Coordination Compounds – JEE Main ChemistryPractice Questions & PYQs

The crystal field splitting energy, $\Delta_o$, is inversely proportional to the wavelength of the absorbed light, $\lambda_{abs}$, as described by the relationship $\Delta_o = \frac{hc}{\lambda_{abs}}$. Comparing the colors absorbed by the complexes, red light has a longer wavelength than green, and green has a longer wavelength than blue, establishing the absorption order $\lambda_{L_3} > \lambda_{L_1} > \lambda_{L_2}$. Consequently, the inverse relationship dictates that the magnitude of splitting energy increases as the wavelength decreases, leading to the increasing order of ligand strength $L_3 < L_1 < L_2$.

The structure of the organometallic complex $Co_2(CO)_8$ is determined by the necessity of satisfying the 18-electron rule for each metal center within the dimer. In this specific molecular configuration, the two cobalt atoms are linked directly by a single metal-metal bond that serves as the foundation of the complex. To achieve optimal electronic stability, two of the eight total carbonyl ligands are situated in bridging positions between the cobalt atoms, while the other six ligands remain terminally bonded to the metal centers. This arrangement results in exactly two bridging CO ligands and one Co-Co bond.

The spin-only magnetic moment follows the relationship $\mu = \sqrt{n(n+2)}$ BM, where $n$ is the number of unpaired electrons. A magnetic moment of 5.9 BM for the $Mn^{II}$ complex implies $n = 5$, indicating that all five $d$-electrons are unpaired in a high-spin configuration. This arrangement occurs exclusively in the presence of a weak field ligand, as stronger field ligands would induce electron pairing. Among the choices, $NCS^-$ is the appropriate weak field ligand, whereas $CN^-$, $CO$, and ethylenediamine are strong field ligands that would result in a lower magnetic moment.

Transition metals generally favor a maximum coordination number of six because their ionic radii constrain the number of donor atoms that can spatially arrange around the center, typically resulting in octahedral geometries. Conversely, inner-transition metals possess larger ionic sizes and increased availability of coordination sites, which allows them to accommodate a higher number of donor atoms and reach a maximum denticity of eight.

Removing the ligands situated along the $z$-axis of an octahedral complex transforms the chemical environment into a square planar geometry, which fundamentally alters the electrostatic interactions between the metal $d$-orbitals and the surrounding ligands. Because there is no longer any direct repulsion along the $z$-axis, the orbitals containing a $z$-component-specifically the $d_{xz}$, $d_{yz}$, and $d_{z^2}$ orbitals-experience a significant decrease in energy, with the $d_{z^2}$ orbital shifting to a lower energy state than its position in an octahedral field. Meanwhile, the $d_{xy}$ and $d_{x^{2-}y^2}$ orbitals, which reside in the plane where the ligands remain, stay at higher energy levels, with the $d_{x^{2-}y^2}$ orbital reaching the highest energy state due to direct head-on interaction with the remaining ligands. This reorganization establishes a distinct splitting pattern where the $d_{xz}$ and $d_{yz}$ orbitals occupy the lowest energy level, followed by the $d_{z^2}$ orbital, then the $d_{xy}$ orbital, and finally the $d_{x^{2-}y^2}$ orbital at the top.

The spin-only magnetic moment of transition metal complexes is determined by the number of unpaired electrons $n$ in their $d$-orbitals, which follows the relationship $\mu = \sqrt{n(n+2)}$ BM. A magnetic moment value of 3.9 BM points to the presence of exactly three unpaired electrons, as the calculation of $\sqrt{3(3+2)}$ results in approximately 3.89 BM.

Identifying the correct metal ions requires examining their $d$-electron configurations. The Vanadium ion in the $+2$ oxidation state has a $3d^3$ configuration, which leaves three electrons unpaired. Similarly, the Cobalt ion in the $+2$ oxidation state has a $3d^7$ configuration, which also accommodates three unpaired electrons in the octahedral environment provided by the water ligands. Other ions such as $Cr^{2+}$, $Mn^{2+}$, and $Fe^{2+}$ have different electron distributions that result in magnetic moments inconsistent with this specific target value.

In coordination chemistry, the magnitude of the crystal field splitting energy ($\Delta_o$) depends directly on the strength of the ligands coordinated to the metal center, with stronger ligands inducing a larger splitting. Because the energy of an absorbed photon ($E$) is directly proportional to $\Delta_o$ and follows the relationship $E = \frac{hc}{\lambda}$, a higher splitting energy results in the absorption of a shorter wavelength ($\lambda$). Based on the spectrochemical series, the ligand field strength increases in the order $Cl^- < H_2O < NH_3$. Consequently, the complexes exhibit an increasing trend in splitting energy, meaning the wavelength of absorbed light follows the inverse order of $[CoCl(NH_3)_5]^{2+} > [Co(NH_3)_5H_2O]^{3+} > [Co(NH_3)_6]^{3+}$.

The coordination number of a central metal ion in a coordination complex is defined by the total number of coordinate covalent bonds established by the surrounding ligands. In the complex $K_4[Th(C_2O_4)_4(OH_2)_2]$, the ligands directly bonded to the Thorium center consist of four oxalate ions ($C_2O_4^{2-}$) and two water molecules ($OH_2$). Because oxalate is a bidentate ligand capable of forming two bonds per ion, the four oxalate groups provide eight coordinate bonds. With water serving as a monodentate ligand that forms one bond each, the two water molecules contribute an additional two bonds, summing to a total coordination number of 10.

The stability of a complex ion is dictated by its crystal field stabilization energy, which depends directly on the electron configuration of the metal center under the influence of strong-field ligands like phenanthroline. In the case of the iron complex, the low-spin $d^6$ configuration of $\mathrm{Fe}^{2+}$ yields a CFSE of $-0.4(6) + 0.6(0) = -2.4$. Upon oxidation, the metal transforms into a low-spin $d^5$ $\mathrm{Fe}^{3+}$ system with a CFSE of $-0.4(5) + 0.6(0) = -2.0$. Because the stabilization energy becomes less negative during this transition, the complex experiences a net loss of stabilization energy.

The coordination number of a central metal ion is determined by the total number of donor atoms from the surrounding ligands that form coordinate covalent bonds with the metal. In the complex $[ {Co}(C l)(e n)_{2} ] C l$, the cobalt ion is bonded to one monodentate chloride ligand and two bidentate ethylenediamine ligands, which provide a total of $1 + (2 \times 2) = 5$ attachment points. For the complex $K_{3} [A l (C_{2} O_{4} )_{3} ]$, the aluminum ion is associated with three oxalate ligands, and since each oxalate ion is bidentate, the total coordination number sums to $3 \times 2 = 6$.

The crystal field splitting energy ($\Delta$) is directly influenced by the field strength of the ligands surrounding the central metal ion, as dictated by the spectrochemical series. Ligands with greater field strength induce a larger separation between the $d$-orbitals compared to those with weaker field strength. Because the cyanide ion ($CN^-$) acts as the strongest field ligand among those present in the provided examples, the complex $K_3[Co(CN)_6]$ exhibits the highest splitting energy.

In an octahedral complex like $K_3[Co(CN)_6]$, where the central $Co^{3+}$ ion is surrounded by six ligands, the incoming ligands approach the metal center specifically along the Cartesian x, y, and z axes. Because the $d_{x^{2-}y^2}$ and $d_{z^2}$ orbitals have lobes oriented directly along these axial directions, they experience the strongest electrostatic repulsion from the ligands due to direct head-on interaction. This alignment contrasts with the $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals, which point between the axes and consequently experience lower repulsion.

Geometric isomerism in octahedral complexes of the general formula $[M(AA)_2X_2]$, where $AA$ is a symmetric bidentate ligand and $X$ is a monodentate ligand, arises because the two $X$ ligands can occupy positions either adjacent to each other or at a $180^\circ$ angle. In the complex $[M(en)_2Cl_2]^{2+}$, the two chloride ions can be positioned trans to one another, thereby creating a distinct trans-isomer. Other configurations, such as tris-chelates or square planar complexes involving bidentate ligands, lack the specific spatial arrangement of monodentate ligands required to exhibit this type of geometric isomerism.

The magnetic behavior of coordination complexes depends on the electronic configuration of the central metal ion and the field strength of the surrounding ligands. In the $\mathrm{[Fe(H_2O)_6]^{2+}}$ cation, the iron center exists in the $+2$ oxidation state with a $d^6$ configuration, and because water acts as a weak-field ligand, it does not induce electron pairing, which leaves four unpaired electrons resulting in a magnetic moment of 4.9 BM. Conversely, in the $\mathrm{[Fe(CN)_6]^{4-}}$ anion, the same $d^6$ iron ion is coordinated by the strong-field cyanide ligand, which forces all electrons to pair up in the lower energy orbitals, resulting in zero unpaired electrons and a magnetic moment of 0 BM.

Organometallic compounds are defined by the presence of at least one direct chemical bond between a metal atom and a carbon atom. In the structure of $Mn_2(CO)_{10}$, the manganese metal centers are linked directly to the carbon atoms of the carbonyl ligands, satisfying this fundamental requirement. Because of this specific interaction between the metal and the carbon atom, the compound is classified as organometallic.

Valence Bond Theory serves as a fundamental framework for describing bonding in coordination compounds, yet it falls short when explaining the optical and precise electronic properties of transition metal complexes. Because the model focuses on hybridization and geometry rather than the splitting of $d$-orbitals, it is unable to account for the absorption spectra that cause these complexes to exhibit specific colors. Furthermore, the theory provides no basis for distinguishing between weak-field and strong-field ligands, nor does it offer the capacity to predict magnetic properties quantitatively, which ultimately limits its utility in describing the complex behavior of these species.

The specific geometric isomer known as cisplatin, chemically denoted as $cis-[Pt(Cl)_2(NH_3)_2]$, functions as a potent anti-tumor agent due to the unique spatial orientation of its ligands. This particular cis configuration is essential for binding effectively to DNA, which disrupts the replication of cancer cells and inhibits their proliferation. Because the biological activity of these coordination complexes is strictly determined by their stereochemistry, the trans isomer lacks the necessary structure to provide the same therapeutic effect.

Biological and industrial systems rely on specific metal ions to function effectively as critical cofactors or catalysts. Vitamin B12 is a well-known coordination compound centered around cobalt, whereas the enzyme carbonic anhydrase requires a zinc ion to perform its catalytic activity. In plant biology, the chlorophyll molecule, with its formula $C_{55}H_{72}O_5N_4Mg$, is defined by its central magnesium atom, while the Wilkinson catalyst, $RhCl(PPh_3)_3$, utilizes rhodium as its key metallic component.

The magnitude of the spin-only magnetic moment of a metal ion in a complex is directly determined by the number of unpaired electrons, $n$, in its d-orbitals according to the relation $\mu = \sqrt{n(n+2)}$ Bohr Magnetons. In $[V(CN)_{6}]^{4-}$, the $V^{2+}$ ion possesses a $d^{3}$ configuration, which results in 3 unpaired electrons. For the $[Cr(NH_{3})_{6}]^{2+}$ complex, the $Cr^{2+}$ ion adopts a low-spin $d^{4}$ configuration, arranging its electrons into one pair and 2 unpaired electrons. The $[Ru(NH_{3})_{6}]^{3+}$ ion follows a $d^{5}$ configuration where, in a low-spin state, the electrons distribute into 2 pairs and 1 unpaired electron. Finally, $[Fe(CN)_{6}]^{4-}$ contains an $Fe^{2+}$ ion with a $d^{6}$ configuration, in which all six electrons are paired, leaving 0 unpaired electrons. By comparing the number of unpaired electrons in each species, the decreasing order of magnetic moments follows the sequence $V^{2+} > Cr^{2+} > Ru^{3+} > Fe^{2+}$.

The electron distribution in octahedral metal complexes is determined by Crystal Field Theory, where the ligand field strength dictates whether electrons occupy high-spin or low-spin configurations based on the splitting of $d$-orbitals. For the $Co^{2+}$ ion, which has a $d^7$ electronic configuration, the high-spin state is $t_{2g}^5 e_g^2$ with three unpaired electrons, while the low-spin state is $t_{2g}^6 e_g^1$ with one unpaired electron, yielding a difference of exactly two. Other ions like $Fe^{2+}$ ($d^6$) and $Mn^{2+}$ ($d^5$) exhibit a difference of four unpaired electrons between spin states, whereas $Ni^{2+}$ ($d^8$) maintains a constant number of unpaired electrons.