III-1 1 PART THREE: Ionic Bonding In . Molecules And Solids So far we have defined several energies of interaction between charged particles. - Ionization Energy - Electron Affinity - Coulombic (Electrostatic) Attraction & Repulsion. We now use these to look at further bonding properties: Mostly solids. Why are solids important? Catalysts Ad & Ab – Sorbents Lasers Fibre Optics Magnetic Memories Optical Switching (Computers) Batteries Fluorescent Lights Superconductors LED’s ………. III-2 2 We Need To Start At The Beginning One of the simplest ionic solids is sodium chloride (NaCl). Various depictions of the rocksalt structure. Not all will be met in this course. III-3 3 Discrete NaCl molecules can exist in the gas phase. NaCl(g) → Na(g) + Cl(g) ∆H for this reaction is called the Bond Dissociation Energy (409 kJ mol-1) • We can judge the stability of solids whether they form or not by looking at the free energy change for: M+(g) + X-(g) → MX(s) ∆G = ∆H - T∆S • If ∆G is –ve then spontaneous. • Note: Process of Lattice formation (solid ) is very exothermic at room temperature (∆S may be neglected). III-4 4 • We will use ∆H’s (enthalpy). Born Haber Cycle + - Na (g) + Cl (g) IP EA Electrostatic (U) _1 Attraction Na(g) + 2 Cl2(g) NaCl(g) ∆H f ( NaCl ) We can calculate U from this cycle Can You Do It ?: watch the signs However: NaCl(g) is NOT NaCl(s) III-5 5 - We want to get an idea of how stable different solids are. - Then U is more complicated. WHY? Sodium Chloride Lattice Cubic Na Cl + Cl Each Na has 2r - 3r Na 6 near neighbour Cl Cl Na Each Cl- has Na + r Cl 6 near neighbour Na • The attractive energy between a Na+ and its 6 near neighbour Cl- is offset by repulsion from 12 next near neighbour Na+. • We must sum these up. III-6 6 First 6 nearest neighbour Na-Cl (Attractive) -q q Na ⋅ Cl E = r × 6 Second 12 next nearest neighbor Na-Na (Repulsive) +q ⋅q E = Na Na × 12 2r Third 8 next nearest neighbour Na-Cl -q q E = Na Cl ×8 3r (and so on … for ever) This is a convergent series. The sum of all the attractive and repulsive terms can be lumped together. -q2 E = r ⋅ A A is called the Madelung Constant. For NaCl and other cubic structures A = 1.74756. III-7 7 • NOTE: In this case the coulombic term is overall attractive. Where is the repulsion to stop the solid collapsing? Born-Meyer Repulsion (DeKock & Gray, p. 457) -ar ER = be (See problem set 4; Q. 4) (remember Van der Waals repulsion?) • Again due to overlap of electron clouds. b is a constant related to compressibility of solid. overall we have III-8 8 E Born Meyer Repulsion be-ar dE = 0 r(dr DIST Coulombic Attraction -Aq q 1 2 ( r (a common value for a is 2.899) • We are almost ready to determine whether bonding in NaCl is Ionic (that is can it be described by Madelung, Coulomb Born and Meyer). • How? â We can Calculate the Lattice Energy. III-9 9 ã We can Measure the Lattice Energy. â Is from Ionic Bonding only. ã Is real value. Lattice Energies (Enthalpies) (p. 455, DeKock & Gray) Definition: lattice engergy is the energy released when 1 mole of a substance is formed from its gas phase ions. e.g. Na+(g) + Cl-(g) → NaCl(s) ∆G = U • first we will determine the lattice energy from experimental values. III-10 10 • Born Haber Cycle + - N a ( g) + e + C l( g) _ EA + T E N a - N a ( g) + C l( g) C l ( g) + (Na (g) 1 _ 2 B E C l 2 _1 N a ( g) + 2 C l2 ( g) + U ( L A T T I C E E N E R G Y ) ∆Ha t _1 N a ( s ) N a ( s ) + 2 C l2 ( g) ∆H f N a C l ( s ) If we go round this cycle we must expend no energy (overall). III-11 11 So, (Follow the Arrows) -∆H +∆H (Na)+1BE(Cl )+IE(Na) f at 2 2 - EA(Cl) + U = 0 U = ∆H −∆H (Na) - 1BE(Cl )−IE+EA f at 2 2 U = -411 – 108 –121 –502 + 354 -1 UNaCl = -788 kJ mol Now Let’s Calculate U (p. 456, DeKock & Gray) • Earlier We wrote down the contributions to Ionic bonding as the sum of Attractive & Repulsive terms. −Aq q 1 2 −ar E= r +be III-12 12 We Now Use the More General Form Given in DeKock and Gray E = EC + ER (Coulombic and Repulsive) For Avogadros number of units + − 2 AN(z )(z )⋅e −ar E = r +Nbe (Z is charge: 1st term is –ve Attractive when charges are of different sign. Now see DeKock and Gray p. 457-459. We Follow Them N ≡ AVOGADRO’S NUMBER III-13 13 ANz+z−e2 −ar E = r + Nbe â E In The Energy Curve r dE = 0 at r = r dr eq So r = r dE__ = 0 eq dr dE + − 2 = 0 = -ANz z e − Nabe−ar 2 dr req ⎛ ⎞ d ⎜1⎟ -1 ⎜ ⎟ = ⎜ r ⎟ 2 dr ⎝ ⎠ r + − 2 ar b = -Az z e e ã ar2 d ear = aear eq dr PLEASE: NOTE MISTAKE IN DEKOCK & GRAY, P. 458, EQUATION 7-8. III-14 14 SUB ã IN â ⎧ ⎫ ⎪ + - 2 ar ⎪ + 2 -Az z−e ⎪-Az z e e ⎪ -ar E = + N⎨ ⎬ e r ⎪ 2 ⎪ eq ⎪ r a ⎪ ⎩⎪ eq ⎭⎪ + 2 + − 2 - CONSTANT E = -Az z e - ANz z e 2 8 -1 req a = 2.9×10 cm areq LATTICE ⎧ ⎫ ANz+z-e2 ⎪ 1 ⎪ Er = - ⎨1 - ⎬ ENERGY eq req ⎪ areq ⎪ ⎩ ⎭ Couloubic + Repulsive BM Term. For NaCl req = 2.814D (See Later) E = -759 kJ mol-1 (Substituting in the Values) -1 Compare to EEXPTL = -788 kJ mol III-15 15 • Good Agreement (within 5%) – we have ignored VDW but this is small. • CONCLUSION: Bonding in NaCl is Substantially Ionic. - Extra Lattice Energy is From Covalent Bonding (Part Five) ************************************* The following may not be covered Kapustinskii Equation • If Madelung Constant for a number of structures is divided by the number of ins/formula unit: approximately same value results. ⎧ ⎫ ⎧ ⎫ ⎪ 1 ⎪ ⎪ 0.345⎪ • Replace ⎨1− ⎬ with ⎨1- ⎬ ⎪ r a ⎪ ⎪ r +r ⎪ ⎩ eq ⎭ ⎩ c a ⎭ ⎧ ⎫ ANz+z-e2 ⎪ 1 ⎪ IN Er = ⋅ ⎨1 - ⎬ eq r ⎪ ar ⎪ eq ⎩ eq ⎭ III-16 16 • Also replace A with 1.21 MJ D mol-1 We Get ⎛ ⎞ -nz+z- ⎜ 0.345⎟ E = ⎜1− ⎟ ⎜ ⎟ d ⎝ rc +ra ⎠ r : cation radius⎫ c ⎪ ⎬ d = rc+ ra ⎪ ra : anion radius ⎭⎪ Example KNO3 n = 2 (2 Ions/formula unit) z+ = z- = 1 + ⎫ r =1.38⎪ ⎬ rc + ra =3.27D - ⎪ r = 1.89⎭⎪ ⎛ ⎞ 2 ⎜ 0.345⎟ -1 E = ⎜1 − ⎟ × 1.21 MJ mol ⎜ ⎟ 3.27 ⎝ 3.27 ⎠ = -622 kJ mol-1 III-17 17 Chemical Significance of Lattice Energies • Lattice Energy (and EA) are principal (only) reasons why ∆Hf is –ve. These alone make the solid stable. • Look Again at the values used in the Born- Haber Calculation for NaCl. • Kapustinskii Equation. III-18 18 • Lattice Energy is a good measure of stability. Increases with Ion Charge with decrease in r. Thermal Stabilities of Ionic Solids (Not in DeKock and Gray) EXAMPLE: Carbonates MCO3(s) → MO(s) + CO2(g) Decomposition Temp: Is where ∆G for above react goes –ve nt Observed to increase as M gets bigger. CaCO3 more stable than MgCO3 . i.e. Ionic Radii Ca2+ Mg2+ 1.00D 0.49D WHY? III-19 19 NOTE: Thermodynamics: ∆G = ∆H - T∆S Decomp occurs when T = ∆H (after ∆G is ∆S –ve) For MCO3 decomp entropy is const – CO2 formation. ∴Enthalpy Change is good Guide of Stability Large Cations Stabilize Large Anions MCO3(s) → MO(s) + CO2(g) ∆H = ∆HL(MO) - ∆HL(MCO3) i.e. Thermal Stability is measured by difference in Lattice Energies. III-20 20 IF MO has much bigger lattice energy than MCO3. THEN MCO3 will be very unstable wrt to MO. Large Cation Small Cation Cation Lattice Small % scale } Large % change }change Cation (From: Inorganic Chemistry, D. Shriver, P. Atkins, C. Langford, p. 132, Pub. W.H. Freeman.) III-21 21 In Kapustinskii Equation ⎛ ⎞ −nz+z− ⎜ 0.345⎟ E = ⎜1 − ⎟ ⎜ ⎟ d ⎝ d ⎠ change in E ∝ 1 - 1 + 2- + 2- rM +r0 rM + rCO3 (all else is same) If M+ is large diff is not large (i.e. If M+ → ∞ we can ignore anion radii) Greatest Change Occurs when r+M is small. III-22 22 CHARGE • Which are more stable M+ carbonates or M2+ carbonates (To thermal Decomp to Oxide) KAPUSTINSKII Difference in Latice Energy between M+ and M2+ ⎧ ⎫ ⎪ 1 1 ⎪ ∆E∝zM+ ⎨ - ⎬ ⎪rM+ +rO2 rM+ +rCO2− ⎪ ⎩⎪ 3 ⎭⎪ DOMINATES ∴ M2+ change is largest 2+ + M carbonates less stable than M *********************************** III-23 23 Structure of Ionic Solids (DeKock & Gray p. 427- )(Shriver 115-119) IONIC MATERIALS: Properties + - • Contain Ions e.g. Na Cl , LiCl, CaF2 • Ionic Bonding Predominates • Low Electrical Conductivity • High Melting Points • Hard and Brittle • Soluble in Polar solvents Structure • Anions and Cations pack together in solid. - Electrostatic Attraction maximized - Electrostatic Repulsion Minimized • Leads to different Geometric Arrangements of Ions III-24 24 Unit Cell • A simple arrangement of atoms which when repeated in 3 Dimensions produces the crystal lattice. COMMON TYPES OF LATTICE III-25 25 MORE ABOUT THESE LATER III-26 26 AB IONIC SOLIDS Madelung Const. (A) CN (B) NaCl 6 6 1.7475 CsCl 8 8 1.7626 ZnS (Zincblende) 4 4 1.6380 ZnS(wurtzite) 4 4 1.6413 CaF2 8 4 2.5193 TiO2 (rutile) 6 3 2.408 Crystal Packing • Can we make some simple rules about crystal packing that enable us to predict these structures? â Ions are essentially spherical ã Pack together by size.