Coordination Compounds – JEE Main ChemistryPractice Questions & PYQs

Assessing chemical equations requires verifying that atoms are conserved, electrical charges are balanced on both sides, and the reactions are thermodynamically feasible. The first reaction fails the conservation of charge, while the second produces the incorrect potassium salt $\mathrm{K_2[Cu(CN)_4]}$ instead of the stable $\mathrm{K_3[Cu(CN)_4]}$. Additionally, the lithium reaction does not proceed in the forward direction because $\mathrm{Li_2O}$ is inherently more stable than the unstable product $\mathrm{K_2O}$. The final reaction is the only one that is both mass-balanced and charge-balanced, accurately representing the decomposition of the complex ion in an acidic medium:

$\mathrm{[CoCl(NH_3)_5]^{+}} + 5\mathrm{H^{+}} \rightarrow \mathrm{Co^{2+}} + 5\mathrm{NH^{+}_4} + \mathrm{Cl^{-}}$

In coordination chemistry, the strength of a ligand is directly proportional to the magnitude of crystal field splitting it induces, which in turn determines the energy of the light absorbed by the complex. This relationship is defined by the equation $E = \frac{hc}{\lambda}$, where energy $E$ is inversely proportional to the wavelength $\lambda$ of the absorbed radiation. Stronger ligands promote larger splitting, necessitating the absorption of higher energy photons associated with shorter wavelengths. Based on the visible spectrum where energy decreases from violet to red, the order of increasing energy for the absorbed colors is red, yellow, green, and blue, leading to the ligand strength sequence $L_1 < L_3 < L_2 < L_4$.

Optical isomerism arises only in coordination complexes that lack an internal plane of symmetry, rendering the molecule chiral. In the specific case of $[Co(NH_3)_3Cl_3]$, the complex forms two geometric isomers known as facial and meridional, both of which contain planes of symmetry. Since these geometric forms are achiral and superimposable on their mirror images, the entire species is incapable of exhibiting optical activity.

Naming coordination compounds requires identifying the coordination sphere components, including the central metal, ligands, and counter-ions, according to systematic IUPAC rules. The term dibromidobis(ethylenediamine)chromium(III) bromide specifies two bromide ligands and two ethylenediamine ligands attached to a chromium ion with an oxidation state of +3, with a bromide counter-ion balancing the charge outside the coordination sphere. By translating these components into chemical symbols, we place the chromium center and its ligands within the coordination bracket as $[\mathrm{Cr}(\mathrm{en})_2\mathrm{Br}_2]$ and append the bromide counter-ion, which results in the formula $[\mathrm{Cr}(\mathrm{en})_2\mathrm{Br}_2]\mathrm{Br}$.

To determine the spin-only magnetic moment, we utilize the formula $\mu = \sqrt{n(n+2)}$, where $n$ signifies the number of unpaired electrons. In the complex $[\mathrm{NiCl}_4]^{2-}$, the nickel ion exists in the +2 oxidation state with a d8 electronic configuration. Since chloride is a weak field ligand, it fails to pair the d-electrons, resulting in 2 unpaired electrons within the metal center. Substituting this value into the equation gives $\sqrt{2(2+2)}$, which simplifies to $\sqrt{8}$ or approximately 2.82 BM.

The distinction between inner and outer orbital complexes hinges on which set of $d$-orbitals the central metal utilizes during hybridization, specifically whether it employs the $(n-1)d$ or the $nd$ subshell. In the complex $[\mathrm{Cr}(\mathrm{NH}_3)_6]\mathrm{Cl}_3$, the chromium ion is in the $+3$ oxidation state with a $3d^3$ electronic configuration, allowing it to undergo $d^2sp^3$ hybridization by utilizing its inner $3d$ orbitals. This classification as an inner orbital complex directly contradicts the statement that it is an outer orbital complex. Furthermore, the molecule exhibits paramagnetism due to the presence of three unpaired electrons in its $3d$ subshell, and the chloride ions located outside the coordination sphere readily react with silver nitrate to produce a white precipitate.

Optical isomerism is exhibited by coordination compounds that lack elements of symmetry, specifically a plane of symmetry, which allows the molecule to exist as non-superimposable mirror images. While the tetrahedral zinc complexes $[\mathrm{Zn}(\mathrm{en})(\mathrm{NH}_3)_2]^{2+}$ and $[\mathrm{Zn}(\mathrm{en})_2]^{2+}$ are inherently inactive due to the presence of a plane of symmetry, and $[\mathrm{Co}(\mathrm{H}_2\mathrm{O})_4(\mathrm{en})]^{3+}$ is similarly inactive because it contains two planes of symmetry, $[\mathrm{Co}(\mathrm{en})_3]^{3+}$ forms an octahedral structure that lacks these symmetry elements entirely.

Identifying the coordination complex structure requires determining how many chloride ions dissociate as free ions to precipitate with silver nitrate. Dividing the 2.675 g sample mass by the molar mass of 267.5 g/mol yields 0.01 moles of $\mathrm{CoCl}_3\cdot 6\,\mathrm{NH}_3$, while dividing the 4.78 g mass of $\mathrm{AgCl}$ by 143.5 g/mol provides 0.03 moles of precipitate. Comparing these values, the ratio of liberated chloride ions per mole of complex is $\frac{0.03}{0.01} = 3$, indicating that 3 chloride ions exist as counter-ions outside the coordination sphere. Therefore, the cobalt atom and all six ammonia molecules must form the coordination sphere, identifying the formula as $[\mathrm{Co}(\mathrm{NH}_3)_6]\mathrm{Cl}_3$.

Optical isomerism in coordination complexes arises when a molecule lacks elements of symmetry, such as a plane of symmetry, which renders the structure chiral. In the case of the octahedral complex $[\mathrm{Co}(\mathrm{en})_2(\mathrm{NH}_3)_2]^{3+}$, the cis isomer provides a geometry where the two bidentate ethylenediamine ligands and two monodentate ammonia ligands are arranged asymmetrically, creating a structure that cannot be superimposed on its mirror image. Because the other provided complexes either possess higher symmetry or lack the specific chelated architecture required to break that symmetry, they do not exhibit optical activity.

Linkage isomerism arises in coordination complexes containing ambidentate ligands, which are chemical species capable of bonding to a metal center through two different donor atoms. The thiocyanate ion, $\mathrm{SCN}^{-}$, serves as a classic example of an ambidentate ligand because it can attach to the central metal through either the nitrogen atom to form an isothiocyanato complex or the sulfur atom to form a thiocyanato complex. Consequently, the pair $[\mathrm{Pd}(\mathrm{PPh}_3)_2(\mathrm{NCS})_2]$ and $[\mathrm{Pd}(\mathrm{PPh}_3)_2(\mathrm{SCN})_2]$ represents this type of isomerism because the shift in the donor atom-from nitrogen to sulfur-alters the specific connectivity of the ligand within the coordination sphere.

The magnitude of crystal field splitting, $\Delta_o$, in an octahedral complex depends primarily on the strength of the ligands coordinated to the central metal ion. Strong-field ligands induce a larger separation between the $t_{2g}$ and $e_g$ orbitals than weak-field ligands, according to the spectrochemical series. Since the Cobalt center, with atomic number 27, is constant across all options, the magnitude of $\Delta_o$ is determined solely by the ligand identity. Because $\mathrm{CN}^{-}$ is the strongest field ligand among the choices provided, the complex $\left[ \mathrm{Co}(\mathrm{CN})_6 \right]^{3-}$ possesses the highest value of $\Delta_o$.

The coordination number of a central metal ion represents the total number of coordinate bonds formed with the ligands. Since both ethylenediamine and the oxalate ion $\mathrm{C}_2\mathrm{O}_4$ are bidentate, each contributes two donor atoms, making the total coordination number equal to $(2 \times 2) + (1 \times 2)$, which is 6.

Calculating the oxidation state requires balancing the charges within the complex to match the total ionic charge. The complex $[E(\text{en})_2(\mathrm{C}_2\mathrm{O}_4)]\mathrm{NO}_2$ dissociates into a cation and a $\mathrm{NO}_2^-$ anion, implying the complex sphere $[E(\text{en})_2(\mathrm{C}_2\mathrm{O}_4)]^+$ has a net charge of $+1$. Given that ethylenediamine is neutral and oxalate carries a charge of $-2$, the oxidation state $x$ of element $E$ satisfies the equation $x + 2(0) + (-2) = +1$, resulting in $x = +3$.

Square planar geometry arises in coordination complexes when the central metal ion undergoes $dsp^2$ hybridization, causing the four attached ligands to arrange themselves in a flat, square configuration. This specific electronic arrangement is characteristic of the platinum complex $[\mathrm{PtCl}_4]^{2-}$, where the central metal facilitates this particular hybridization pathway. In contrast, the other transition metal complexes listed typically adopt a tetrahedral geometry with these ligands, making the platinum complex the unique example of square planar symmetry in this set.

Metal carbonyl complexes such as $\mathrm{Fe}(\mathrm{CO})_5$ rely on a synergistic bonding arrangement where the carbon monoxide ligand initially donates a lone pair to the iron atom to establish a $\sigma$-bond. Simultaneously, the iron atom engages in back-bonding by transferring electron density from its filled $d$-orbitals into the empty $\pi^*$ antibonding orbitals of the carbon atom through side-wise overlap, which effectively generates a $\pi$-bond. Consequently, this bidirectional interaction results in a chemical linkage that fundamentally possesses both $\sigma$ and $\pi$ characters.

The properties of the $[\mathrm{NiX}_4]^{2-}$ complex are dictated by the electronic state of the central nickel ion, which must be in the $+2$ oxidation state given the four uninegative ligands and the net charge of $-2$. This results in a $3d^8$ configuration that retains two unpaired electrons in this coordination environment. This specific electronic arrangement leads to $sp^3$ hybridization, which defines the tetrahedral geometry of the complex ion.

In coordination chemistry, IUPAC nomenclature dictates that we name the ligands alphabetically before the central metal, and for the complex $[\mathrm{Co}(\mathrm{NO}_2)(\mathrm{NH}_3)_5]\mathrm{Cl}_2$, this means prioritizing the five ammine ligands over the nitrito-$\mathrm{N}$ ligand. By grouping the five ammonia molecules as pentaammine, we then account for the anionic nitrito-$\mathrm{N}$ ligand and the central cobalt atom. Calculating the oxidation state requires balancing the total charge of the complex with the -1 charge of the $\mathrm{NO}_2^-$ ion and the -1 charge of each of the two outer $\mathrm{Cl}^-$ ions, which confirms that cobalt exists in the +3 state. This systematic arrangement leads directly to the designation of pentaammine nitrito-$\mathrm{N}$-cobalt (III) chloride.

EDTA functions as a hexadentate ligand by providing six donor sites-specifically four oxygen atoms and two nitrogen atoms-that bind simultaneously to the central metal. Since an octahedral complex is defined by a coordination number of six, a single EDTA molecule is sufficient to fully satisfy the bonding geometry around a $\mathrm{Ca}^{2+}$ ion.

Optical isomerism in coordination compounds occurs when a complex lacks both a plane of symmetry and a center of symmetry, allowing it to exist as non-superimposable mirror images. The complex $[\mathrm{Cr}(\mathrm{C}_2\mathrm{O}_4)_3]^{-3}$ features a central metal ion bonded to three bidentate oxalate ligands in an octahedral arrangement, creating a propeller-like geometry devoid of any symmetry elements, which makes it chiral. In contrast, the other listed complexes contain either identical monodentate ligands or planar geometries that inherently possess multiple planes of symmetry, rendering them achiral.

The spin-only magnetic moment of a metal ion is calculated using the formula $\mu = \sqrt{n(n+2)} \, \text{BM}$, where $n$ represents the number of unpaired electrons. In a strong ligand field, a $d^4$ configuration forces electron pairing in the lower energy orbitals, resulting in an electronic distribution of $t_{2g}^4 e_g^0$ and leaving $n=2$ unpaired electrons. Substituting this value into the equation yields $\mu = \sqrt{2(2+2)} = \sqrt{8} \approx 2.82 \, \text{BM}$, which aligns with the provided value of 2.84 BM. Other configurations lead to different results, specifically $d^4$ in a weak field with $n=4$ yielding $\mu \approx 4.89 \, \text{BM}$, $d^3$ in any field with $n=3$ yielding $\mu \approx 3.87 \, \text{BM}$, and $d^5$ in a strong field with $n=1$ yielding $\mu \approx 1.73 \, \text{BM}$.

The naming of coordination compounds relies on identifying the oxidation state of the central metal atom, which for $\mathrm{K}_3[\mathrm{Fe}(\mathrm{CN})_6]$ reveals that the iron atom exists in the +3 state to balance the complex. Given that the three potassium ions contribute a total charge of +3, the $[\mathrm{Fe}(\mathrm{CN})_6]$ unit must carry a -3 charge, and since each cyanide ligand contributes a -1 charge, the iron atom is correctly identified as having a +3 oxidation state. Because the complex ion acts as an anion, the metal is named using the -ate suffix, resulting in potassium hexacyanoferrate (III).