE Main ChemistryPractice Questions & PYQs

The structure of blue vitriol is accurately represented as $[\mathrm{Cu}(\mathrm{H}_2\mathrm{O})_4] \mathrm{SO}_4 \cdot \mathrm{H}_2\mathrm{O}$, indicating that 4 water molecules act as ligands directly coordinated to the central copper ion, which defines its secondary valency. The single remaining water molecule occupies a position outside the coordination sphere, serving as a structural stabilizer by forming hydrogen bonds with the sulfate anion and the coordinated water molecules.

Geometrical isomerism in coordination compounds arises from different spatial arrangements of ligands around a central metal ion. The complex $[\mathrm{Co}(\mathrm{NH}_3)_3(\mathrm{NO}_2)_3]$ follows the $MA_3B_3$ pattern, which permits two distinct geometrical configurations: the facial (fac) isomer and the meridional (mer) isomer, implying $X = 2$. Conversely, the complex $[\mathrm{Cr}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}$ contains three identical bidentate chelating ligands that occupy octahedral positions in a fixed, symmetrical manner, preventing any rearrangement into distinct geometrical isomers, which means $Y = 0$. Summing these individual counts leads to $X + Y = 2 + 0 = 2$.

The molecular structure of $[ {Mn}_{2}( {CO})_{10}]$ is defined by two square pyramidal ${Mn}( {CO})_{5}$ units linked directly to each other through a ${Mn}-{Mn}$ bond. Since each of the ten carbonyl ligands is coordinated terminally to a single manganese center rather than spanning the distance between the two metal atoms, the structure does not contain any bridging carbonyls. Therefore, the number of bridging CO ligands in this complex is 0.

This chemical interaction serves as a primary diagnostic test for detecting ferric ions in solution. When potassium ferrocyanide ($\mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6]$) is added to ferric chloride ($\mathrm{FeCl}_3$), a reaction occurs where the iron (III) ions interact with the hexacyanoferrate (II) anions to yield the compound iron (III) hexacyanoferrate (II), represented by $\mathrm{FeCl}_3 + \mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6] \rightarrow \mathrm{Fe}_4[\mathrm{Fe}(\mathrm{CN})_6]_3$. The formation of this specific coordination complex is responsible for the distinct Prussian blue color observed, which uniquely identifies the presence of iron in the +3 oxidation state.

Isomerism in coordination compounds arises when complexes share the same molecular formula but display different structural arrangements, with the specific type determined by ligand behavior or spatial geometry. The complex $[\mathrm{Co}(\mathrm{NH}_3)_6] [\mathrm{Cr}(\mathrm{CN})_6]$ facilitates coordination isomerism through the interchange of ligands between its cationic and anionic spheres, whereas $[\mathrm{Co}(\mathrm{NH}_3)_3 (\mathrm{NO}_2)_3]$ demonstrates linkage isomerism because the ambidentate $\mathrm{NO}_2$ ligand bonds through either nitrogen or oxygen. Solvate isomerism applies to $[\mathrm{Cr}(\mathrm{H}_2\mathrm{O})_6]\mathrm{Cl}_3$ because water molecules act as both coordinate ligands and molecules of crystallization, and $\text{cis-}[\mathrm{CrCl}_2(\mathrm{ox})_2]^{3-}$ exhibits optical isomerism because it forms non-superimposable mirror images due to its chirality.

The stability constant of a complex ion, $K_f$, and its dissociation constant, $K_d$, are reciprocals of one another because the dissociation reaction is the direct reverse of the formation reaction. This relationship is expressed by the equation $K_d = \frac{1}{K_f}$. Substituting the given value $K_f = 2.1 \times 10^{13}$ into the formula results in $K_d = \frac{1}{2.1 \times 10^{13}}$, which yields approximately $4.76 \times 10^{-14}$. Given the problem format $K_d = y \times 10^{-14}$, identifying the value of $y$ leads to $y \approx 4.76$, which corresponds to 5 when rounded to the nearest integer.

A chemical species exhibits a response to an external magnetic field only if it possesses unpaired electrons, rendering it paramagnetic. In the case of $[{Fe}({H}_{2} {O})_{6}]^{3+}$, the central ${Fe}^{3+}$ ion adopts a ${3d}^{5}$ electronic configuration with five unpaired electrons, creating a paramagnetic state that allows for interaction with an external field. In contrast, complexes such as $[{Ni}({CN})_{4}]^{2-}$, $[{Co}({CN})_{6}]^{3-}$, and $[{Ni}({CO})_{4}]$ are diamagnetic, as all electrons within these structures are paired, effectively nullifying any response to magnetic influence.

The precipitation of 1 mole of $\mathrm{AgCl}$ from the complex $\mathrm{MCl}_3 \cdot 2\mathrm{L}$ upon treatment with silver nitrate reveals that only one chloride ion is situated outside the coordination sphere, while the other two chloride ions are directly bonded to the metal. Because the complex is octahedral, the central metal must satisfy a coordination number of six. Subtracting the two coordination sites occupied by these chloride ions leaves four sites to be filled by the two ligands $\mathrm{L}$. Since two $\mathrm{L}$ units must account for these four sites, each ligand must be bidentate, confirming a denticity of 2.

An $Fe^{2+}$ ion has an electronic configuration of $3d^6$. When it forms an octahedral complex in the presence of a strong field ligand, the crystal field splitting energy is greater than the pairing energy, which forces the electrons to pair up within the lower energy orbitals. Consequently, all six $d$-electrons occupy the $t_{2g}$ set as three pairs, leaving no unpaired electrons. Given that the spin-only magnetic moment is calculated using the formula $\mu = \sqrt{n(n+2)}$ BM, where $n$ represents the number of unpaired electrons, substituting $n=0$ results in a magnetic moment of 0 BM.

Optical isomerism in coordination complexes occurs when a molecule lacks elements of symmetry, such as a plane or center of inversion, rendering it chiral. In the complex $[\mathrm{Cr}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}$, the central chromium atom is coordinated by three symmetrical bidentate oxalate ligands, a configuration that results in an entirely asymmetric structure. Since this arrangement is non-superimposable on its mirror image, it exists as a pair of enantiomers, resulting in 2 possible optical isomers.

This complex salt dissociates in solution into a cationic component, $[\mathrm{Ag}(\mathrm{NH}_3)_2]^+$, and an anionic component, $[\mathrm{Ag}(\mathrm{CN})_2]^-$. In the cation, ammonia acts as a neutral ligand with a charge of zero, so the oxidation state of the silver ion is determined by the equation $\mathrm{Ag} + 2(0) = +1$, resulting in a value of +1. Within the anion, each cyanide ligand carries a -1 charge, leading to the calculation $\mathrm{Ag} + 2(-1) = -1$, which confirms that this silver ion also has an oxidation state of +1. The sum of these two oxidation states is 1 + 1, which equals 2.

Geometrical isomerism arises from distinct ligand arrangements in space, which is possible in square planar and octahedral coordination geometries but restricted in tetrahedral geometries where all ligand positions are equivalent. The square planar complex $[\mathrm{PtCl}_2(\mathrm{NH}_3)_2]$, conforming to the $[\mathrm{MA}_2\mathrm{B}_2]$ pattern, exhibits 2 isomers corresponding to the cis and trans configurations. The tetrahedral $[\mathrm{Ni}(\mathrm{CO})_4]$ complex follows an $[\mathrm{MA}_4]$ arrangement where all coordination sites are equivalent, resulting in 0 geometrical isomers. The octahedral $[\mathrm{Ru}(\mathrm{H}_2\mathrm{O})_3\mathrm{Cl}_3]$ complex, of the $[\mathrm{MA}_3\mathrm{B}_3]$ type, allows for 2 distinct isomers known as the facial (fac) and meridional (mer) isomers. Finally, the octahedral $[\mathrm{CoCl}_2(\mathrm{NH}_3)_4]^{+}$ complex follows the $[\mathrm{MA}_4\mathrm{B}_2]$ pattern, which supports 2 geometrical isomers in the form of cis and trans configurations.

The electronic structure and magnetic character of transition metal complexes are largely governed by the field strength of the ligands, where strong field ligands such as $CN^-$ force the $d$-electrons to pair up to facilitate inner orbital hybridization. For the complex $[Mn(CN)_6]^{4-}$, manganese is in the +2 oxidation state with a $d^5$ configuration; the presence of cyanide ligands forces electron pairing to produce $d^2sp^3$ hybridisation and results in a paramagnetic state due to the presence of an unpaired electron. Likewise, in the $[Fe(CN)_6]^{3-}$ complex, iron is in the +3 oxidation state, also featuring a $d^5$ configuration that necessitates electron pairing by the cyanide ligands to achieve $d^2sp^3$ hybridisation and demonstrate paramagnetic behaviour.

Werner's coordination theory distinguishes between primary valency, which represents the ionizable chloride ions outside the coordination sphere, and secondary valency, which corresponds to the coordination number or the total number of donor atoms directly bonded to the central metal ion. Since 3 moles of the complex produce 3 moles of $\mathrm{AgCl}$ upon treatment with excess silver nitrate, it implies that each mole of the complex releases exactly one chloride ion, leaving the structure as $[\mathrm{Co}(\mathrm{en})_2\mathrm{Cl}_2]\mathrm{Cl}$. Because ethylenediamine is a bidentate ligand that occupies two coordination sites and each of the two chloride ions inside the bracket acts as a monodentate ligand occupying one site, the secondary valency is calculated as $(2 \times 2) + (2 \times 1) = 6$.

The number of unpaired electrons in a coordination complex is determined by the electronic configuration of the central metal ion and the relative magnitude of the crystal field splitting energy compared to the pairing energy. In $[\mathrm{Co}(\mathrm{NH}_3)_6]\mathrm{Cl}_2$, the $\mathrm{Co}^{2+}$ ion has a $3d^7$ configuration, and because the splitting energy is less than the pairing energy ($\Delta_0 < \text{P.E.}$), the electrons do not pair up, resulting in 3 unpaired electrons. In contrast, for $[\mathrm{Co}(\mathrm{NH}_3)_6]\mathrm{Cl}_3$, the $\mathrm{Co}^{3+}$ ion adopts a $3d^6$ configuration where the ammonia ligands create a strong field such that the splitting energy exceeds the pairing energy ($\Delta_0 > \text{P.E.}$), causing all electrons to pair up and leaving 0 unpaired electrons.

The exchange of ligands in a coordination complex is primarily dictated by their denticity, which defines the number of coordinate bonds each ligand forms with the central metal ion. Ammonia acts as a monodentate ligand, contributing one lone pair per molecule, while ethylene diamine (en) functions as a bidentate ligand, capable of occupying two coordination sites simultaneously. Within the complex $[\mathrm{Co}(\mathrm{NH}_3)_4\mathrm{Cl}_2]^+$, the four ammonia ligands occupy four distinct coordination sites around the central cobalt atom. Since one bidentate ethylene diamine molecule takes the place of two monodentate ammonia molecules, replacing all four ammonia ligands requires exactly two equivalents of ethylene diamine to form the corresponding complex $[\mathrm{Co}(\mathrm{en})_2\mathrm{Cl}_2]^+$.

Geometrical isomerism in octahedral complexes arises when ligands can be arranged in non-equivalent spatial orientations, such as the cis-trans forms of $\mathrm{[CoCl_2(en)_2]}$ and $\mathrm{[Co(NH_3)_4Cl_2]^+}$, or the facial-meridional configurations found in $\mathrm{[Co(NH_3)_3(NO_2)_3]}$. A complex with the general formula $\mathrm{MA_5B}$, such as $\mathrm{[Co(CN)_5(NC)]^{3-}}$, possesses no such capability because the single unique ligand occupies a site that is indistinguishable from the others, meaning no distinct structural arrangements can be generated by its position. Consequently, this specific configuration prevents the molecule from displaying geometrical isomerism.

Silver nitrate reacts exclusively with chloride ions that are not tightly bound within the coordination complex. Since the reaction produces three moles of $\mathrm{AgCl}$ for every mole of $\mathrm{CrCl}_3 \cdot 3\mathrm{NH}_3 \cdot 3\mathrm{H}_2\mathrm{O}$, it indicates that all three chloride ions reside in the ionization sphere rather than the coordination sphere. Ligands satisfying the secondary valency occupy fixed positions directly attached to the central metal, whereas ionizable groups exist outside this inner structure. Because every available chloride ion has been accounted for by the precipitation process, none remain to satisfy the secondary valency of the metal ion.

The spin-only magnetic moment of a transition metal complex is determined by the number of unpaired electrons, $n$, within the central metal ion as expressed by the relationship $\mu = \sqrt{n(n+2)}$ BM. This relationship indicates that the magnetic moment is directly dependent on the number of unpaired electrons, meaning a higher count corresponds to a stronger magnetic moment.

$[\mathrm{FeF}_6]^{3-}$ contains $\mathrm{Fe}^{3+}$ with a $\mathrm{3d^5}$ configuration and weak-field fluoride ligands, which leaves 5 unpaired electrons. In contrast, $[\mathrm{NiCl}_4]^{2-}$ features $\mathrm{Ni}^{2+}$ with a $\mathrm{3d^8}$ configuration and 2 unpaired electrons, while $[\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+}$ involves $\mathrm{Cu}^{2+}$ with a $\mathrm{3d^9}$ configuration and 1 unpaired electron. Finally, the strong-field ligand ammonia in $[\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}$ forces the $\mathrm{Co}^{3+}$ ion into a $\mathrm{3d^6}$ configuration with 0 unpaired electrons. These counts establish the decreasing magnetic moment order as (i) > (iii) > (iv) > (ii), based on the unpaired electron counts of 5, 2, 1, and 0 respectively.

In the reactant $\mathrm{NiCl}_2$, the nickel center is in the $+2$ oxidation state, which corresponds to a $d^8$ electronic configuration containing two unpaired electrons. Upon reacting with excess sodium cyanide in the presence of a strong oxidizing agent, the nickel is converted to the $+4$ oxidation state within the $[\mathrm{Ni}(\mathrm{CN})_6]^{2-}$ complex, resulting in a $d^6$ configuration. Because the cyanide ion acts as a strong field ligand, it forces the pairing of all six d-electrons to achieve a low-spin state, leaving zero unpaired electrons at the metal center. Consequently, the total change in the number of unpaired electrons is calculated as $2 - 0 = 2$.