WHY it's so large: each ion is attracted to many neighbours in all directions, not just one partner. Summing over the whole infinite lattice multiplies the pairwise attraction.
WHAT we want: total electrostatic potential energy of the whole crystal per mole.
Step 1 — one pair. Coulomb potential energy between two ions charges z+e and z−e at separation r0:
Epair=4πε01r0(z+e)(z−e)Why this step? This is the fundamental law; everything scales from it.
Step 2 — sum the whole lattice. A given ion feels nearest neighbours (attraction), next-nearest (repulsion), etc. This infinite alternating sum converges to a geometric constant called the ==Madelung constant A== (e.g. A=1.748 for NaCl structure).
Eattr=−4πε0r0NAAz+z−e2Why this step?A packages "the geometry of the whole crystal" into one number, so we don't re-sum forever.
Step 3 — add short-range repulsion. Electron clouds repel when squeezed (Pauli). Born modelled this as ∝r−n, giving the Born exponentn (7–12). Minimising total energy at the equilibrium r0 leaves a correction factor (1−n1):
HOW to read it:U grows with charge productz+z− (biggest lever!) and shrinks with ionic separationr0. Small, highly-charged ions ⇒ enormous lattice energy (MgO ≈ –3800 kJ/mol vs NaCl ≈ –788).
WHY needed: For a random compound you may not know the crystal structure, so A is unavailable. Kapustinskii noticed A/ν (Madelung per ion) is roughly constant, and folded all constants into one number.
HOW: you only need charges, ion count, and ionic radii — no Madelung constant, no crystal structure. The (1−34.5/(r++r−)) term mimics the Born repulsion correction.
WHY: Lattice energy can't be measured directly. But total enthalpy round any closed loop =0 (Hess's Law). So we build a loop from elements → compound by two routes and solve for the unknown U.
Born–Haber: experimental, exact, needs thermodynamic data. Also tells us covalent character: if Born-Haber U (experimental) is more negative than Born-Landé/Kapustinskii predicts, extra covalent bonding is present (Fajans' rules).
Kapustinskii: theoretical estimate, needs only radii & charges. Great when you lack data.
Energy released when 1 mol solid ionic compound forms from its gaseous ions; exothermic (negative).
What is the Madelung constant?
A geometric constant summing all attractive/repulsive Coulomb interactions in a crystal (NaCl ≈ 1.748).
Write the Born–Landé equation.
U=−4πε0r0NAAz+z−e2(1−n1), n = Born exponent.
Why introduce the (1−1/n) factor?
Accounts for short-range Pauli/Born repulsion of electron clouds, evaluated at equilibrium r0.
State the Kapustinskii equation.
U≈−r++r−1.202×105νz+z−(1−r++r−34.5) kJ/mol, radii in pm.
When is Kapustinskii preferred over Born–Landé?
When the crystal structure (hence Madelung constant) is unknown; needs only charges, ion count, radii.
Rearrange Born–Haber to find U.
U=ΔHf−ΔHatom−IE1−21D−EA.
Why is MgO lattice energy much larger than NaCl?
Charge product 4 vs 1 and smaller ions (smaller r0); U∝z+z−/r0.
How does Born–Haber reveal covalent character?
Experimental U more exothermic than ionic-model prediction ⇒ extra covalent bonding (Fajans).
Is the 2nd electron affinity of oxygen +ve or –ve? Why?
Endothermic (+); forcing an electron onto an already-negative O− costs energy.
Recall Feynman: explain to a 12-year-old
Imagine tiny magnetic balls: red (+) and blue (–). Pulling an electron off sodium to make it "red" actually costs effort. So why does salt happily exist? Because once you have a whole box of red and blue balls, they snap together into a super-tight grid, releasing a lot of energy — way more than you spent. The Born–Haber cycle is like a bank statement: we can't directly see how much energy the snap-together released, but we know the final balance (how much energy salt has) and every other transaction, so we subtract to find the mystery amount. Kapustinskii is a cheat-sheet formula that guesses that snap energy just from how big the balls are and how strong their charges are.
Dekho, ionic bond ka asli sawaal ye hai: Na se electron nikaal ke Cl ko dena to energy maangta hai (ionisation endothermic hai), phir bhi NaCl banta kaise hai? Jawab hai lattice energy — jab bikhre hue gas-phase ions ek crystal grid me chipakte hain, tab bahut saari energy release hoti hai. Yehi energy baaki sab kharcha cover kar deti hai aur upar se compound stable banata hai. Har ion apne saare padosiyon se attract hota hai, isliye ye energy itni badi hoti hai (isko Madelung constant se count karte hain).
Lattice energy ko directly maapa nahi ja sakta, isliye Born–Haber cycle use karte hain — ye bas Hess's Law ka loop hai. Elements se compound tak do raaste banao: ek seedha (ΔHf), doosra steps ke through (atomise → ionise → ½ dissociate → electron affinity → lattice). Dono ka total same hona chahiye, to unknown U ko subtract karke nikaal lo. Formula yaad rakho: U=ΔHf−ΔHatom−IE1−21D−EA.
Agar crystal structure pata nahi (matlab Madelung constant nahi), tab Kapustinskii equation kaam aata hai — sirf charges, ion count ν, aur ionic radii (pm me) chahiye. Yaad rakho main funda: lattice energy ka strength charge-product z+z− par sabse zyada depend karta hai, aur ions jitne chhote (chhota r0) utni strong bonding. Isliye MgO (charge 2×2=4, chhote ions) ka lattice energy NaCl se kayi guna bada hota hai, tabhi MgO ka melting point itna high hai. Sign ka dhyaan rakhna — endothermic +ve, exothermic –ve, warna poora answer galat aa jaayega.
