Comprehensive University Study Notes: Chemical Bonding, Periodic Trends, Thermodynamics, Coordination Chemistry, and Cardiology

Chemical Bonding and Lattice Energy (LE)

• Lattice Energy Factors: The LE of an ionic compound depends on the size and charge of the ions.

• Trends and Reasoning:   - Trend: \text{NaI} < \text{NaBr} < \text{NaCl} < \text{NaF}.     - Reason: As anion size decreases, ions get closer, and LE increases ($\text{LE} \propto \frac{1}{r_{ion}}$).   - Trend: \text{BaCl}_2 < \text{SrCl}_2 < \text{CaCl}_2 < \text{MgCl}_2 < \text{BeCl}_2.     - Reason: Cation charge is fixed ($+2$), but smaller cation size leads to stronger attraction and higher LE.   - Trend: \text{NaCl} < \text{MgCl}_2 < \text{AlCl}_3.     - Reason: Increased cation charge leads to stronger electrostatic attraction, hence LE increases.   - Trend: \text{MgO} < \text{Al}_2\text{O}_3.     - Reason: Effective cation charge per anion is higher in the $\text{Al}^{3+}/\text{O}^{2-}$ lattice, increasing attraction and LE.

Formal Charge and Lewis Structures

• Formal Charge (F.C.) Calculation: $\text{F.C.} = [\text{Total valence electrons in free atom}] - [\text{Total non-bonding electrons}] - [\frac{1}{2}(\text{Total bonding electrons})]$.

• HNO3 Lewis Structure Example: The formal charges on the atoms marked (1) to (4) in the representation are $(1) = 0, (2) = +1, (3) = 0, (4) = -1$.

VSEPR Theory Postulates

• Basis: The shape of a molecule depends on the number of valence shell electron pairs (bonded and non-bonded) around the central atom.

• Repulsion: Electron pairs repel one another because their clouds are negatively charged.

• Orientation: Pairs occupy positions in space that minimize repulsion and maximize distance.

• Sphere Model: The valence shell is treated as a sphere with electron pairs localized at a maximum distance.

• Multiple Bonds: Multiple bonds are treated as a single super pair.

• Resonance: The model is applicable to any resonance structure representing a molecule.

• Repulsion Strength Hierarchy: \text{Lone pair (lp) - Lone pair (lp)} > \text{Lone pair (lp) - Bond pair (bp)} > \text{Bond pair (bp) - Bond pair (bp)}.

Valence Bond Theory (VBT) and H2 Formation

• Interaction Forces: As two Hydrogen atoms (A and B) approach, new forces arise:   - Attractive Forces: Between nucleus $N_A$ and electron $e_A$; $N_B$ and $e_B$ (own); and nucleus $N_A$ and $e_B$; $N_B$ and $e_A$ (other's).   - Repulsive Forces: Between electrons $e_A - e_B$ and nuclei $N_A - N_B$.

• Net Interaction: Experimentally, net attraction exceeds repulsion. Potential energy decreases until it reaches a minimum at a bond length of $74\,pm$.

• Bond Enthalpy: For $H_2$, energy released reaching the minimum is $435.8\,kJ\,mol^{-1}$. Conversely, the same amount of energy is required to dissociate one mole of $H_2$.

Molecular Geometry and Hybridization Chart

• Linear: $180^{\circ}$; Examples: $\text{BeCl}_2, \text{CO}_2, \text{HgCl}_2$.

• Trigonal Planar: $120^{\circ}$; Examples: $\text{BF}_3, \text{SO}_3, \text{NO}_3^-$; Bent (<120^{\circ}): $\text{SO}_2, \text{O}_3, \text{NO}_2^-$.

• Tetrahedral: $109.5^{\circ}$; Examples: $\text{SiCl}_4, \text{CH}_4, \text{NH}_4^+$; Trigonal Pyramidal ($\sim 107^{\circ}$): $\text{NH}_3, \text{PCl}_3, \text{AsH}_3$; Bent/V-shape ($\sim 104.5^{\circ}$): $\text{H}_2\text{O}, \text{OF}_2, \text{H}_2\text{S}$.

• Trigonal Bipyramidal: $90^{\circ}, 120^{\circ}$; Examples: $\text{PCl}_5, \text{PF}_5$; Seesaw: $\text{SF}_4, \text{SeF}_4$; T-shaped: $\text{ClF}_3, \text{BrF}_3$.

• Octahedral: $90^{\circ}$; Examples: $\text{SF}_6, [\text{PF}_6]^-$; Square Pyramidal: $\text{BrF}_5, \text{IF}_5, \text{XeOF}_4$; Square Planar: $\text{XeF}_4, [\text{PtCl}_4]^{2-}, [\text{Ni(CN)}_4]^{2-}$.

• Pentagonal Bipyramidal: $72^{\circ}, 90^{\circ}$; Examples: $\text{IF}_7$.

Dipole Moment ($\mu$)

• Geometry and Symmetry: $\mu = 0$ for non-polar symmetric molecules like $\text{BF}_3, \text{BeCl}_2, \text{CH}_4, \text{CCl}_4, \text{SbF}_5$, and Trans- isomers ($\text{C}_2\text{H}_2\text{Cl}_2$, $\text{N}_2\text{F}_2$).

• Disubstituted Benzene (Identical Substituents):   - Ortho ($o$): $\mu = \text{high}$ (vectors add).   - Meta ($m$): $\mu = \text{small}$ (partial cancellation).   - Para ($p$): $\mu = 0$ (exact cancellation).

• Disubstituted Benzene (Different Substituents - X withdrawing, Y donating):   - Order: \text{ortho (3.76 D)} < \text{meta (4.16 D)} < \text{para (4.35 D)}.

• Specific Comparisons:   - \text{NH}_3 (4.90 \times 10^{-30}\,Cm) > \text{NF}_3 (0.80 \times 10^{-30}\,Cm).   - \text{H}_2\text{O} > \text{F}_2\text{O}.   - \text{CH}_3\text{CN} > \text{CH}_3\text{NC}.   - \text{NO}_2 (\text{bent}) > \text{NO}_2^+ (\text{linear, } \mu=0).   - Exception: Hydroquinone (1,4-dihydroxybenzene) has $\mu = 1.64\,D$ (non-zero) because lone pairs on Oxygen are not involved in resonance.

Hydrogen Bonding

• Condition: Hydrogen connected to highly electronegative element (F, O, N).

• Strength Order: \text{HF} > \text{H}_2\text{O} > \text{NH}_3 (Electronegativity dependence).

• Consequences:   - $\text{NH}_3$ and $\text{H}_2\text{O}$ have unusually high melting/boiling points for their groups.   - Solubility of lower alcohols and ammonia in water.   - Viscosity increases with H-bonding.   - Volatility decreases.   - Ice structure: Ice has lower density than water; Impure water has different H-Bond structure.   - Intramolecular H-bonding leads to sharp melting points (e.g., ortho-nitrophenol).

Molecular Orbital Theory (MOT)

• Species Data Table (Nitrogen):   - N2: Bond Order (BO) $= 3.0$, Diamagnetic.   - N2+: BO $= 2.5$, Paramagnetic.   - N2-: BO $= 2.5$, Paramagnetic.   - N2(2+): BO $= 2.0$, Diamagnetic.   - N2(2-): BO $= 2.0$, Paramagnetic.

• Bond Length/Strength: Higher BO implies shorter bond length and higher bond dissociation energy (BDE).

• Energy Levels:   - For light elements (B2, C2, N2): \pi_{2p} < \sigma_{2p}.   - For heavy elements (O2, F2): \sigma_{2p} < \pi_{2p}.

Periodic Table Nomenclature and Trends

• Naming Z > 100: Atomic number 119 is Ununennium.

• Atomic Radii (Group 13): \text{B} < \text{Ga} < \text{Al} < \text{In} < \text{Tl}.   - Ga Anomaly: Presence of $10d$ electrons in Gallium causes poor shielding, leading to increased effective nuclear charge ($Z_{eff}$) and size contraction.   - In/Tl: Further contraction due to $d$ and $f$ electron shielding (Lanthanide contraction/Inert pair effect).

• Transition Series Size (3d, 4d, 5d):   - 3d Series: \text{Sc} > \text{Ti} > \text{V} > \text{Cr} > \text{Mn} > \text{Fe} \approx \text{Co} \approx \text{Ni} < \text{Cu} < \text{Zn}.   - Comparison: 3d < 4d \approx 5d (e.g., $\text{Zr} \approx \text{Hf}$ due to Lanthanide contraction).

• Ionization Enthalpy (IE):   - Period 2 Trend: \text{Li} < \text{B} < \text{Be} < \text{C} < \text{O} < \text{N} < \text{F} < \text{Ne}.   - Stability Rule: Removing electrons from half-filled ($p^3$) or fully-filled ($s^2$) subshells requires extra energy (\text{Be} > \text{B} and \text{N} > \text{O}).

• Electron Gain Enthalpy (EGE/EA):   - Group 17: \text{Cl} > \text{F} > \text{Br} > \text{I} (Fluorine's small $2p$ orbital creates stronger e-e repulsions than Chlorine's $3p$).   - Group 13: \text{B} < \text{Ga} < \text{Tl} < \text{In} < \text{Al}.

Thermodynamics: Basic Concepts

• Functions:   - State Functions: Depend only on final and initial states ($\Delta U, \Delta H, P, V, T, G, S$). $\Delta = 0$ for cyclic processes.   - Path Functions: Depend on path taken ($q, w, C$). Non-zero for cyclic processes.

• Properties:   - Extensive: Mass dependent ($U, H, G, m, S, V$). Additive.   - Intensive: Independent of amount ($T$, Molar heat capacity, BP, MP, Density). Non-additive. Ratio of two extensive properties is intensive.

• Spontaneity (Gibbs Free Energy):   - $\Delta G = \Delta H - T\Delta S$   - \Delta G < 0: Spontaneous.   - $\Delta G = 0$: Equilibrium.   - \Delta G > 0: Non-Spontaneous.   - Table:     - \Delta H < 0, \Delta S > 0: Spontaneous at all T.     - \Delta H > 0, \Delta S > 0: Spontaneous at high T.     - \Delta H < 0, \Delta S < 0: Spontaneous at low T.

Thermodynamic Formulas

• Internal Energy: $\Delta U = q + w$.

• Work Done:   - Isochoric: $\Delta V = 0, w = 0$.   - Isobaric: $w = -P_{ext}(V_2 - V_1)$.   - Isothermal Reversible: $w = -2.303nRT \log(\frac{V_2}{V_1})$.   - Adiabatic: $w = \frac{P_2V_2 - P_1V_1}{\gamma - 1}$; where $\gamma = \frac{C_p}{C_v}$.

• Entropy ($\Delta S$):   - Fusion: $\Delta S = \frac{\Delta H_{fusion}}{T}$.   - Vaporization: $\Delta S = \frac{\Delta H_{vap}}{T}$.   - General: $\Delta S = nC_v \ln(\frac{T_2}{T_1}) + nR \ln(\frac{V_2}{V_1})$.

• Hess's Law: The total enthalpy change for a reaction is the sum of changes in individual steps ($\Delta H = \Delta H_1 + \Delta H_2$).

Coordination Compounds

• Ligands: Can be monodentate, bidentate, or polydentate. EDTA is hexadentate (binds through 2 Nitrogen and 4 Oxygen atoms).

• Effective Atomic Number (EAN): $\text{EAN} = Z - \text{oxidation state} + (2 \times \text{Coordination Number})$. Stable if EAN matches a noble gas (#36, #54, #86).

• Isomerism:   - Structural: Ionisation, Hydrate, Linkage (ambidentate ligands like $NO_2$), Coordination.   - Geometrical: Fac-mer (for $MA_3B_3$ octahedral); Cis-trans.   - Optical: Enantiomeric pairs (common in $M(AA)_3$ or $cis-M(AA)_2a_2$).

• Crystal Field Theory (CFT):   - Octahedral Splitting ($\Delta_o$): $t_{2g}$ (lower) and $e_g$ (higher).   - Tetrahedral Splitting ($\Delta_t$): $e$ (lower) and $t_2$ (higher). $\Delta_t \approx \frac{4}{9} \Delta_o$.   - Low Spin: \Delta_o > P (Strong Field Ligand).   - High Spin: \Delta_o < P (Weak Field Ligand).   - Spectrochemical Series: I^- < Br^- < Cl^- < S^{2-} < F^- < OH^- < C_2O_4^{2-} < H_2O < EDTA^{4-} < NH_3 < en < NO_2^- < CN^- < CO.

Equilibrium and Le Chatelier's Principle

• Factors Affecting K: Only Temperature ($\log\frac{K_2}{K_1} = \frac{\Delta H^{\circ}}{2.303R}(\frac{1}{T_1} - \frac{1}{T_2})$).

• Le Chatelier Applications:   - Concentration: Add reactant $\rightarrow$ forward.   - Temperature: Endothermic ($+ve$) favored by high T; Exothermic ($-ve$) by low T.   - Pressure: Increase P shifts to side with fewer gas moles.   - Inert Gas: No effect at constant V; At constant P, shifts to higher mole side.

Ionic Equilibrium

• pH Formulas:   - Strong Acid: $\text{pH} = -\log[H^+]$.   - Weak Acid: $\text{pH} = \frac{1}{2}(\text{p}K_a - \log c)$.   - Buffer (Henderson): $\text{pH} = \text{p}K_a + \log(\frac{[Salt]}{[Acid]})$.

• Solubility Product (Ksp): For $A_xB_y \rightleftharpoons xA^{y+} + yB^{x-}$, $K_{sp} = [A^{y+}]^x[B^{x-}]^y = x^x y^y S^{x+y}$.

• Common Ion Effect: Solubility decreases in the presence of a common ion.

Cardiology: Arrhythmias and Medications

• Cardiac Conduction: SA node $\rightarrow$ AV node $\rightarrow$ His bundle $\rightarrow$ Bundle branches $\rightarrow$ Purkinje fibers.

• Vaughan Williams Classification:   - Class IA: Procainamide ($Na^+$ and $K^+$ blocker). Side effect: Drug-induced SLE.   - Class IB: Lidocaine ($Na^+$ blocker for ischemic tissue). SE: CNS toxicity (seizures).   - Class IC: Flecainide. Avoid in Structural Heart Disease (SHD).   - Class II: $\beta$-blockers. Avoid in Asthma/COPD.   - Class III: Amiodarone (K+ blocker). Long-term usage risky in young; SE: Pulmonary, Thyroid toxicity.   - Class IV: Verapamil (Ca2+ blocker). SE: Constipation, Edema.   - Class V: Adenosine (A1 activator). SE: Bronchospasm.

Cardiology: ACS and Diagnosis

• Infarct Locations (ECG):   - Septal: V1–V2 (LAD).   - Anterior: V3–V4 (LAD).   - Inforior: II, III, aVF (RCA).   - Lateral: I, aVL, V5–V6 (LCx).   - Right Ventricle: V4R (RCA).

• MI Complications:   - Acute MR: Papillary muscle rupture (2–7 days); systolic murmur at apex.   - VSD: 2–7 days; harsh PSM at LSB.   - FWR (Free Wall Rupture): 3–7 days; causes tamponade/collapse.

• Modified Duke’s Criteria (Endocarditis):   - Major: Positive blood cultures (typical pathogens), Image evidence (Echo vegetation/PET uptake).   - Minor: Fever (>38^{\circ}C), Predisposing factors (IVDU, prosthetic valve), Vascular/Immunological phenomena.

Heart Failure Management

• The "Fantastic Four" (HFrEF): ARNi, Beta-blockers, MRA, SGLT2i.

• NYHA Classes:   - I: Asymptomatic.   - II: Ordinary activity symptoms.   - III: Less than ordinary activity symptoms.   - IV: Symptoms at rest.

• Non-Survival Benefit Drugs: CCBs, Digoxin, Nitrates, Diuretics (used for congestion relief only).

Questions & Discussion

• Q: On which factors does the LE of an ionic compound depend?

• A: The size and charge of the ion (Option 1).

• Q: Among $H_2S, H_2O, NF_3, NH_3$, and $CHCl_3$, which has the lowest dipole moment?

• A: The molecule with the lowest dipole moment is determined by symmetry and electronegativity; central atom lone pairs are evaluated based on structure (JEE Main 2026 Shift 2).

• Q: Stability of $\text{XeO}_2\text{F}_2$?

• A: It has a see-saw shape, 5 electron pairs, and specific bond angles ($O-Xe-O$ and $F-Xe-F$) nearly at $180^{\circ}$.