10.12.2011-EXAM 2 start

10.12.2011-EXAM 2 start - Chem 260 Lecture 16, October 12,...

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Unformatted text preview: Chem 260 Lecture 16, October 12, 2011 Chemistry 260 Today in Chemistry 260 •  •  •  •  •  •  •  Sigh of relief (?) after the exam.. non ­covalent interactions (intermolecular forces) ionic bonds electrostatic interactions have a profound distance dependences intermolecular force have distinct distance dependences hydrogen bonds are a special case of electrostatic interactions intermolecular forces inCluence bulk properties of matter Next in Chemistry 260 •  reading: AD 17; Ch. 9 Oxtoby •  gases and the Cirst law of thermodynamics Lecture 16 October 12, 2011 Formation of Ionic Bonds From thrash to Nobel prize discovery.. Why does an NaCl crystal have a lower energy than a gas of widely ­separated Na and Cl atoms? The 2010 Nobel Prize in Physics has gone to graphene discoverers, Andre Geim, and Konstantin Novoselov, of the United Kingdom's University of Manchester discovering that sticky tape would peel off single-atom thick layers of graphene for study. 1. sodium atom ionization Na(g ) !!" Na + (g ) + e2. chlorine atom ionization Cl(g ) + e- !!" Cl- (g ) energy required: 496 kJ/mol energy released: 349 kJ/mol Na+(g) + Cl(g) + e ­ Energy "We had been trying several other methods in our lab. And there was a senior researcher who was preparing samples of graphite (bulk carbon samples) for the attempts. The way you clean graphite is just cover it with tape and pull the tape off, and then throw it away. So once, I just picked it up out of the trash and we analyzed it." The rest is history. .. Let s consider this as a three ­step process: 2. 1. Na+(g) + Cl ­(g) Na(g) + Cl(g) After 1 & 2, +145 kJ/mol ABOVE energy of separate atoms Electrostatic Interactions Formation of Ionic Bonds 1. sodium atom ionization Na(g ) !!" Na + (g ) + e2. chlorine atom ionization Cl(g ) + e- !!" Cl- (g ) energy required: 496 kJ/mol energy released: 349 kJ/mol 3. Coulombic attraction Cl- (g ) + Na + (g ) !!" NaCl(s) Energy Na+(g) + Cl(g) + e ­ 2. 1. energy released: 530 kJ/mol ΔE between gaseous atoms and an NaCl solid is HUGE:  ­383 kJ/mol Na+(g) + Cl ­(g) Na(g) + Cl(g) 3. NaCl(s) Lecture 16 Step 1 needs to be small enough to allow this formation to be energetically favorable Typically, only metallic elements have ionization energies that are low enough for monoatomic cation formation to be energetically feasible. 1. Ionic Interactions: r + A •  1/r long range interaction  ­ B •  proportional to the product of charges •  not directional V (r ) = q A qB 4πε o r V (r ) = − V (r ) = | q A qB | 4πε o r | q A qB | 4πε o r qA and qB are of opposite charge If qA and qB are of the same charge 1 Chem 260 Lecture 16, October 12, 2011 Each ion in a solid experiences electrostatic attractions from other oppositely charged ions and repulsions from all the other charged ions. Lattice Energy Interaction Between Ions The energy required for the formation of ionic bonds is supplied largely by the Coulombic attraction between oppositely charged ions. Potential energy (lattice energy) is the sum of all of these contributions We must extend the Coulombic potential energy expression to incorporate many attractions and repulsions at varying distances (multiples of d) from the ion in question d For a one ­dimensional array, where the ions have +z and –z charge the potential felt by one ion: ∞ (z e)(z e) q1qn =∑ 1 n n = 2 4πε o r n n = 2 4πε o r n 1 1 For one mole of a three ­dimensional array: ∞ V (r ) = = V1 (r ) = ∑ q A qB 4πε o rAB An actual ionic solid is an inCinite array of cations and ions (lattice) stacked together to yield the lowest ­energy arrangement. (z Ae)(z B e)  ­ 1 d + d 3 d e 4 + d n … 2  ­ att 4πε o rAB The equivalent of Coulombic attraction energy in an ionic solid is its LATTICE ENERGY High lattice energy: ions (small and highly charged) interact very strongly with each other. V1 = V1 = Intermolecular Interactions Klaus Schulten  ­ UIUC V (r ) = − A t rac ive u rep e lsiv att c ra tiv 4πε o 2d 4πε o 3d 4πε o 4d z 2e 2 ⎛ 1 1 1 z 2e 2 z 2e 2 ⎞ ⇒ −2 ln 2 ⎜1 − + − + ⎟ = − ln 2 4πε o d ⎝ 2 3 4 4πε o d 4πε o d ⎠ V= for NaCl, A = 1.748 V (potential) Electrostatic Forces Non ­bonding interactions govern many important processes. In this case the electrophoretically driven translocation of DNA through a membrane in alpha ­ hemolysin. − qNa+ qCl − 4πε 0 r + b rn Repulsive interaction F (force) Non ­bonding interactions are electrostatic in nature – reClecting the interactions of charges, charge distributions, the distortability of charge distributions. −δ2 + δ2 + l - + Attractive Assume r >> l, rearrange, expand and keep only the leading term Vid (r ) = − q Aδ 2l − q A µ B = 4πε o r 2 4πε o r 2 Repulsive Vid (r) ! " 1/r2 is a long range interaction qAµ B 3. Dipole  ­ Dipole Interactions: + - r θ +- For stationary dipoles r2 The potential is orientation dependent + qµ Vid (r ) = − A B 2 cosθ 4πε o r Lecture 16  ­ θ r + l !! "µ A µ B 4 #0r 3 Dipoles are vector quantities, µ A , µ B and κ represents the orientation dependence of the potential between the dipole moments + - κ=2 -+ r − q Aδ 2 q Aδ 2 + 4πε o (r − 1 l ) 4πε o (r + 1 l ) 2 2 Vdd (r) = ! Electrostatic Interactions +- Vid (r ) = 2. Ion  ­ Dipole Interactions: attractive F<0 We will consider some of the important pairing of electrostatic interaction found in molecular systems - Sum the attractive and repulsive potential energies to get the potential Electrostatic Interactions repulsive F>0 dV d 2r = ma = m 2 dr dr dt + J. Mathé, A. Aksimentiev, D. R. Nelson, K. Schulten, and A. Meller PNAS USA, 102:12377 ­12382, 2005. F =− 4πε o d A is Madelung constant, which represents the geometric relations in the speciCic kind of crystal (− ze )(ze ) + (− ze )(− ze ) + (− ze )(ze ) + (− ze )(− ze ) + 4πε o d z A z B N Ae 2 κ=1 Vdd (r) ! " !! µA µB r3 For randomly ­oriented and rotating dipoles (i.e. liquid …) Vdd (r) = ! !2 !2 2 µ Aµ B # 1 & %( 3 4 " 0 r 6 $ kT ' 2 Chem 260 Lecture 16, October 12, 2011 Vid (r) ! Vi - ind (r) = " Electrostatic Interactions Electrostatic Interactions 4. Ion – Induced Dipole Interactions: 4. Ion – Induced Dipole Interactions: - + + + + + r - The presence of an ion can induce the formation of a dipole.  ­  ­  ­  ­  ­ + + + + + r - ! * µ A = ! A EB * µ A qB 4 #0r 2 ! EB = qB 4!" 0 r 2 qB $q Vi - ind (r) = ! # AB 4 " 0 r 2 4%" 0 r 2 2 The presence of an ion can induce the formation of a dipole. Polarizability is related to the volume of the electron cloud #q & *A Vi - ind (r) = ! % B ( ) 4 r $ 4 "0 ' Vi - ind (r) ! " a  = polarizability α (length)3 2 qB# A r4 Polarizability is related to the volume of the electron cloud. αNe < αAr < αKr < αXe The ability of an electron distribution to be polarized by an external charge distribution or electric Cield. Always attractive potential, since the dipole is induced by the charge Electrostatic Interactions 5. Dipole – Induced Dipole Interactions:  ­  ­  ­  ­  ­ + + + + + r  ­ + µµ Vdd (r ) = − A B3 4πε o r Electrostatic Interactions 6. Induced Dipole – Induced Dipole Interactions aka London Dispersion interactions: The presence of a dipole can induce the formation of a dipole. µ IND = E r Ionization energy of the atom or molecule 1 2αµ 2 Vd −id (r ) = − 2 4πε 0 r 6 Clearly atoms can only get so close before repulsive interactions become dominant. δ+ δ ­ The presence of an instantaneous dipole can induce the formation of a dipole. ⎛µ⎞ ⎜ 3⎟ ⎝r ⎠ Repulsive Interactions r δ+ δ ­ V =− 3 Iα 2 size 4 (4πε 0 )2 r 6 Repulsive Interactions But … the interaction is not hard sphere because electron clouds can deform. Clearly atoms can only get so close before repulsive interactions become dominant. Molecules/atoms cannot occupy the same space Molecules/atoms cannot occupy the same space Extremely short range But … the interaction is not hard sphere because electron clouds can deform. Extremely short range: 1 1 → 12 r9 r Lecture 16 Tennis Ball like 1 1 → 12 r9 r Billiard Ball like 3 Chem 260 Lecture 16, October 12, 2011 Lennard ­Jones 6 ­12 Potential Lennard ­Jones 6 ­12 Potential Repulsive potential ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ V(r) = 4ε ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎢⎝ r ⎠ ⎝ r ⎠ ⎥ ⎣ ⎦ ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ V(r) = 4ε ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎢⎝ r ⎠ ⎝ r ⎠ ⎥ ⎣ ⎦ A B C Attractive Potential: dipole ­dipole dipole ­induced dipole dispersion For a Lennard ­Jones 6 ­12 potential: •  The parameter ε deCines the well depth (B) •  The parameter σ deCines the separation where repulsion exceeds attraction (A) Theoretical simulations often use Lennard ­Jonesium with a physically reasonable realistic potential  ­ but still an analytical formula. Hydrogen Bonds What are Hydrogen Bonds? Hydrogen bond: special type of dipole ­dipole bond exists between an electronegative atom and a hydrogen atom bonded to another electronegative atom. Always involves a hydrogen atom. + •• + •• Hydrogen bonded to an electronegative element leaves a bare proton sp3 A strong interaction between the proton and an electron pair on a nearby electronegative element. + Hydrogen Bonding determines the structure and important properties of both solid and liquid water. SiH4 2 3 4 SnH4 HCl μ= 1.09 D HO μ= 1.5 D HN μ= 1.3 D 1 5 Period Nitrogen, Oxygen and Fluorine form Hydrogen Bonds (Chlorine and Sulfur occasionally show a slight trend) Lecture 16 HBr GeH4 SbH3 HI Not polar No lone pair PH3 CH4 H2Te H2Se HCl  ­100  ­200 AsH3 H2S NH3 Liquid Water Density (g/mL) HF 0 Water – an irregular network of hydrogen bonds. μ= 1.91 D Boiling Point oC HF H2O 100 Boiling points as a function of heavy atom size: Ice  ­ A very regular porous structure 0.97  ­20 Temp. (oC) 80 4 Chem 260 Lecture 16, October 12, 2011 Today in Chemistry 260 Weak hydrogen bonds between O ­H or N ­H and π electron density can also play a signiCicant role in protein structure and dynamics – as several amino acid side chains are aromatic. (strategic hydrating water molecules (solvation)) •  •  •  •  •  •  non ­covalent interactions (intermolecular forces) ionic bonds electrostatic interactions have a profound distance dependences intermolecular force have distinct distance dependences hydrogen bonds are a special case of electrostatic interactions intermolecular forces inCluence bulk properties of matter Next in Chemistry 260 A few kJ/mol •  reading: (Mon) AD 17 (Wed) Ch. 9 Oxtoby •  gases and the Cirst law of thermodynamics • Reading Quizzes resume http://www.emsl.pnl.gov/docs/annual_reports/tms/annual_report1999/1619b ­contents.html Lecture 16 5 ...
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