Lattice Enthalpy Equilibrium Distance Cohesive Energy AH is the standa molar enthalpy change for the following proces Mtas+Xgas→Ma △H<0 - otal derations are neglected the most stable crystal structure of a given compound is the Lattice Energy(U)of Ionic Compounds emble one mole of a crystalline ionic compound nto free ZTe 1 ZTe Bohr-Madelung equation LAttice Energy of lonic Compounds: Bohr-Madelung Z+z-e- equation ANZ'Z'e Find B and n at equilibrium. dE N=6.02x10=moh cThe Madelung constant endent of the ionic charges 0→B=2ze2 elf know the crystal structure, you can choose a suitable ladelung constant, and the distance between the ions r you can estimate the lattice energy of ion compoun Total energy at ro Azel To What is n? Compressibility= zns (wurtzite) 2ns (ine blende) igg Applications of lattice Enthalpy The Kapustinskii Equation Calculations Kapustinskii noticed that A/v, is almost athermal stabilities of ionic solids constant for all structures v is the number of ions in the formula unit stabilities of oxidation states of cations r=r+r, unit.pm Solubility of salts in water Variation in A /v with structure is partially calculations of electron affinity data canceled by change in ionic radii with coordination number stabilities of "non existent 125200uZZ,34.54 Two definitions: The lattice enthalpy change is the standard molar enthalpy change for the following process: M+ (gas) + X- (gas) ® MX(solid) If entropy considerations are neglected the most stable crystal structure of a given compound is the one with the highest lattice enthalpy. Lattice Energy (U) of Ionic Compounds: disassemble one mole of a crystalline ionic compound at 0K into free components o DHL H 0 o D L < Lattice Enthalpy o U = -DHL Equilibrium Distance & Cohesive Energy ) n 1 (1 r Z Z e E E E 0 2 attractive repulsive = - - = + + - Ep r n r B r Z Z e + - 2 - total At equilibrium: (Erepulsive) (Eattractive) 0 2 attractive r Z Z e E + - = - Find B and n at equilibrium: repulsive n r B E = n 2 Total attractive repulsive r B r Z Z e E = E + E = - + + - 0 dr dE Total = 0 r = r n 1 0 2 n 1 0 2 0 2 r n Z Z e 0 B r nB r Z Z e - + - + + - Þ - + = Þ = Total energy at r0 : ) n 1 (1 r Z Z e E 0 2 r r0 = - - + - = What is n? Compressibility Þ n » 9 Bohr-Madelung equation Lattice Energy of Ionic Compounds: Bohr-Madelung equation： N = 6.02x1023 mol-1 The Madelung constantis independent of the ionic charges and the lattice dimensions, but is only valid for one specific structure type If know the crystal structure, you can choose a suitable Madelung constant, and the distance between the ions ro , you can estimate the lattice energy of ion compound. ) n 1 (1 r ANZ Z e U 0 2 = - + - Structure Type Madelung Constant CsCl 1.763 NaCl 1.748 ZnS (Wurtzite) 1.641 ZnS (Zinc Blende) 1.638 thermal stabilities of ionic solids stabilities of oxidation states of cations solubility of salts in water calculations of electron affinity data stabilities of “non existent”compounds Applications of Lattice Enthalpy Calculations The Kapustinskii Equation Kapustinskii noticed that A /n, is almost constant for all structures νis the number of ions in the formula unit ro = r++r-, unit: pm Variation in A /n with structure is partially canceled by change in ionic radii with coordination number ) r 34.5 (1 r 125200 Z Z U 0 0 - u = + -