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Inorganic Chemistry Formulas

Complete chapter-wise formula sheet for Inorganic Chemistry (Chemistry) covering key equations, parameters, traps, and concept diagrams for JEE Main & Advanced.

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Inorganic Chemistry367 Qs

Periodic Table & Periodic Properties

Ionization enthalpy, electron gain enthalpy, electronegativity (Pauling & Mulliken scales), screening effect, and atomic radii trends.

7 Formulas

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Inorganic Chemistry894 Qs

p-Block Elements

Group 15 (N, P, As), Group 16 (O, S), Group 17 (Halogens), Group 18 (Noble Gases) — oxoacids, interhalogen compounds, allotropes, and trend rules.

9 Formulas

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Inorganic Chemistry698 Qs

Chemical Bonding & VSEPR

VSEPR molecular geometries, steric number hybridization, bond order from MOT, dipole moments, and hydrogen bonding.

7 Formulas Diagram

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Inorganic Chemistry772 Qs

Coordination Compounds

Werner theory, crystal field splitting (CFT), spectrochemical series, magnetic moments, and isomerism.

9 Formulas

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Inorganic Chemistry589 Qs

d- & f-Block Elements

Transition element trends, variable oxidation states, lanthanide contraction, catalytic properties, and potassium permanganate/dichromate reactions.

8 Formulas

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Inorganic Chemistry512 Qs

Principles of Practical Chemistry & Salt Analysis

Systematic qualitative analysis of cations (Groups 0 to VI) and anions, confirmatory tests, flame tests, borax bead test, and organic functional group identification.

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Formulas Reference (Inorganic Chemistry)

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Inorganic ChemistryHigh Yield (2 Qs in JEE)367 PYQs

Periodic Table & Periodic Properties

Ionization enthalpy, electron gain enthalpy, electronegativity (Pauling & Mulliken scales), screening effect, and atomic radii trends.

Chapter

Effective Nuclear Charge (Slater's Rules)

Z_{\text{eff}} = Z - \sigma, \quad \text{Shielding Power: } s > p > d > f

Net positive nuclear attraction felt by valence electrons after screening.

Poor shielding of 3d and 4f electrons causes scandide and lanthanide contractions.

Electronegativity Scales (Pauling & Mulliken)

\chi_A - \chi_B = 0.208 \sqrt{\Delta} \; (\text{in kcal}), \quad \chi_{\text{Mulliken}} = \frac{\text{IE} + \text{EA}}{2 \text{ (in eV)}} \approx 2.8 \chi_{\text{Pauling}}

Tendency of bonded atom to attract shared electron pair.

Fluorine has maximum electronegativity = 4.0 on Pauling scale.

Ionization Enthalpy & Anomalies

\text{IE}_1(\text{Be}) > \text{IE}_1(\text{B}), \quad \text{IE}_1(\text{N}) > \text{IE}_1(\text{O}), \quad \text{IE}_1(\text{P}) > \text{IE}_1(\text{S})

Penetration effect (2s² > 2p¹) and extra stability of half-filled subshells (2p³ > 2p⁴).

Successive ionization energies strictly increase: IE₁ < IE₂ < IE₃ < IE₄.

Electron Gain Enthalpy (\Delta_{eg}H) Anomalies

|\Delta_{eg}H|: \; \text{Cl} > \text{F} > \text{Br} > \text{I}, \quad \text{S} > \text{Se} > \text{Te} > \text{Po} > \text{O}

Compact 2p orbital in F and O creates strong electron-electron repulsion, making 3p elements (Cl, S) have more negative electron gain enthalpy.

Noble gases have positive Δ_eg H. Nitrogen, Be, and Mg have Δ_eg H close to zero or slightly positive.

Allred-Rochow Scale of Electronegativity

\chi_{\text{AR}} = 0.359 \frac{Z_{\text{eff}}}{r^2} + 0.744 \quad (r \text{ in \AA})

Electrostatic force exerted by effective nuclear charge on an electron at the covalent radius distance.

Pauling scale connection: χ_Pauling ≈ χ_AR ≈ χ_Mulliken / 2.8.

Lanthanide Contraction & Pairs with Identical Radii

r(\text{Zr}^{4+}) \approx r(\text{Hf}^{4+}) \approx 0.80\,\text{\AA}, \quad r(\text{Nb}^{5+}) \approx r(\text{Ta}^{5+}), \quad r(\text{Mo}^{6+}) \approx r(\text{W}^{6+})

Poor shielding of 14 inner 4f electrons causes atomic/ionic radii of 4d and 5d transition series to be almost identical.

Explains why separation of Zr and Hf is extremely difficult chemically.

Hydration Enthalpy & Aqueous Ionic Mobility

\Delta H_{\text{hyd}} \propto \frac{z}{r} \implies \text{Hydrated Radius: } \text{Li}^+_{\text{aq}} > \text{Na}^+_{\text{aq}} > \text{K}^+_{\text{aq}} > \text{Cs}^+_{\text{aq}}, \quad \text{Mobility: } \text{Cs}^+ > \text{Rb}^+ > \text{K}^+ > \text{Na}^+ > \text{Li}^+

Smaller gaseous cations have higher charge density, attract more water molecules, and become bulkier with slower electrical conductivity in aqueous solution.

Li⁺ has smallest gaseous ionic radius but largest hydrated radius in water.

Inorganic ChemistryTop Priority (3-4 Qs in JEE)894 PYQs

p-Block Elements

Group 15 (N, P, As), Group 16 (O, S), Group 17 (Halogens), Group 18 (Noble Gases) — oxoacids, interhalogen compounds, allotropes, and trend rules.

Chapter

Oxidation States of Group 15, 16, 17 Elements

\text{Group 15: } -3, +1, +2, +3, +4, +5 \quad \text{Group 16: } -2, +2, +4, +6 \quad \text{Group 17: } -1, +1, +3, +5, +7

p-Block elements exhibit multiple oxidation states due to availability of d-orbitals (from 3rd period onward). Fluorine has fixed OS = −1 (no d-orbital, most electronegative).

Nitrogen does NOT show +5 OS in fluoride (NF₅ does not exist) because N has no d-orbitals to expand octet. Maximum OS of N is +4 in NO₂ (and +5 only in N₂O₅ / NO₃⁻).

Phosphorus Oxoacids — Basicity & Reducing Power

\begin{array}{lcc} \text{Acid} & \text{Basicity} & \text{Reducing?} \\ H_3PO_4 & 3 & \text{No} \\ H_3PO_3 & 2 & \text{Yes} \\ H_3PO_2 & 1 & \text{Yes (strong)} \\ H_4P_2O_7 & 4 & \text{No} \end{array}

Basicity = number of ionisable P−OH groups. P−H bonds are not ionisable. Reducing power arises from P−H bond which donates H to oxidising agent.

Memory rule: Count only OH groups directly bonded to P. H₃PO₂ has one −OH and two P−H bonds → monobasic, strong reducing agent. All metaphosphoric acids (HPO₃)ₙ have basicity 1.

Nitrogen Oxides Oxidation State Ladder

N_2O \xrightarrow{+1} NO \xrightarrow{+2} N_2O_3 \xrightarrow{+3} NO_2 \xrightarrow{+4} N_2O_4 \xrightarrow{+4} N_2O_5 \xrightarrow{+5}

Nitrogen oxides in increasing oxidation state. NO and NO₂ are paramagnetic (odd-electron species). N₂O₄ is the dimer of NO₂ (diamagnetic).

Only NO₂ (brown gas) and N₂O₄ (colourless) are in equilibrium: 2NO₂ ⇌ N₂O₄ (K_p decreases with temperature → more NO₂ at high T, Le Chatelier). N₂O is laughing gas (+1 OS), used as anaesthetic.

Oxoacids of Sulphur — Structure & OS

H_2S_2O_7 \text{ (pyrosulphuric, oleum, OS +7)}, \quad H_2SO_4 \text{ (+6)}, \quad H_2SO_3 \text{ (+4)}, \quad H_2S_2O_8 \text{ (peroxodisulphuric, Marshall's acid, OS +6)}

Key sulphur oxoacids with S oxidation states. Oleum (H₂S₂O₇) = SO₃ dissolved in H₂SO₄. Marshall's acid contains -O-O- peroxo linkage. Thiosulphate Na₂S₂O₃ contains S in OS 0 and +5 (average +2).

H₂S₂O₃ (thiosulphuric acid): average OS of S = +2 but one S is -2 and other is +6 (non-equivalent). Hot conc. H₂SO₄ acts as oxidising agent (reduces to SO₂); cold dil. H₂SO₄ acts as acid.

Interhalogen Compounds — Formula & Geometry

\text{Type XY: ClF, BrF, BrCl} \quad \text{XY}_3\text{: ClF}_3 \text{ (T-shape)} \quad \text{XY}_5\text{: ClF}_5\text{, BrF}_5 \text{ (Square pyramidal)} \quad \text{XY}_7\text{: IF}_7 \text{ (Pentagonal bipyramidal)}

Interhalogen compounds XYₙ where X is the heavier halogen and n = 1, 3, 5, 7. Geometry determined by VSEPR including lone pairs.

ClF₃ has 2 lone pairs on Cl → T-shape (sp³d). BrF₅ has 1 lone pair on Br → square pyramidal (sp³d²). IF₇ has 0 lone pairs on I → pentagonal bipyramidal (sp³d³). All are powerful fluorinating agents.

Noble Gas Compounds of Xenon — Structure & Shape

\begin{array}{lll} \text{Compound} & \text{Hybridisation} & \text{Shape} \\ XeF_2 & sp^3d & \text{Linear} \\ XeF_4 & sp^3d^2 & \text{Square planar} \\ XeF_6 & sp^3d^3 & \text{Distorted octahedral} \\ XeO_3 & sp^3 & \text{Pyramidal} \\ XeO_4 & sp^3 & \text{Tetrahedral} \end{array}

Xenon fluorides and oxides. XeF₂ and XeF₄ have lone pairs on Xe making them linear and square planar respectively (VSEPR).

XeF₂ is a mild fluorinating agent. XeF₄ reacts with water to give Xe + O₂ + HF (disproportionation): 6XeF₄ + 12H₂O → 4Xe + 2XeO₃ + 24HF + 3O₂. Never confuse XeF₄ (sp³d²) with SF₄ (sp³d, seesaw).

Disproportionation of Halogen Acids & Oxyhalogen Acids

\text{Hot NaOH: } 3Cl_2 + 6NaOH \xrightarrow{\Delta} 5NaCl + NaClO_3 + 3H_2O

Disproportionation of halogens in alkali. In cold dilute NaOH: Cl₂ + 2NaOH → NaCl + NaOCl + H₂O (hypohalite formation). Bleaching powder: Ca(OCl)Cl formed by Cl₂ + Ca(OH)₂ → Ca(OCl)Cl + H₂O.

Oxidising power order of oxyacids: HOCl > HOBr > HOI. Acid strength order (opposite to oxidising power): HClO₄ > HClO₃ > HClO₂ > HOCl. HOCl is the strongest oxidising halogen oxyacid.

Allotropes of Phosphorus & Sulphur — Key Properties

\text{P}_4 \text{ (white, P−P−P angle } 60°, \text{most reactive)}, \quad \text{Red P} \text{ (polymer)}, \quad \text{Black P} \text{ (graphite-like, most stable)}

Sulphur allotropes: rhombic S₈ (stable below 96°C), monoclinic S₈ (stable 96–119°C), plastic S (amorphous, above 160°C). White phosphorus is soluble in CS₂ and is poisonous; red phosphorus is non-toxic polymer.

White P₄ has tetrahedral structure with bond angle 60° (highly strained → very reactive). Reacts with conc. NaOH: P₄ + 3NaOH + 3H₂O → 3NaH₂PO₂ + PH₃↑ (disproportionation). Contact process for H₂SO₄: 2SO₂ + O₂ ⇌ 2SO₃ (V₂O₅ catalyst, 450°C, 2 atm).

Acidic Strength & Reducing Power Trends in Group 16, 17

\text{Acid strength: HF} < \text{HCl} < \text{HBr} < \text{HI (bond energy ↓)} \quad \text{Reducing power: HF} < \text{HCl} < \text{HBr} < \text{HI}

Hydrohalic acid strength increases down the group as H−X bond dissociation enthalpy decreases. HF is the weakest acid but forms strongest H-bonds. HF etches glass: SiO₂ + 4HF → SiF₄ + 2H₂O.

Bond angle in H₂O > H₂S > H₂Se > H₂Te (O uses pure p-orbitals; as we go down, angles → 90° as pure p-orbitals used for bonding). Thermal stability of hydrides: H₂O > H₂S > H₂Se > H₂Te (bond energy ↓ down group).

Inorganic ChemistryTop Priority (3-4 Qs in JEE)698 PYQs

Chemical Bonding & VSEPR

VSEPR molecular geometries, steric number hybridization, bond order from MOT, dipole moments, and hydrogen bonding.

Chapter

Steric Number & Hybridization

\text{Steric No} = \frac{1}{2}[V + M - C + A] = \sigma\text{-bonds} + \text{lone pairs}

V: valence e⁻, M: monovalent atoms (H, F, Cl), C: positive charge, A: negative charge.

SN: 2 = sp (180°), 3 = sp² (120°), 4 = sp³ (109.5°), 5 = sp³d, 6 = sp³d².

Molecular Orbital Theory (MOT) Bond Order

\text{Bond Order} = \frac{N_b - N_a}{2}, \quad \text{Bond Length} \propto \frac{1}{\text{Bond Order}}

N_b: bonding electrons, N_a: antibonding electrons.

14 electrons (N₂) has BO = 3. Each added or removed electron changes BO by ±0.5.

Dipole Moment & Percentage Ionic Character

\mu = q \times d, \quad \% \text{ Ionic Character} = \frac{\mu_{\text{observed}}}{\mu_{\text{theoretical}}} \times 100\%

Measures molecular bond polarity (1 Debye = 3.336 × 10⁻³⁰ C m).

Symmetric molecules with no lone pairs (like CCl₄, BF₃, CO₂) have net μ = 0.

Formal Charge Calculation

\text{Formal Charge} = V - L - \frac{1}{2}S

V: valence electrons in free atom, L: lone pair non-bonding electrons, S: shared bonding electrons.

Lowest formal charge configuration represents the most stable Lewis resonance structure.

Fajan's Rules (Covalent Character in Ionic Bonds)

\text{Polarizing Power} \propto \frac{\text{Charge}}{\text{Cation Radius}}, \quad \text{Polarizability} \propto \text{Anion Radius}

Covalent character increases with: (1) high charge on cation/anion, (2) smaller cation, (3) larger anion, and (4) pseudo-inert gas electron configuration 18e⁻ (Cu⁺, Ag⁺) over 8e⁻ (Na⁺, K⁺).

Higher covalent character lowers melting point and increases solubility in non-polar organic solvents (e.g. AgI is yellow/covalent, AgF is white/ionic).

Bond Angle Hierarchy Rules

\text{Hybridization } (sp > sp^2 > sp^3) \to \text{No. of Lone Pairs } \downarrow \to \text{EN of Central Atom } \uparrow \to \text{EN of Surrounding Atoms } \downarrow

Systematic order for comparing bond angles across molecules.

Drago's Rule: In PH₃, AsH₃, H₂S, H₂Se, no hybridization occurs; bond angles are close to 90° pure p-orbital angles.

Back-Bonding & 3-Center-2-Electron Bonds

p\pi - p\pi \; (\text{in } BF_3), \quad p\pi - d\pi \; (\text{in } N(SiH_3)_3), \quad B_2H_6 \; (\text{Banana } 3c-2e^- \text{ bridge bonds})

Transfer of lone pair electrons from filled orbital into adjacent empty p or d orbital increases bond order and reduces Lewis acidity.

N(CH₃)₃ is pyramidal with sp³ N, whereas N(SiH₃)₃ is planar with sp² N due to pπ-dπ back-donation into empty d-orbitals of Si.

Inorganic ChemistryTop Priority (3-4 Qs in JEE)772 PYQs

Coordination Compounds

Werner theory, crystal field splitting (CFT), spectrochemical series, magnetic moments, and isomerism.

Chapter

Crystal Field Splitting (Octahedral & Tetrahedral)

\Delta_t = \frac{4}{9}\Delta_o, \quad \text{CFSE}_{\text{oct}} = (-0.4 n_{t_{2g}} + 0.6 n_{e_g})\Delta_o + m P

Splitting of degenerate d-orbitals into t_2g and e_g sets.

If Δ_o > P (strong field), electrons pair up in t_2g (low spin).

Spin-Only Magnetic Moment

\mu = \sqrt{n(n + 2)} \text{ BM} \quad (n = \text{number of unpaired electrons})

Bohr Magneton (BM) value indicating paramagnetism.

n = 1 -> 1.73 BM, n = 2 -> 2.83 BM, n = 3 -> 3.87 BM, n = 4 -> 4.90 BM, n = 5 -> 5.92 BM.

Spectrochemical Series of Ligands

\text{I}^- < \text{Br}^- < \text{Cl}^- < \text{F}^- < \text{OH}^- < \text{C}_2\text{O}_4^{2-} < \text{H}_2\text{O} < \text{NCS}^- < \text{EDTA}^{4-} < \text{NH}_3 < \text{en} < \text{CN}^- < \text{CO}

Empirical ordering of ligands by their crystal field splitting power Δ.

Carbonyl (CO) and cyanide (CN⁻) are the strongest field ligands.

Effective Atomic Number (EAN Rule)

\text{EAN} = Z - (\text{Oxidation State}) + 2 \times (\text{Coordination Number})

Sidgwick's stability rule: complex is exceptionally stable when EAN equals the atomic number of the next noble gas.

Metals in low or zero oxidation states (metal carbonyls) obey the 18-electron rule.

Synergic Bonding in Metal Carbonyls

M \xleftarrow{\sigma} \text{CO} \quad + \quad M(d) \xrightarrow{\pi} \text{CO}(\pi^*), \quad \text{Bond Length } (\text{C-O}) \propto \frac{1}{\nu_{\text{CO}}} \propto \text{Negative charge on } M

Dual bonding: ligand-to-metal σ donation and metal d-to-CO π* back-donation strengthens M-C bond while weakening C-O bond.

Decreasing order of C-O bond strength (and stretching frequency): [Mn(CO)₆]⁺ > [Cr(CO)₆] > [V(CO)₆]⁻.

Square Planar Crystal Field Splitting (d⁸ Ions)

\Delta_{sp} \approx 1.3 \Delta_o, \quad \text{Energy Order: } d_{x^2-y^2} \gg d_{xy} > d_{z^2} > d_{xz} \approx d_{yz}

Extreme tetragonal elongation removes axial ligands, placing d_{x²-y²} at highest energy. Characteristic of Pt(II), Pd(II), and [Ni(CN)₄]²⁻.

All 4d and 5d metals form square planar low-spin diamagnetic complexes with coordination number 4 regardless of ligand strength.

Octahedral & Square Planar Isomerism Summary

[Ma_2b_2] \to \text{cis/trans (2)}, \quad [Mabcd] \to 3\,\text{GI}, \quad [Ma_3b_3] \to \text{fac/mer (2)}, \quad [M(AA)_2b_2] \to \text{cis (chiral) } + \text{ trans (achiral)}

Geometrical (GI) and Optical (OI) isomer counts. Square planar complexes cannot show optical activity due to molecular plane.

Tris-bidentate complex [M(AA)₃] (like [Co(en)₃]³⁺) has NO plane of symmetry and exists as an enantiomeric pair (d and l).

CFSE Values for Octahedral d^n Configurations

\text{CFSE (oct, high spin): } d^1\!=\!-0.4, d^2\!=\!-0.8, d^3\!=\!-1.2, d^4\!=\!-0.6, d^5\!=\!0, d^6\!=\!-0.4, d^7\!=\!-0.8, d^8\!=\!-1.2, d^9\!=\!-0.6, d^{10}\!=\!0 \;(\times\Delta_o)

Crystal Field Stabilisation Energy in units of Δ_o for high-spin octahedral complexes (no extra pairing energy P). Low-spin complexes have greater CFSE (more electrons in t_2g): e.g. d⁶ low-spin = -2.4Δ_o + P.

d³ and d⁸ have maximum CFSE in high-spin octahedral field (-1.2Δ_o) → most stable complexes (Cr³⁺ and Ni²⁺ form very stable octahedral complexes). d⁰, d⁵ (HS), d¹⁰ have zero CFSE.

Stability Constant (K_f) & Lability of Complexes

K_f = \frac{[\text{ML}_n]}{[\text{M}][\text{L}]^n}, \quad \log K_f \propto \text{Stability}, \quad \beta_n = K_{f1} \times K_{f2} \times \cdots \times K_{fn} \; (\text{overall stability})

Formation constant K_f (also called stability constant) measures thermodynamic stability of a complex. β_n is the cumulative/overall stability constant for stepwise addition of n ligands.

EDTA forms highly stable 1:1 chelate complexes (log K_f ~ 18 for Ca²⁺). Chelate effect: polydentate ligands are more stable than monodentate equivalents due to entropy gain. Lability ≠ thermodynamic stability (e.g., [Co(NH₃)₆]³⁺ is thermodynamically stable but kinetically inert).

Inorganic ChemistryHigh Yield (2-3 Qs in JEE)589 PYQs

d- & f-Block Elements

Transition element trends, variable oxidation states, lanthanide contraction, catalytic properties, and potassium permanganate/dichromate reactions.

Chapter

Oxidation States & Redox Equivalent Weights

\text{KMnO}_4 (\text{Acidic}): \text{Mn}^{7+} + 5e^- \to \text{Mn}^{2+} \implies n = 5, \quad \text{K}_2\text{Cr}_2\text{O}_7 (\text{Acidic}): \text{Cr}_2^{6+} + 6e^- \to 2\text{Cr}^{3+} \implies n = 6

Stoichiometric electron transfer in analytical volumetric titrations.

Equivalent weight = Molar mass / n-factor (M/5 for acidic KMnO₄, M/6 for acidic K₂Cr₂O₇).

Lanthanide Contraction Phenomenon

r(\text{Zr}) \approx r(\text{Hf}) \approx 1.60 \text{ \AA}, \quad r(\text{Nb}) \approx r(\text{Ta})

Poor shielding effect of 4f electrons causes abnormal similarity in 4d and 5d series atomic and ionic sizes.

Causes extreme difficulty in chemical separation of Zr and Hf.

Chromate-Dichromate Equilibrium

2 \text{CrO}_4^{2-} \; (\text{Yellow}) + 2\text{H}^+ \rightleftharpoons \text{Cr}_2\text{O}_7^{2-} \; (\text{Orange}) + \text{H}_2\text{O}

pH-dependent equilibrium: yellow chromate in base, orange dichromate in acid.

Oxidation state of Chromium remains +6 throughout the interconversion.

Standard Electrode Potentials & Thermodynamic Cycle

E^\circ_{M^{2+}/M} \propto -(\Delta H_{\text{sub}} + \text{IE}_1 + \text{IE}_2 + \Delta H_{\text{hyd}}), \quad E^\circ_{\text{Cu}^{2+}/\text{Cu}} = +0.34\,\text{V} > 0

Standard reduction potential determined by balance between sublimation, ionization enthalpies and hydration enthalpy. Cu cannot liberate H₂ from dilute acids.

E°(Mn³⁺/Mn²⁺) = +1.57 V is unusually high because Mn²⁺ achieves stable half-filled 3d⁵ configuration.

Chromyl Chloride Test (Confirmatory Test for Cl⁻)

\text{K}_2\text{Cr}_2\text{O}_7 + 4\text{NaCl} + 6\text{H}_2\text{SO}_4 \to 2\text{CrO}_2\text{Cl}_2\uparrow \; (\text{Red Vapor}) \xrightarrow{\text{NaOH}} \text{Na}_2\text{CrO}_4 \xrightarrow{\text{Pb(OAc)}_2} \text{PbCrO}_4\downarrow \; (\text{Yellow})

Qualitative test for ionic chlorides. Covalent chlorides and AgCl, Hg₂Cl₂, HgCl₂, PbCl₂ do NOT respond to this test.

Fluorides, bromides, and iodides do not form volatile chromyl halides.

KMnO₄ in Neutral & Strongly Alkaline Media

\text{Neutral/Weak Base: } \text{MnO}_4^- + 3e^- + 2\text{H}_2\text{O} \to \text{MnO}_2\downarrow + 4\text{OH}^- \; (n=3), \quad \text{Strong Base: } \text{MnO}_4^- + e^- \to \text{MnO}_4^{2-} \; (n=1)

In neutral/faintly alkaline medium, KMnO₄ oxidizes iodide to iodate (I⁻ → IO₃⁻) and thiosulfate to sulfate (S₂O₃²⁻ → SO₄²⁻).

In acidic medium, I⁻ is oxidized to I₂ (not IO₃⁻).

Interstitial Compounds & Catalytic Properties

\text{Compounds: } \text{TiC}, \; \text{Mn}_4\text{N}, \; \text{Fe}_3\text{H}, \; \text{VH}_{0.56} \implies \text{Higher M.P., Hardness, Metallic Conduction}

Transition metals trap small non-metal atoms (H, B, C, N) inside octahedral/tetrahedral voids of the metallic lattice without changing lattice type.

Transition elements are excellent catalysts (V₂O₅, finely divided Fe, Raney Ni) due to variable oxidation states and surface d-orbital adsorption.

Actinoid Contraction & Variable Oxidation States

\text{Contraction: } 5f > 4f \implies \text{Actinoid Contraction} > \text{Lanthanoid Contraction}, \quad \text{Max ON: } \text{Np, Pu } (+7)

Poorer shielding of 5f electrons causes steeper radius decrease across actinoid series than 4f across lanthanoids.

5f, 6d, and 7s energy levels are extremely close in energy, allowing actinoids to exhibit variable oxidation states from +3 up to +7.

Inorganic ChemistryHigh Yield (2 Qs in JEE Main)512 PYQs

Principles of Practical Chemistry & Salt Analysis

Systematic qualitative analysis of cations (Groups 0 to VI) and anions, confirmatory tests, flame tests, borax bead test, and organic functional group identification.

Chapter

Cation Group Separation Scheme (Groups 0 to VI)

\begin{array}{llll} \text{Group} & \text{Reagent} & \text{Cations} & \text{Precipitate Form} \\ \text{0} & \text{NaOH} & \text{NH}_4^+ & \text{NH}_3\uparrow \text{ (Nessler's reagent: brown ppt)} \\ \text{I} & \text{Dil. HCl} & \text{Pb}^{2+}, \text{Ag}^+, \text{Hg}_2^{2+} & \text{Chlorides (PbCl}_2 \text{ white, hot-water sol.)} \\ \text{II-A/B} & \text{H}_2\text{S + dil. HCl} & \text{Cu}^{2+}, \text{Pb}^{2+}, \text{Bi}^{3+}, \text{Cd}^{2+}, \text{As}^{3+} & \text{Sulphides (CuS black, CdS yellow, As}_2\text{S}_3 \text{ yellow)} \\ \text{III} & \text{NH}_4\text{OH + NH}_4\text{Cl} & \text{Fe}^{3+}, \text{Al}^{3+}, \text{Cr}^{3+} & \text{Hydroxides (Fe(OH)}_3 \text{ brown, Al(OH)}_3 \text{ gelatinous, Cr(OH)}_3 \text{ green)} \\ \text{IV} & \text{H}_2\text{S + NH}_4\text{OH} & \text{Co}^{2+}, \text{Ni}^{2+}, \text{Zn}^{2+}, \text{Mn}^{2+} & \text{Sulphides (ZnS dirty white, MnS buff/flesh, CoS/NiS black)} \\ \text{V} & (\text{NH}_4)_2\text{CO}_3 & \text{Ba}^{2+}, \text{Sr}^{2+}, \text{Ca}^{2+} & \text{Carbonates (white)} \\ \text{VI} & \text{Na}_2\text{HPO}_4 & \text{Mg}^{2+} & \text{Mg(NH}_4)\text{PO}_4 \text{ (white crystalline)} \end{array}

Systematic precipitation order governed by solubility product (K_sp). Group II sulphides have very low K_sp and precipitate even with low S²⁻ in acid; Group IV sulphides have higher K_sp and require basic medium.

NH₄Cl is added before NH₄OH in Group III to suppress OH⁻ concentration by common ion effect, preventing premature precipitation of Group IV and Mg(OH)₂.

Confirmatory Tests for Acid Radicals (Anions)

\text{Brown Ring: } \text{Fe}^{2+} + \text{NO}_3^- + \text{H}_2\text{SO}_4 \to [\text{Fe}(\text{H}_2\text{O})_5(\text{NO})]^{2+} \; (\text{Brown ring at interface, Fe in +1 OS})

Key confirmatory tests for anions: Nitrate (Brown Ring test), Chloride (Chromyl Chloride test), Sulphate (BaCl₂ gives white BaSO₄ insoluble in conc. HCl), and Carbonate (CO₂ turns lime water milky).

In [Fe(H₂O)₅(NO)]²⁺, NO exists as NO⁺ (nitrosonium), so oxidation state of Fe is +1 (paramagnetic, 3 unpaired electrons, μ = 3.87 BM).

Chromyl Chloride Test (Chloride Detection)

4\text{NaCl} + \text{K}_2\text{Cr}_2\text{O}_7 + 6\text{H}_2\text{SO}_4 \xrightarrow{\Delta} 2\text{CrO}_2\text{Cl}_2\uparrow \text{ (Deep red-brown vapor)} \xrightarrow{+\text{NaOH}} \text{Na}_2\text{CrO}_4 \text{ (Yellow)} \xrightarrow{+\text{Pb(OAc)}_2} \text{PbCrO}_4\downarrow \text{ (Yellow ppt)}

Confirmatory test for ionic chlorides. Heating solid chloride with potassium dichromate and conc. H₂SO₄ liberates red-brown vapors of chromyl chloride (CrO₂Cl₂).

Bromides and iodides evolve Br₂ (reddish) and I₂ (violet), but their vapors do NOT give a yellow precipitate with lead acetate. Does not work for AgCl, PbCl₂, Hg₂Cl₂.

Flame Test Characteristic Colors

\begin{array}{llll} \text{Metal} & \text{Color} & \text{Metal} & \text{Color} \\ \text{Li} & \text{Crimson red} & \text{Ca} & \text{Brick red} \\ \text{Na} & \text{Golden yellow} & \text{Sr} & \text{Crimson red} \\ \text{K} & \text{Violet / Lilac} & \text{Ba} & \text{Apple green} \\ \text{Rb} & \text{Red-violet} & \text{Cu} & \text{Blue-green} \\ \text{Cs} & \text{Blue} & \text{Pb} & \text{Greyish-white} \end{array}

Excitation of valence electrons by Bunsen flame imparts characteristic emission spectrum colours. Beryllium (Be) and Magnesium (Mg) do NOT give flame colour due to high ionization enthalpy.

Viewing through cobalt blue glass: Sodium yellow is absorbed (invisible); Potassium lilac appears crimson/violet.

Borax Bead Test (Metaborate Formation)

\text{Na}_2\text{B}_4\text{O}_7\cdot 10\text{H}_2\text{O} \xrightarrow{\Delta} \text{Na}_2\text{B}_4\text{O}_7 \xrightarrow{\text{strong }\Delta} 2\text{NaBO}_2 + \text{B}_2\text{O}_3 \; (\text{Glassy bead}) \xrightarrow{+\text{CoO}} \text{Co(BO}_2)_2 \; (\text{Deep Blue})

Heating borax with transition metal salts forms characteristic colored metaborate beads in oxidizing and reducing flames.

Key bead colors in oxidizing flame: Cobalt (Deep Blue), Copper (Blue in hot/cold), Chromium (Green), Iron (Yellow in cold, brown in hot), Manganese (Violet/Amethyst).

Organic Functional Group Detection Tests

\begin{array}{lll} \text{Functional Group} & \text{Test Reagent} & \text{Observation} \\ \text{Unsaturation (C=C)} & \text{Br}_2/\text{CCl}_4 \;\text{or}\; \text{Bayer's (alk. KMnO}_4) & \text{Decolourization} \\ \text{Alcoholic (-OH)} & \text{Ceric Ammonium Nitrate (CAN)} & \text{Red coloration} \\ \text{Phenolic (-OH)} & \text{Neutral FeCl}_3 & \text{Violet/purple coloration} \\ \text{Carbonyl (C=O)} & \text{2,4-DNP (Brady's reagent)} & \text{Orange-yellow precipitate} \\ \text{Aldehyde (-CHO)} & \text{Tollens' reagent } [\text{Ag(NH}_3)_2]^+ & \text{Silver mirror on tube wall} \\ \text{Aldehyde (aliphatic)} & \text{Fehling's solution (A+B)} & \text{Red precipitate (Cu}_2\text{O)} \\ \text{Carboxylic (-COOH)} & \text{Sat. NaHCO}_3 & \text{Brisk effervescence of CO}_2\uparrow \\ \text{1° Amine (-NH}_2) & \text{CHCl}_3 + \text{alc. KOH (Carbylamine)} & \text{Foul smelling isocyanide (R-NC)} \end{array}

Standard organic functional group identification tests prescribed in the JEE practical chemistry curriculum.

Lucas test for alcohol classification: ZnCl₂ + conc. HCl: 3° alcohol gives immediate turbidity; 2° takes 5 mins; 1° does not react at room temperature.

Nessler's Reagent & Ammonium Detection

\text{Nessler's Reagent: } \text{K}_2[\text{HgI}_4] \; (\text{alkaline solution}), \quad 2[\text{HgI}_4]^{2-} + \text{NH}_4^+ + 4\text{OH}^- \to \text{HgO}\cdot\text{Hg}(\text{NH}_2)\text{I}\downarrow \text{ (Brown ppt: Iodide of Millon's base)} + 7\text{I}^- + 3\text{H}_2\text{O}

Potassium tetraiodomercurate(II) in alkaline KOH precipitates brown iodide of Millon's base with trace quantities of ammonium ions or ammonia.

Very sensitive test: even tap water traces of ammonia produce distinct yellow-brown coloration.

Mohr's Salt & Potash Alum Preparation

\text{Mohr's Salt: } \text{FeSO}_4\cdot(\text{NH}_4)_2\text{SO}_4\cdot 6\text{H}_2\text{O}, \quad \text{Potash Alum: } \text{K}_2\text{SO}_4\cdot\text{Al}_2(\text{SO}_4)_3\cdot 24\text{H}_2\text{O}

Standard double salts synthesized by equimolar crystallization in acidic medium to prevent hydrolysis.

Mohr's salt is preferred over FeSO₄ for standard solutions in redox titrations because it is resistant to aerial oxidation (Fe²⁺ remains stable).