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George Mason University General Chemistry 211 Chapter 10 The Shapes (Geometry) of Molecules

George Mason University General Chemistry 211 Chapter 10 The Shapes (Geometry) of Molecules Acknowledgements Course Text: Chemistry: the Molecular Nature of Matter and Change, 6 th edition, 2011, Martin S. Silberberg, McGraw-Hill

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George Mason University General Chemistry 211 Chapter 10 The Shapes (Geometry) of Molecules

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  1. George Mason University • General Chemistry 211 • Chapter 10 • The Shapes (Geometry) of Molecules • Acknowledgements • Course Text: Chemistry: the Molecular Nature of Matter and Change, 6th edition, 2011, Martin S. Silberberg, McGraw-Hill • The Chemistry 211/212 General Chemistry courses taught at George Mason are intended for those students enrolled in a science /engineering oriented curricula, with particular emphasis on chemistry, biochemistry, and biology The material on these slides is taken primarily from the course text but the instructor has modified, condensed, or otherwise reorganized selected material.Additional material from other sources may also be included. Interpretation of course material to clarify concepts and solutions to problems is the sole responsibility of this instructor.

  2. Lewis Electron-Dot Symbols • A Lewis electron-dot symbol is a symbol in which the electrons in the valence shell of an atom or ion are represented by dots placed around the letter symbol of the element • Note that the group number indicates the number of valence electrons Group VI Group II Group III Group IV Group V Group VII Group VIII Group I : : : : . . Ar : : : Mg Al P S Cl Si . . . . . . . . . . : : : . . . 3s1 3s2 3s23p1 3s23p2 3s23p3 3s23p4 3s23p5 3s23p6 Na .

  3. Lewis Electron-Dot Formulas : F . : : : F Mg . . . : : : : [ F ] [ F ] - - 2+ Mg : : : : : : • A Lewis electron-dot formulais an illustration used to represent the transfer of electrons during the formation of an ionic bond • The Magnesium has two electrons to give, whereas the Fluorines have only one “vacancy” each • Consequently, Magnesium can accommodate two Fluorine atoms

  4. Lewis Structures • The tendency of atoms in a molecule to have eight electrons (ns2np6) in their outer shell (two for hydrogen) is called the octet rule • You can represent the formation of the covalent bond in H2 as follows: • This uses the Lewis dot symbols for the hydrogen atom and represents the covalent bond by a pair of dots + H H H H    

  5. The Electron Probability Distribution for the H2 Molecule

  6. Lewis Structures : H H • The shared electrons in H2 spend part of the time in the region around each atom • In this sense, each atom in H2 has a helium (1s2) configuration

  7. Lewis Structures • The formation of a bond between H and Cl to give an HCl molecule can be represented in a similar way • Thus, hydrogen has two valence electrons about it (as in He) and Cl has eight valence electrons about it (as in Ar) : : . Cl H Cl : : : . + H : :

  8. Lewis Structures • Formulas such as these are referred to as Lewis electron-dot formulas or Lewis structures • An electron pair is either a: • bonding pair(shared between two atoms) • lone pair(electron pair that is not shared) Hydrogen has no unbonded pairs Chlorine has 3 unbonded pairs : : : H Cl :

  9. Lewis Structures • Rules for obtaining Lewis electron dot formulas • Calculate the number of valence electrons for the molecule from: • group # for each atom (1-8) • add the charge of Anion • subtract the charge of a Cation • Put atom with the lowest group number and lowest electronegativity as the central atom • Arrange the other elements (ligands) around the central atom

  10. Lewis Structures • Rules for Lewis Dot Formulas • Distribute electrons to atoms surrounding the central atom to satisfy the octet rule for each atom • Distribute the remaining electrons as pairs to the central atom • If the Central atom is deficient in electrons to complete the octet; move electron pairs from surrounding atoms to complete central atom valence electron needs, that is form one or more double bonds (possibly triple bonds) around the central atom

  11. Practice Problem • Write a lewis structure for CCl2F2 Step 1: Arrange Atoms (Carbon is “Central Atom” because is has the lowest group number and lowest electronegativity Step 2: Determine total number of valence electrons 1 x C(4) + 2 x Cl(7) + 2 x F(7) = 32 Step 3: Draw single bonds to central atom and subtract 2 e- for each single bond (4 x 2 = 8) 32 – 8 = 24 remaining Step 4: Distribute the 24 remaining electrons in pairs around surrounding atoms (3 electron pairs around each Fluoride atom)

  12. Writing Lewis Dot Formulas • The Lewis electron-dot formula of a covalent compound is a simple two-dimensional representation of the positions of electrons in a molecule • Bonding electron pairs are indicated by either two dots or a dash • In addition, these formulas show the positions of lone pairs of electrons

  13. Writing Lewis Dot Formulas • The following rules allow you to write electron-dot formulas even when the central atom does not follow the octet rule • To illustrate, draw the structure of: Phosphorus Trichloride Con’t on next slide

  14. Writing Lewis Dot Formulas • Step 1: Total all valence electrons in the molecular formula. That is, total the group numbers of all the atoms in the formula • For a polyatomic anion, add the number of negative charges to this total • For a polyatomic cation, subtract the number of positive charges from this total P 3s23p3 Cl 3s23p5 (2+3) + 3x(2+5) = 5+21 26 total electrons 5 e- (7 e-) x 3 Con’t on next slide

  15. Writing Lewis Dot Formulas • Step 2: • Arrange the atoms radially, with the least electronegative atom in the center • Place one pair of electrons between the central atom and each peripheral atom Cl Cl P 26 – 6 = 20 remaining Cl Con’t on next slide

  16. Writing Lewis Dot Formulas • Step 3: Distribute the remaining electrons to the peripheral atoms to satisfy the octet rule : : : : Cl Cl : : P : : Cl : 26 – (3 x 6 + 6) = 2 remaining Con’t on next slide

  17. Writing Lewis Dot Formulas : Step 4: Distribute any remaining electrons (2) to the central atom. If the number of electrons on the central atom is less than the number of electrons required to complete the octet for that atom, use one or more electrons pairs from other atoms to form double or triple bonds : : : : : : Cl Cl P Phosphorus has an octet of electrons No double bonds required : : Cl :

  18. Exceptions to the Octet Rule • Although many molecules obey the octet rule, there are exceptions where the central atom has more than eight electrons • Generally, if a nonmetal is in the third period or greater it can accommodate as many as twelve electrons, if it is the central atom • These elements have unfilled “d” subshells that can be used for bonding

  19. Exceptions to the Octet Rule : : F : • For example, the bonding in phosphorus pentafluoride, PF5, shows ten electrons surrounding the phosphorus Total valence electrons 5 x 7 (F) + 5 (P) = 40 Distribute electrons to F atoms 5 x 6 = 30 Establish bonding pairs 5 x 2 = 10 Remaining electrons 40 – 30 – 10 = 0 Phosphorus has “0” non-bonding pairs F F P : : : : F F : : : : : : : : Since Phosphorus is in Period 3, PF5 is a “hypervalent” molecule The phosphorus utilizes electrons from other shells (vacant orbitals) to create a valence shell with more than 8 electrons

  20. Exceptions to the Octet Rule : : : : F : F : : F : F : : : : • In Xenon Tetrafluoride, XeF4, the Xenon atom must accommodate two extra lone pairs Total valence electrons 4 x 7 + 8 = 36 Distribute electrons to F atoms 4 x 6 = 24 Establish bonding pairs 4 x 2 = 8 Remaining electrons 36 – 24 – 8 = 4 Add 2 non-bonding pairs to Xe Xe violates “octet” rule XeF4 is a “hypervalent” molecule and utilizes vacant “d” orbitals to create a valence shell with more than 8 electrons : Xe :

  21. Delocalized Bonding: Resonance : : : O : : O O : • The structure of Ozone, O3, can be represented by two different Lewis electron-dot formulas Experiments show, however, that both bonds are identical Ozone (O3) : O : : or : O O : :

  22. Delocalized Bonding: Resonance O O O • According to Resonance Theory, these two equal bonds are represented as one pair of bonding electrons spread over the region of all three atoms • This is called delocalized bonding, in which a bonding pair of electrons is spread over a number of atoms Ozone (O3)

  23. Resonance & Bond Order • Recall (Chap 9) – Bond Order • The number of electron pairs being shared by any pair of “Bonded Atoms” or • The number of electron pairs divided by the number of bonded-atom pairs • Ex. Ozone

  24. Practice Problem In the following compounds, the Carbon atoms form a “single ring.” Draw a Lewis structure for each compound, identify cases for which “resonance” exists, and determine the C-C bond order(s). C3H4 C3H6

  25. Practice Problem C4H6 C4H4

  26. Practice Problem C6H6

  27. Formal Charge & Lewis Structures • In certain instances, more than one feasible Lewis structure can be illustrated for a moleculeFor example, H, C and N • The concept of “formal charge” can help discern which structure is the most likely • Formal Charge: • An atom’s formal charge is: • Total number of valence electrons • Minus all unshared electrons • Minus ½ of its shared electrons • Formal Charges must sum to actual charge of species: • Zero Charge for a Molecule • Ionic Charge for an Ion : : H C N H N C or

  28. Formal Charge & Lewis Structures • When you can write several Lewis structures, choose the one having the least formal charge Form I Form II group number 1 e- 4 e- 5 e- 1 e- 5 e- 4e- : +1 : -1 H C N H N C or FC: Total Valence e- – unshared e- – ½ shared e- I IV V I V IV “domain” electrons FCH: [1 - 0 - ½(2)] = 0 FCC: [4 - 0 - ½(8)] = 0 FCN: [5 - 2 - ½(6)] = 0 FCH: [1 - 0 - ½(2)] = 0 FCC: [4 - 2 - ½(6)] = -1 FCN: [5 - 0 - ½(8)] = +1 Preferred Form - Form I (Least Formal Charge) Note: HCN is a neutral molecule Sum of Formal Charges in the preferred form (0) equals molecular charge (0)

  29. Formal Charge & Lewis Structures Ozone FCOA: [6 - 4 - ½(4)] = 0 FCOB: [6 - 2 - ½(6)] = +1 FCOC: [6 - 6 - ½(2)] = -1 FCOA: [6 - 6 - ½(2)] = -1 FCOB: [6 - 2 - ½(6)] = +1 FCOC: [6 - 4 - ½(4)] = 0 Both “Resonance” forms have the same formal charge and thus, are identical Note: Ozone (O3) is a neutral molecule Sum of Formal Charges (0) equals molecular charge (0)

  30. Formal Charge & Lewis Structures Boron Trifuoride BF3 FC B = 3 – 0 -(1/2 * 6) = 0 Even though B violates “Octet Rule”, this is the preferred form because it has “less” formal charge FC B = 3 – 0 -(1/2 * 8) = -1 FC F = 7 – 4 - (1/2 * 4) = +1 F F F F B B     F F     S S     Sulfur Dioxide SO2     O O O O           FC S = 6 – 2 – (1/2 * 8) = 0 Preferred Form (Less Formal Charge) FC S = 6 – 2 – (1/2 * 6) = 1

  31. Resonance/Formal Charge – Nitrate Ion • Total Valence electrons - 3 x 6 (O) + 1 x 5 (N) + 1 (ion charge) = 24 • Add 1 pair electrons between central atom and each other atom – 3 x 2 = 6 • Add electrons to oxygen atoms to complete octet • Nitrogen still missing 2 electrons to complete octet • Borrow 2 electrons from one oxygen to form double bond • Formal Charge – Nitrogen: 5 – (0 + ½*8) = 5 – 4 = +1 • Formal Charge – Single bonded Oxygen: 6 – (6 + ½*2) = 6 – 7 = -1 x 2 = -2 • Formal Charge – Double bonded Oxygen: 6 – (4 + ½*4) = 6 – 6 = 0 • Net Charge of ion is: +1 +(-2) = -1

  32. Resonance/Formal Charge – Cyanate Ion FCN = 5 – (6 + ½*2) = -2 FCC = 4 – (0 + ½*8) = 0 FCO = 6 – (2 + ½*6) = +1 FCN = 5 – (4 + ½*4) = -1 FCC = 4 – (0 + ½*8) = 0 FCO = 6 – (4 + ½*4) = 0 FCN = 5 – (2 + ½*6) = 0 FCC = 4 – (0 + ½*8) = 0 FCO = 6 – (6 + ½*2) = -1 • Preferred Form: • Eliminate I – Higher formal charge on Nitrogen than Carbon & Oxygen • Positive formal charge on Oxygen, which is more electronegative than Nitrogen • Eliminate II – Forms II & III have the same magnitude of formal charges, but form III has a -1 charge on the more electronegative Oxygen atom • Forms II & III both contribute to the resonant hybrid of the Cyanate Ion, • but form III is the more important • Note: Net formal charge in form III is same as ionic charge (-1)

  33. Formal Charge vs Oxidation No • “Formal Charge” is used to examine resonance hybrid structures , whereas “Oxidation Number” is used to monitor “REDOX” reactions • Formal Charge - Bonding electrons are assigned equally to the atoms as if the bonding were “Nonpolar” covalent, i.e., each atom has half the electrons making up the bond • Formal Charge = valence e- – (unbonded e- + ½ bonding e-) • Oxidation Number - Bonding electrons are transferred completely to the more electronegative atom, as if the bonding were “Ionic” • Ox No. = valence e- – (unbonded e- + bonding e-)

  34. Formal Charge vs Oxidation No FC (-2) (0) (+1) (-1) (0) (0) (0) (0) (-1) N 5 – (6 + ½ (1)) = -2 C 4 – (0 + ½ (8)) = 0 O 6 – (2 + ½ (6)) = +1 N 5 – (4 + ½ (4)) = -1 C 4 – (0 + ½ (8)) = 0 O 6 – (4 + ½ (4)) = 0 N 5 – (2 + ½ (6)) = 0 C 4 – (0 + ½ (8)) = 0 O 6 – (6 + ½ (2)) = -1 ON (-3) (+4) (-2) (-3) (+4) (-2) (-3) (+4) (-2) N 5 – (6 + 2)) = -3 C 4 – (0 + 0)) = +4 O 6 – (2 + 6)) = -2 N 5 – (4 + 4)) = -3 C 4 – (0 + 0)) = +4 O 6 – (4 + 4)) = -2 N 5 – (2 + 6)) = -3 C 4 – (0 + 0)) = +4 O 6 – (6 + 2)) = -2 Note: Both Nitrogen (N) & Oxygen (O) are more electronegative than Carbon (C); thus, in the computation of Oxidation Number all the electrons are transferred to the N & O leaving C with no lone pairs and no bonded pairs Note: Oxidation Nos do not change from one resonance form to another (electronegativities remain same)

  35. The Valence-Shell Electron Pair Repulsion Model (VSEPR) • The Valence-Shell Electron Pair Repulsion (VSEPR) model predicts the shapes of molecules and ions by assuming that the valence shell electron pairs are arranged as far from one another as possible • Molecular geometry – The shape of a molecule is determined by the positions of atomic nuclei relative to each other, i.e., angular arrangement • Central Atom • Place atom with “Lower Group Number” in center(N in NF3 needs more electrons to complete octet) • If atoms have same group number (SO3 or ClF3), place the atom with the “Higher Period Number” in the center (Sulfur & Chlorine)

  36. VSEPR Model of Molecular Shapes • The following rules and figures will help discern electron pair arrangements • Select the Central Atom (Least Electronegative Atom) • Draw the Lewis structure • Determine how many bonding electron pairs are around the central atom. • Determine the number of non-bonding electron pairs • Count a multiple bond as “one pair” • Arrange the electron pairs as far apart as possible to minimize electron repulsions • Note the number of bonding and lone pairs

  37. VSEPR Model of Molecular Shapes • To predict the relative positions of atoms around a given atom using the VSEPR model, you first note the arrangement of the electron pairs around that central atom • Molecular Notation: A – The Central Atom (Least Electronegative atom) X – The Ligands (Bonding Pairs) a – The Number of Ligands E – Non-Bonding Electron Pairs b – The Number of Non-Bonding Electron Pairs • Double & Triple Bonds count as a “single” electron pair • The Geometric arrangement is determined by: sum (a + b) AXaEb

  38. VSEPR Model of Molecular Shapes

  39. VSEPR Model of Molecular Shapes

  40. Arrangement of Electron Pairs About an Atom: Basic Shapes CS2 HCN BeF2 NO2+

  41. Arrangement of Electron Pairs About an Atom: Basic Shapes SO3 BF3 NO3− NO2–CO32− SO2 O3 PbCl2 SnBr2

  42. Arrangement of Electron Pairs About an Atom: Basic Shapes CH4 SiCl4SO42- ClO4- NH3 PF3 ClO3 H3O+ H2O OF2 SCl2

  43. Arrangement of Electron Pairs About an Atom: Basic Shapes PF5 AsF5 SOF4 SF4, XeO2F2, IF4+,IO2F2- ClF3 BrF3 XeF2I3-IF2-

  44. Arrangement of Electron Pairs About an Atom: Basic Shapes SF6 IOF5 BrF5 TeF5- XeOF4 XeF4ICl4-

  45. Electron Pair Arrangement

  46. Electron Pair Arrangement

  47. Linear Geometry • Two electron pairs (linear arrangement) • Double bonds count as a “single electron pair”  2 bonding pairs 0 non-bonding pairs AXaEb= a + b = 2 + 0 = 2 (Linear) • Thus, according to the VSEPR model, the bonds are arranged linearly (bond angle = 180o) • Molecular shape of carbon dioxide is linear : : Carbon is central atom because it has lower group number : :

  48. Trigonal Planar Geometry • Three electron pairs on Central atom • The three groups of electron pairs are arranged in a trigonal plane. Thus, the molecular shape of COCl2 is trigonal planar. The Bond angle is 120o Central Atom - Carbon 3 bonding electron pairs (double bond counts as 1 pair) 0 non-bonding electron pairs a + b = 3 + 0 = 3  Trigonal Planar : : O C : : : : Cl Cl : :

  49. Trigonal Planar Geometry • Effect of Double Bonds • Bond angles deviate from ideal angles when surrounding atoms and electron groups are not identical • A double bond has greater electron density and repels two single bonds more strongly than they repel each other 122o 120o H H       C O C O 120o 116o     H H Actual Ideal

  50. Trigonal Planar Geometry • Effect of Lone Pairs • The molecular shape is defined only by the positions of the nuclei • When one of the three electron pairs in a trigonal planar molecule is a lone (non-bonding) pair, it is held by only one nucleus • It is less confined and exerts a stronger repulsive force than a bonding pair • This results in a decrease in the angle between the bonding pairs The normal Trigonal Planar angle between the bonding pairs is 120o

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