Coordination Compounds – JEE Main ChemistryPractice Questions & PYQs

The crystal field splitting energy $\Delta_0$ represents the gap between the $t_{2g}$ and $e_g$ orbitals, and for a $d^1$ complex like the titanium(III) ion, the crystal field stabilization energy is defined as $-0.4 \Delta_0$. Equating this expression to the given value of $-96.0 \text{ kJ/mol}$ allows the determination of the molar splitting energy as $\Delta_0 = 240 \text{ kJ/mol}$, or $2.4 \times 10^5 \text{ J/mol}$.

The energy required for an electronic transition in a single ion is calculated by dividing the molar energy by Avogadro's constant, $N_A = 6 \times 10^{23} \text{ /mol}$, yielding $E = 4 \times 10^{-19} \text{ J}$. Applying the relation $E = \frac{hc}{\lambda}$ and substituting the constants $h = 6.4 × 10^{-34} \text{ Js}$ and $c = 3.0 × 10^8 \text{ m/s}$ leads to the wavelength calculation: $\lambda = \frac{6.4 \times 10^{-34} \times 3.0 \times 10^8}{4 \times 10^{-19}} = 4.8 \times 10^{-7} \text{ m}$ Converting this value to nanometers results \in a wavelength of $480 \text{ nm}$.

Ambidentate ligands are chemical species capable of forming coordinate bonds with a metal atom through two distinct donor atoms depending on the environment. In the complex $[\mathrm{M}(\mathrm{en})(\mathrm{SCN})_4]$, the ethylenediamine ligand acts as a standard chelating agent, while the thiocyanate ion is an ambidentate ligand because it can bond via either the sulfur or nitrogen atom. With four thiocyanate ions present in the coordination sphere, the total count of ambidentate ligands is 4.

The magnitude of crystal field splitting is determined by the position of the ligands in the spectrochemical series, which ranks them by their ability to induce d-orbital separation. Cyanide ($\mathrm{CN}^-$) functions as a strong field ligand that generates a significantly larger energy gap between the $t_{2g}$ and $e_g$ orbitals compared to the other ligands present in the options. Consequently, the complex $[\mathrm{Fe}(\mathrm{CN})_6]^{3-}$ exhibits the most pronounced splitting of d-orbitals because it coordinates with the most potent field-inducing ligand in this set.

The ability of a coordination complex to precipitate silver chloride upon the addition of $\mathrm{AgNO}_3$ depends entirely on whether chloride ions are positioned outside the coordination sphere as ionizable counter-ions. Only these non-coordinated chloride ions can interact with silver ions to form the precipitate, while chlorides bonded directly to the central metal atom remain within the sphere and do not react. Evaluating the complexes provided, $[\mathrm{Co}(\mathrm{NH}_3)_4\mathrm{Cl}_2]\mathrm{Cl}$ contains one ionizable chloride, which yields 1 mole of $\mathrm{AgCl}$. The complex $[\mathrm{Ni}(\mathrm{H}_2\mathrm{O})_6]\mathrm{Cl}_2$ possesses two counter-ions, resulting in the production of 2 moles of $\mathrm{AgCl}$. In the case of $[\mathrm{Pt}(\mathrm{NH}_3)_2\mathrm{Cl}_2]$, all chloride ligands are directly bonded within the coordination sphere, so no precipitation occurs, yielding 0 moles of $\mathrm{AgCl}$. Finally, $[\mathrm{Pd}(\mathrm{NH}_3)_4]\mathrm{Cl}_2$ contributes two ionizable chloride ions, accounting for an additional 2 moles of $\mathrm{AgCl}$. Summing these individual contributions results in a total of 5 moles of precipitated $\mathrm{AgCl}$.

Crystal field theory conceptualizes metal-ligand bonding as an electrostatic interaction where ligands act as point charges that induce splitting in the central metal's d-orbitals. While this model effectively accounts for magnetic properties, the observation of color via electronic transitions, and the link between crystal field stabilization energy and thermodynamic stability, it remains unable to explain the specific arrangement of ligands in the spectrochemical series. This series is essentially an empirical observation categorized by experimental $\Delta$ values rather than a theoretical outcome predicted by the core principles of the theory itself.

Chlorophyll is fundamentally characterized by the central coordination of magnesium rather than cobalt, and the photographic fixing process employs a hypo solution to dissolve undecomposed $\mathrm{AgBr}$ by forming the stable complex $[\mathrm{Ag}(\mathrm{S}_2\mathrm{O}_3)_2]^{3-}$, not the cyanide-containing species $[\mathrm{Ag}(\mathrm{CN})_2]^{-}$. The remaining associations are chemically accurate, as EDTA is standard for water hardness determination, D-Penicillamine functions as a chelating ligand, and Wilkinson's catalyst corresponds to $[(\mathrm{Ph}_3\mathrm{P})_3\mathrm{RhCl}]$.

When cobalt(II) chloride dissolves in water, the cobalt ion coordinates with six water molecules to form the octahedral hexaaquacobalt(II) complex, $[Co(H_2O)_6]^{2+}$, which imparts a pink color to the solution. Adding concentrated hydrochloric acid introduces an excess of chloride ions that displace the water ligands to produce the tetrachlorocobaltate(II) complex, $[CoCl_4]^{2-}$, which is deep blue in color and adopts a tetrahedral geometry due to the steric hindrance associated with the larger chloride ligands.

The spin-only magnetic moment of transition metal complexes is determined by the number of unpaired electrons $n$ according to the formula $\mu = \sqrt{n(n+2)}$ BM. In $[\mathrm{FeF}_6]^{3-}$, the $\mathrm{Fe}^{3+}$ ion has a $3d^5$ configuration, and because the fluoride ligands are weak-field, all five electrons remain unpaired, resulting in a magnetic moment of $\mu = \sqrt{35}$ BM. Similarly, the $\mathrm{Co}^{3+}$ ion in $[\mathrm{CoF}_6]^{3-}$ adopts a $3d^6$ high-spin configuration with four unpaired electrons and a magnetic moment of $\mu = \sqrt{24}$ BM, whereas the strong-field oxalate ligands in $[\mathrm{Co}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}$ force all $3d^6$ electrons to pair, leading to zero unpaired electrons and a magnetic moment of 0 BM. Comparing these values, the final order of magnetic moments is $[\mathrm{FeF}_6]^{3-} > [\mathrm{CoF}_6]^{3-} > [\mathrm{Co}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}$.

The spin-only magnetic moment of a coordination complex depends directly on the number of unpaired electrons, which determines the magnitude of $\mu$ through the relation $\mu = \sqrt{n(n+2)}$ BM. In $\left[ \mathrm{Fe(CN)_6} \right]^{3-}$, the $Fe^{3+}$ ion with a $3d^5$ configuration experiences a strong field from the cyanide ligands that forces electron pairing, resulting in 1 unpaired electron. Similarly, $\left[ \mathrm{Mn(CN)_6} \right]^{3-}$ involves a $Mn^{3+}$ ion with a $3d^4$ configuration and a strong-field ligand, which leaves 2 unpaired electrons. In the case of $\left[ \mathrm{CoF_6} \right]^{3-}$, the $Co^{3+}$ ion with a $3d^6$ configuration interacts with weak-field fluoride ligands, giving rise to 4 unpaired electrons. Finally, $\left[ \mathrm{MnBr_4} \right]^{2-}$ features a $Mn^{2+}$ ion with a $3d^5$ configuration and weak-field bromide ligands, providing 5 unpaired electrons. These counts of 1, 2, 4, and 5 unpaired electrons dictate the increasing order of their magnetic moments.

Linkage isomerism arises when a coordination complex contains an ambidentate ligand, which is a species capable of bonding to the central metal atom through two different donor atoms. The nitrite ion present in $[ \mathrm{Co} ( \mathrm{NH}_3 )_5 \mathrm{NO}_2 ]^{2+}$ acts as this type of ligand because it can coordinate via either its nitrogen atom or its oxygen atom. This dual binding capability results in the formation of two distinct linkage isomers, making it the only complex among the choices capable of this phenomenon.

The central metal ion in $\mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6]$ is $\mathrm{Fe}^{+2}$, which features an electronic configuration of $[\mathrm{Ar}]\,3\,d^6$. Because $\mathrm{CN}^-$ is a strong field ligand, it induces a large crystal field splitting in the octahedral geometry, forcing all 6 electrons to occupy the lower energy $t_{2g}$ set. Filling these orbitals with 6 electrons effectively results in 3 pairs.

In analytical chemistry, identifying inorganic substances often relies on recognizing the characteristic colours of precipitates formed during qualitative testing. The compound $\mathrm{Mg}(\mathrm{NH}_4)\mathrm{PO}_4$ is recognized as a white precipitate, while $\mathrm{K}_3[\mathrm{Co}(\mathrm{NO}_2)_6]$ is distinct for its bright yellow colour. Manganese compounds like $\mathrm{MnO}(\mathrm{OH})_2$ typically manifest as a brown residue, and the classic Prussian blue pigment is identified by the complex $\mathrm{Fe}_4[\mathrm{Fe}(\mathrm{CN})_6]_3$. Mapping these chemical identities to their visible appearances reveals that A corresponds to II, B links to III, C connects to I, and D pairs with IV.

The transition from a 3d metal like nickel to a 5d metal like platinum significantly alters the coordination behavior of the complex due to differences in crystal field splitting. While $[\mathrm{NiCl}_2\mathrm{Br}_2]^{2-}$ adopts a tetrahedral geometry with weak field ligands and exhibits paramagnetism due to unpaired electrons, replacing it with platinum forces a square planar geometry, resulting in diamagnetic properties where all electrons are paired. This shift from tetrahedral to square planar geometry enables the platinum complex to exhibit geometrical isomerism, which was impossible in the tetrahedral nickel system. Since both complex types lack the structural features necessary for chirality, they remain optically inactive, making optical isomerism the only property among those listed that does not change.

The wavelength of light absorbed by a coordination complex is inversely proportional to its Crystal Field Splitting Energy, a relationship defined by the formula:
$\Delta_0 = \frac{hc}{\lambda}$
Because water acts as a stronger field ligand than the chloride ion, the complex $[\mathrm{Co}(\mathrm{NH}_3)_5(\mathrm{H}_2\mathrm{O})]^{3+}$ possesses a greater $\Delta_0$ value and consequently absorbs light at a shorter wavelength than $[\mathrm{CoCl}(\mathrm{NH}_3)_5]^{2+}$, rendering the assertion false. The reason statement is factually true because the crystal field splitting energy, and thus the wavelength of light absorbed, is indeed influenced by the oxidation state of the central metal ion.

The crystal field splitting energy $\Delta_0$ is inversely proportional to the wavelength of absorbed light, denoted by $\Delta_0 \propto \frac{1}{\lambda}$, meaning the strongest field ligand creates the largest energy gap and thus the shortest absorption wavelength. Since cyanide is the strongest ligand in the set, $[\mathrm{Co}(\mathrm{CN})_6]^{3-}$ exhibits the highest splitting and absorbs the light at the shortest wavelength.

In this complex, the cobalt ion is in the $+3$ oxidation state with a $d^6$ configuration. The strong field cyanide ligands force the six electrons to pair in the lower energy orbitals, resulting in a $t_{2g}^6 e_g^0$ arrangement. With zero unpaired electrons, the spin-only magnetic moment calculated from $\sqrt{n(n+2)}$ is 0 B.M.

The spin-only magnetic moment of a coordination complex is determined by the number of unpaired electrons, $n$, according to the formula $\mu = \sqrt{n(n+2)}$ B.M.

For the complex $[\mathrm{Co}(\mathrm{H}_2\mathrm{O})_6]\mathrm{Cl}_2$, the cobalt ion is in the $+2$ oxidation state with a $3d^7$ electronic configuration. Since $\mathrm{H}_2\mathrm{O}$ acts as a weak field ligand, these electrons are arranged to create 3 unpaired electrons, resulting in a magnetic moment of $\sqrt{15}$ B.M.

In the complex $[\mathrm{Cr}(\mathrm{H}_2\mathrm{O})_6]\mathrm{Cl}_3$, the chromium ion is in the $+3$ oxidation state, which corresponds to a $3d^3$ electronic configuration. In this state, the three electrons occupy separate orbitals, also resulting in 3 unpaired electrons and a magnetic moment of $\sqrt{15}$ B.M. Because both complexes contain the same number of unpaired electrons, the difference between their spin-only magnetic moment values is 0.

The crystal field splitting, represented as $\Delta_0$, for octahedral complexes depends critically on the transition series to which the central metal ion belongs, assuming a consistent oxidation state and ligand set. In this group of complexes, $\Delta_0$ increases as we transition from the $3d$ to the $4d$ and then to the $5d$ series. While $\mathrm{Cr}^{3+}$ and $\mathrm{Fe}^{3+}$ are $3d$ ions and $\mathrm{Mo}^{3+}$ is a $4d$ ion, the inclusion of the $5d$ metal $\mathrm{Os}^{3+}$ establishes the highest energy gap. Consequently, $[\mathrm{Os}(\mathrm{H}_2\mathrm{O})_6]^{3+}$ demonstrates the largest crystal field splitting because the $5d$ orbitals interact more strongly with the ligands than those of the lighter transition elements.

The oxidation state and coordination number of a metal in a complex are determined by evaluating its charge environment and ligand binding geometry. In $\mathrm{Na}[\mathrm{Co}(\mathrm{bpy})\mathrm{Cl}_4]$, the sodium ion contributes a +1 charge, the four chloride ions provide a total of -4, and the neutral bipyridine ligand means the cobalt center must possess an oxidation state of 3 to balance the molecule. Since bipyridine acts as a bidentate ligand by occupying two coordination sites and the four chloride ligands occupy four separate sites, the coordination number for the cobalt center is 6. Summing the magnitude of the oxidation state of 3 and the coordination number of 6 gives 9.

The oxidation state of the central iron atom in the brown complex $[\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_5(\mathrm{NO})]^{2+}$ relies on the principle that the sum of the oxidation states of all components in a complex ion equals its overall charge. Because both water and nitric oxide function as neutral ligands with a charge of zero, the iron atom directly balances the +2 charge of the complex. By assigning $x$ as the oxidation state of iron, the equation $x + 5(0) + (0) = +2$ demonstrates that the oxidation state of iron is 2.

Crystal Field Theory establishes that the energy of light absorbed by a transition metal complex is directly proportional to the magnitude of crystal field splitting, denoted as $\Delta$. Because stronger ligands induce a larger energy gap between the $t_{2g}$ and $e_g$ orbitals, complexes featuring stronger ligands require higher energy photons for electronic excitation. Applying the spectrochemical series, where ethylenediamine is a stronger ligand than ammonia, which is in turn stronger than water, leads to the increasing order of energy absorption: $[\mathrm{Ni}(\mathrm{H}_2\mathrm{O})_6]^{2+} < [\mathrm{Ni}(\mathrm{NH}_3)_6]^{2+} < [\mathrm{Ni}(\mathrm{en})_3]^{2+}$.