### Related Formula textCFSE = left( -0.4 n_mathrmt_2mathrmg + 0.6 n_mathrme_mathrmg right) Delta_mathrmo + n_mathrmp P$\text{CFSE} = \left( -0.4 n_{\mathrm{t}_{2\mathrm{g}}} + 0.6 n_{\mathrm{e}_{\mathrm{g}}} \right) \Delta_{\mathrm{o}} + n_{\mathrm{p}} P$ ### Core Logic Crystal Field Stabilization Energy (CFSE) is maximized (becomes most negative) when electrons populate lower-energy mathrmt_2g$\mathrm{t_{2g}}$ orbitals and stay out of higher-energy mathrme_g$\mathrm{e_g}$ orbitals. This is favored by strong-field ligands (SFL) that induce large Delta_o$\Delta_o$ splitting, leading to low-spin configurations. ### Step 1: Analyze Ligand Strength and Configuration Let us check each of the given complexes: 1. [mathrmCo(en)_3]^3+$[\mathrm{Co(en)_3}]^{3+}$: Here mathrmCo^3+$\mathrm{Co^{3+}}$ has a 3mathrmd^6$3\mathrm{d^6}$ configuration. Since ethylenediamine (mathrmen$\mathrm{en}$) is a strong-field ligand, it causes pairing of all 6$6$ electrons in the mathrmt_2g$\mathrm{t_{2g}}$ subshell. The configuration is mathrmt_2mathrmg^6mathrme_mathrmg^0$\mathrm{t}_{2\mathrm{g}}^{6}\mathrm{e}_{\mathrm{g}}^{0}$.

2. [mathrmCoF_6]^3-$[\mathrm{CoF_6}]^{3-}$: mathrmCo^3+$\mathrm{Co^{3+}}$ is 3mathrmd^6$3\mathrm{d^6}$. Since mathrmF^-$\mathrm{F^-}$ is a weak-field ligand (WFL), no pairing occurs. The configuration is mathrmt_2mathrmg^4mathrme_mathrmg^2$\mathrm{t}_{2\mathrm{g}}^{4}\mathrm{e}_{\mathrm{g}}^{2}$. 3. [mathrmMn(H_2O)_6]^2+$[\mathrm{Mn(H_2O)_6}]^{2+}$: mathrmMn^2+$\mathrm{Mn^{2+}}$ is 3mathrmd^5$3\mathrm{d^5}$. Since mathrmH_2O$\mathrm{H_2O}$ is a weak-field ligand, the configuration is high-spin: mathrmt_2mathrmg^3mathrme_mathrmg^2$\mathrm{t}_{2\mathrm{g}}^{3}\mathrm{e}_{\mathrm{g}}^{2}$. 4. [mathrmZn(H_2O)_6]^2+$[\mathrm{Zn(H_2O)_6}]^{2+}$: mathrmZn^2+$\mathrm{Zn^{2+}}$ is 3mathrmd^10$3\mathrm{d^{10}}$. The d-subshell is fully filled, yielding mathrmt_2mathrmg^6mathrme_mathrmg^4$\mathrm{t}_{2\mathrm{g}}^{6}\mathrm{e}_{\mathrm{g}}^{4}$. ### Step 2: Compare CFSE Values Calculating CFSE (neglecting pairing energy term for simplicity): - For [mathrmCo(en)_3]^3+$[\mathrm{Co(en)_3}]^{3+}$: textCFSE = 6 times (-0.4 Delta_o) = -2.4 Delta_o$\text{CFSE} = 6 \times (-0.4 \Delta_o) = -2.4 \Delta_o$ - For [mathrmCoF_6]^3-$[\mathrm{CoF_6}]^{3-}$: textCFSE = [4(-0.4) + 2(0.6)] Delta_o = -0.4 Delta_o$\text{CFSE} = [4(-0.4) + 2(0.6)] \Delta_o = -0.4 \Delta_o$ - For [mathrmMn(H_2O)_6]^2+$[\mathrm{Mn(H_2O)_6}]^{2+}$: textCFSE = [3(-0.4) + 2(0.6)] Delta_o = 0$\text{CFSE} = [3(-0.4) + 2(0.6)] \Delta_o = 0$ - For [mathrmZn(H_2O)_6]^2+$[\mathrm{Zn(H_2O)_6}]^{2+}$: textCFSE = [6(-0.4) + 4(0.6)] Delta_o = 0$\text{CFSE} = [6(-0.4) + 4(0.6)] \Delta_o = 0$ Hence, [mathrmCo(en)_3]^3+$[\mathrm{Co(en)_3}]^{3+}$ has the highest crystal field stabilization energy, corresponding to the d-orbital electronic configuration mathrmt_2mathrmg^6mathrme_mathrmg^0$\mathrm{t}_{2\mathrm{g}}^{6}\mathrm{e}_{\mathrm{g}}^{0}$. ### Pattern Recognition For octahedral complexes of mathrmd^6$\mathrm{d^6}$ metals, a low-spin configuration (mathrmt_2mathrmg^6mathrme_mathrmg^0$\mathrm{t}_{2\mathrm{g}}^{6}\mathrm{e}_{\mathrm{g}}^{0}$) achieves the theoretical maximum orbital stabilization since the mathrme_g$\mathrm{e_g}$ levels are completely empty and mathrmt_2g$\mathrm{t_{2g}}$ is fully filled. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Coordination Compounds

### Related Formula mu_textspin-only = sqrtn(n+2)~mathrmB.M.$\mu_{\text{spin-only}} = \sqrt{n(n+2)}~\mathrm{B.M.}$ ### Core Logic Let's find the oxidation state of Manganese in the complex [mathrmMnCl_6]^3-$[\mathrm{MnCl}_6]^{3-}$: x + 6(-1) = -3 implies x = +3$x + 6(-1) = -3 \implies x = +3$ Thus, manganese is in the +3$+3$ oxidation state: mathrmMn^3+ = [mathrmAr]3mathrmd^4$\mathrm{Mn^{3+}} = [\mathrm{Ar}]3\mathrm{d}^4$. ### Step 1: Determine Ligand Splitting and Orbitals mathrmCl^-$\mathrm{Cl^-}$ is a weak-field ligand (WFL). Consequently, crystal field splitting is small (Delta_o < P$\Delta_o < P$), and no pairing of the 3mathrmd$3\mathrm{d}$ electrons occurs. The distribution of the 4$4$ electrons in the 3mathrmd$3\mathrm{d}$ orbitals remains high-spin: textUnpaired electrons (n) = 4$\text{Unpaired electrons (n)} = 4$ Because the inner 3mathrmd$3\mathrm{d}$ orbitals are not empty (since they contain 4 singly occupied orbitals), the complex must utilize the outer 4mathrmd$4\mathrm{d}$ orbitals for hybridization. ### Step 2: Assign Hybridization The vacant outer orbitals used for bonding are one 4mathrms$4\mathrm{s}$, three 4mathrmp$4\mathrm{p}$, and two 4mathrmd$4\mathrm{d}$ orbitals, which hybridize to form six **mathrmsp^3d^2$\mathrm{sp^3d^2}$** hybrid orbitals. Since there are four unpaired electrons, the complex is **paramagnetic** with four unpaired electrons. ### Pattern Recognition Whenever WFL (like halides mathrmCl^-$\mathrm{Cl^-}$, mathrmF^-$\mathrm{F^-}$) are present with octahedral transition metal complexes with mathrmd^4$\mathrm{d^4}$ to mathrmd^7$\mathrm{d^7}$ configuration, they always yield high-spin, outer orbital complexes with mathrmsp^3d^2$\mathrm{sp^3d^2}$ hybridization. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Coordination Compounds

### Related Formula mu = sqrtn_textunpaired(n_textunpaired+2)~mathrmB.M.$\mu = \sqrt{n_{\text{unpaired}}(n_{\text{unpaired}}+2)}~\mathrm{B.M.}$ ### Core Logic This question requires three distinct sequential conceptual steps: 1. Determine the count n$n$ of diamagnetic complexes. 2. Identify which of the metal ions (Ni, Zn, Mn, Cu) has the lowest enthalpy of atomisation. 3. Compute the spin-only magnetic moment of that metal in its +n$+n$ state. ### Step 1: Count Diamagnetic Complexes to find n - mathrmK_2[NiCl_4]$\mathrm{K_2[NiCl_4]}$: mathrmNi^2+ = 3mathrmd^8$\mathrm{Ni^{2+}} = 3\mathrm{d^8}$. Weak field chloride ligand leads to 2 unpaired electrons implies$\implies$ **Paramagnetic**. - mathrm[Zn(H_2O)_6]Cl_2$\mathrm{[Zn(H_2O)_6]Cl_2}$: mathrmZn^2+ = 3mathrmd^10$\mathrm{Zn^{2+}} = 3\mathrm{d^{10}}$. Completely filled subshell implies$\implies$ **Diamagnetic**. - mathrmK_3[Mn(CN)_6]$\mathrm{K_3[Mn(CN)_6]}$: mathrmMn^3+ = 3mathrmd^4$\mathrm{Mn^{3+}} = 3\mathrm{d^4}$. Strong field cyanide ligand gives low-spin state with 2 unpaired electrons implies$\implies$ **Paramagnetic**. - mathrm[Cu(PPh_3)_3I]$\mathrm{[Cu(PPh_3)_3I]}$: mathrmCu^+$\mathrm{Cu^+}$ = 3mathrmd^10$3\mathrm{d^{10}}$. Completely filled subshell implies$\implies$ **Diamagnetic**. Thus, there are exactly 2 diamagnetic complexes: **n = 2$n = 2$**. ### Step 2: Identify Metal with Lowest Enthalpy of Atomisation Among the transition metals of the 3d series (Ni, Zn, Mn, Cu), **Zinc (Zn)** has the lowest enthalpy of atomisation (126~mathrmkJ~mol^-1$126~\mathrm{kJ~mol^{-1}}$). This is because Zinc has a fully occupied d-subshell (3mathrmd^104mathrms^2$3\mathrm{d^{10}}4\mathrm{s^2}$) and lacks any unpaired d-electrons to participate in metallic bonding. ### Step 3: Calculate Spin-only Magnetic Moment of M^n+ With M = textZinc$M = \text{Zinc}$ and n = 2$n = 2$, the ion is mathrmZn^2+$\mathrm{Zn^{2+}}$. Electronic configuration of mathrmZn^2+$\mathrm{Zn^{2+}}$ is [mathrmAr]3mathrmd^10$[\mathrm{Ar}]3\mathrm{d^{10}}$, which contains zero unpaired electrons (n_textunpaired = 0$n_{\text{unpaired}} = 0$). Therefore, the spin-only magnetic moment is: mu = 0~mathrmB.M.$\mu = 0~\mathrm{B.M.}$ ### Pattern Recognition Zinc is always a unique outlier in the d-block. Because it has a completely filled d^10$d^{10}$ shell in both its atomic and +2$+2$ oxidation states, it exhibits no d-orbital metallic bonding (leading to lowest melting point, boiling point, and atomisation enthalpy in the 3d series) and is always diamagnetic. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Coordination Compounds Class 12 Chemistry: d- and f-Block Elements

### Related Formula Crystal Field Splitting configuration rule for strong field ligands: Delta_0 > P implies textElectrons fill mathrmt_2g text completely before entering mathrme_g$\Delta_0 > P \implies \text{Electrons fill } \mathrm{t_{2g}} \text{ completely before entering } \mathrm{e_g}$ ### Core Logic Let's isolate properties step-by-step: 1. Among the given first-row elements (mathrmMn, Cr, Co, Fe$\mathrm{Mn, Cr, Co, Fe}$), Cobalt (mathrmCo$\mathrm{Co}$) possesses the highest standard electrode potential value for the 3+/2+$3+/2+$ couple: E^circ(mathrmCo^3+/Co^2+) = +1.81mathrm~V$E^\circ(\mathrm{Co^{3+}/Co^{2+}}) = +1.81\mathrm{~V}$ 2. The oxidation state configuration within complex [mathrmCo(mathrmCN)_6]^4-$[\mathrm{Co}(\mathrm{CN})_6]^{4-}$ is mathrmCo^2+$\mathrm{Co^{2+}}$, which has a mathrmd^7$\mathrm{d^7}$ valence configuration. 3. Cyanide (mathrmCN^-$\mathrm{CN^-}$) acts as a strong field ligand, forcing maximum electron pairing within the lower energy levels. ### Step 1: Subshell Filling Matrix Distribute 7 electrons across the split crystal field levels: * First 6 electrons fill the lower mathrmt_2g$\mathrm{t_{2g}}$ levels completely, forming paired tracks. * The 7th electron has no choice but to step up to the higher level. This structural splitting is visualized below:

Therefore, the number of electrons present in the mathrme_g$\mathrm{e_g}$ orbital block is exactly 1. ### Pattern Recognition Always double check the specific oxidation state value: [mathrmCo(mathrmCN)_6]^4-$[\mathrm{Co}(\mathrm{CN})_6]^{4-}$ gives mathrmCo^2+$\mathrm{Co^{2+}}$ (mathrmd^7$\mathrm{d^7}$), whereas [mathrmCo(mathrmCN)_6]^3-$[\mathrm{Co}(\mathrm{CN})_6]^{3-}$ would be mathrmCo^3+$\mathrm{Co^{3+}}$ (mathrmd^6$\mathrm{d^6}$), which has zero electrons in its mathrme_g$\mathrm{e_g}$ level. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Coordination Compounds Class 12 Chemistry: d- and f-Block Elements

### Related Formula Crystal field splitting values relation for matching configuration choices: Delta_mathrmt = frac49Delta_0$\Delta_{\mathrm{t}} = \frac{4}{9}\Delta_0$ ### Core Logic Let's verify both rules based on Crystal Field Theory principles: * **Statement I**: In octahedral configurations, if pairing penalty energy P$P$ exceeds field split magnitude Delta_0$\Delta_0$, electrons prefer moving to upper sub-shells, creating high-spin states. Conversely, if Delta_0 > P$\Delta_0 > P$, forced pairing occurs, creating low-spin complexes. (Statement I is accurate). * **Statement II**: Because tetrahedral configurations separate by an extremely narrow gap magnitude Delta_mathrmt$\Delta_{\mathrm{t}}$ (about half of octahedral field splits), the value almost never exceeds standard pairing energy P$P$. Electrons consistently choose higher sub-levels rather than pairing up, meaning low-spin arrangements are extremely rare. (Statement II is accurate). ### Step 1: Verdict Therefore, both Statement I and Statement II are correct. ### Pattern Recognition Tetrahedral configurations are systematically assumed to be high-spin unless special structural properties dictate otherwise, due to the Delta_mathrmt < P$\Delta_{\mathrm{t}} < P$ constraint. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Coordination Compounds