'X' is the number of electrons in t2g$\mathrm{t}_{2\mathrm{g}}$ orbitals of the most stable complex ion among [Fe(NH₃)₆]³⁺$[\mathrm{Fe}(\mathrm{NH}_3)_6]^{3+}$, [Fe(Cl₆)]³⁻$[\mathrm{Fe}(\mathrm{Cl}_6)]^{3-}$, [Fe(C₂O₄)₃]³⁻$[\mathrm{Fe}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}$ and [Fe(H₂O)₆]³⁺$[\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_6]^{3+}$. The nature of oxide of vanadium of the type V₂OX$\mathrm{V}_2\mathrm{O}_\mathrm{X}$ is:

Core Logic

This pathway corresponds to the standard confirmatory test for cobalt (Co²⁺$\mathrm{Co}^{2+}$) ions in qualitative inorganic analysis:

• CoS$\mathrm{CoS}$ dissolves in aqua regia to yield cobalt chloride (CoCl₂$\mathrm{CoCl}_2$):

• Treating this solution with potassium nitrite (KNO₂$\mathrm{KNO}_{2}$) in the presence of acetic acid (AcOH$\mathrm{AcOH}$) oxidizes Co²⁺$\mathrm{Co}^{2+}$ to Co³⁺$\mathrm{Co}^{3+}$, precipitating potassium cobaltinitrite as a characteristic yellow solid:

Pattern Recognition

A yellow precipitate formed specifically upon adding KNO₂$\mathrm{KNO}_2$ and acetic acid is a definitive signature of potassium cobaltinitrite, K₃[Co(NO₂)₆]$\mathrm{K}_3[\mathrm{Co}(\mathrm{NO}_2)_6]$. This confirms the starting sulfide was CoS$\mathrm{CoS}$.

Chapter Mix

Class 12 Chemistry: Coordination Compounds Class 11 Chemistry: Qualitative Analysis

Core Logic

An aqueous nickel (II) chloride solution contains the green hexaquarickel(II) complex, [Ni(H₂O)₆]²⁺$[\mathrm{Ni}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}$. Ethane-1,2-diamine ('en') is a bidentate ligand that binds more strongly than water, shifting the crystal field splitting parameter (Δₒ$\Delta_o$) to higher energies as it replaces water molecules:

• Initial state:

• Adding 1 equivalent of 'en' forms a mono-en complex:

• Adding a 2nd equivalent forms a bis-en complex:

• Adding a 3rd equivalent forms the tris-en complex:

This progressive ligand replacement shifts the absorption spectrum, changing the solution's visible color from Green arrow$\rightarrow$ Pale Blue arrow$\rightarrow$ Blue arrow$\rightarrow$ Violet.

Pattern Recognition

Replacing weak-field ligands (like H₂O$\mathrm{H}_2\mathrm{O}$) with stronger bidentate chelating ligands (like 'en') increases crystal field splitting. For Ni²⁺$\mathrm{Ni}^{2+}$, this ligand substitution always follows the specific chromatic progression: Green arrow$\rightarrow$ Pale Blue arrow$\rightarrow$ Blue arrow$\rightarrow$ Violet.

Chapter Mix

Class 12 Chemistry: Coordination Compounds

Core Logic

Consider an octahedral coordination environment for a d⁴$d^4$ transition metal ion configuration:

• Weak Field Ligand (WFL):

The crystal field splitting energy is smaller than the pairing energy (Δₒ < P$\Delta_o < P$). Consequently, electrons prefer to occupy the higher-energy eg$e_g$ orbitals rather than pair up in the lower-energy t2g$t_{2g}$ orbitals. This leads to a high spin complex with the configuration:

• Strong Field Ligand (SFL):

The splitting energy is larger than the pairing energy (Δₒ > P$\Delta_o > P$). Electrons pair up in the t2g$t_{2g}$ orbitals before occupying the eg$e_g$ subshell, resulting in a low spin complex with the configuration:

Pattern Recognition

An electron occupying an eg$e_g$ orbital before the t2g$t_{2g}$ orbitals are fully paired requires a weak-field ligand. This configuration maximizes the number of unpaired electrons, which is the defining characteristic of a high-spin complex.

Chapter Mix

Class 12 Chemistry: Coordination Compounds

Related Formula

Core Logic

Since 1 mole of the complex yields 2 moles of AgCl(s)$AgCl_{(s)}$, there must be exactly 2 chloride ions outside the coordination sphere to undergo precipitation:

This dissociation produces a total of 3 moles of ions per mole of the complex, perfectly consistent with the problem constraints.

Pattern Recognition

Number of precipitated AgCl$AgCl$ moles directly equates to the count of counter-anions located outside the square brackets.

Chapter Mix

Class 12 Chemistry: Coordination Compounds

Related Formula

Coordination Number 6 corresponds to either d²sp³$d^2sp^3$ or sp³d²$sp^3d^2$ configuration templates. Coordination Number 4 corresponds to either sp³$sp^3$ or dsp²$dsp^2$ configuration templates.

Core Logic

Analyzing metal orbital dynamics under varying ligand fields:

• (A) [CoF₆]³⁻$[CoF_6]^{3-}$: Co³⁺$Co^{3+}$ (3d⁶$3d^6$) with a weak field ligand (F^-$F^-$) arrow$\rightarrow$ no pairing occurs arrow$\rightarrow$ utilizes outer orbitals arrow$\rightarrow$ sp³d²$sp^3d^2$.
• (B) [NiCl₄]²⁻$[NiCl_4]^{2-}$: Ni²⁺$Ni^{2+}$ (3d⁸$3d^8$) with a weak field ligand (Cl^-$Cl^-$) arrow$\rightarrow$ no pairing occurs arrow$\rightarrow$ tetrahedral profile arrow$\rightarrow$ sp³$sp^3$.
• (C) [Co(NH₃)₆]³⁺$[Co(NH_3)_6]^{3+}$: Co³⁺$Co^{3+}$ (3d⁶$3d^6$) with a strong field ligand (NH₃$NH_3$) arrow$\rightarrow$ electrons pair up arrow$\rightarrow$ inner orbital configuration arrow$\rightarrow$ d²sp³$d^2sp^3$.
• (D) [Ni(CN)₄]²⁻$[Ni(CN)_4]^{2-}$: Ni²⁺$Ni^{2+}$ (3d⁸$3d^8$) with a strong field ligand (CN^-$CN^-$) arrow$\rightarrow$ forced pairing opens a 3d$3d$ slot arrow$\rightarrow$ square planar geometry arrow$\rightarrow$ dsp²$dsp^2$.

Step 1: Final Pairing Match

The completed matching configuration aligns cleanly with: (A)-(III), (B)-(II), (C)-(I), (D)-(IV).

Pattern Recognition

Isolate coordination frameworks quickly:

• Nickel(II) with weak field ligands (Cl^-$Cl^-$) yields sp³$sp^3$, while with strong field ligands (CN^-$CN^-$) it yields dsp²$dsp^2$.
• Cobalt(III) with weak field ligands (F^-$F^-$) yields sp³d²$sp^3d^2$, while with strong field ligands (NH₃$NH_3$) it yields d²sp³$d^2sp^3$.

Chapter Mix

Class 12 Chemistry: Coordination Compounds