Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 110	General Chemistry	Fall 2003
Lecture Notes::Lec 18_8 October	© R. Paselk 2003
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Orbitals and Covalent Bonding

VSEPR Theory and Molecular Geometry

Another great limitation of Lewis structures is that they tell us nothing about molecular shape. So to determine shape we added another tool, VSEPR Theory, to our chemical toolbox.

VSEPR (Valence Shell Electron Pair Repulsion) Theory is based on three assumptions:

• Electron pairs will orient around a central point to minimize repulsion.
• Lone-pairs of electrons will have greater repulsion than bonded pairs of electrons (note that the atoms are ignored in terms of repulsion).
• Repulsion is strong at 90° and weaker at 120° (weakest at 180°).

VSEPR predicts geometry based on these assumptions in a few simple, sequential, steps:

1. Draw a correct Lewis Structure.
2. Determine the Steric Number = the number of bonded atoms + the number of lone pairs.
3. Maximize the angles between electron pairs, placing the lone (unbonded) pairs at the extremes.

Examples of the various molecular geometries discussed belwo may be found in the Molecular Geometry Supplement.

For central atoms with eight outer electrons (octets) there are three possible electron pair geometries:

1. Linear with angles of 180° ( a single pair and a triple bond, or two double bonds).
2. Trigonal planar with angles of 120° (one double bond and two single pairs).
3. Tetrahedral with angles of 109.5° (four single pairs). [model]

These three electron pair geometries can lead to five molecular geometries:

• Linear (e.g. carbon monoxide)
  • CO₂
    • valence electrons = 4 + 2x6 = 16
    • 6y + 2 = 20, thus 4 fewer electrons than required for all single bonds, 4/2 = 2 multi-bonds (2 double or 1 triple)
    • LS: from symmetry C will be central atom, therefore= :O::C::O:
    • Considering C as the central atom, have 2 bonded atoms and no lone-pairs, therefore
    • steric number = 2, so linear electronic geometry, and
    • linear molecular geometry
• Trigonal planar (e.g. formaldehyde, CH₂O)
  • formaldehyde, CH₂O
    • valence electrons = 4 + 2x1 + 6 = 12
    • 6y + 2 = 6 x 2 + 2 = 14; so molecule has 2 fewer electrons than required for all single bonds, 1 double bond
    • LS: from symmetry C will be central atom, therefore=
    • Considering C as the central atom, have 3 bonded atoms and no lone-pairs, therefore
    • steric number = 3, so trigonal planar electronic geometry, and 3 atoms so
    • trigonal planar molecular geometry
• Tetrahedral (e.g. methane, CH₄)
  • valence electrons = 4 + 4x1= 8
  • four bonds possible, since only 4 pairs, single bonds because only have H's bound to C.
  • LS: from symmetry C will be central atom, therefore=
  • Considering C as the central atom, have 4 bonded atoms and no lone-pairs, therefore
  • steric number = 4, so tetrahedral electronic geometry, and 4 atoms so
  • tetrahedral molecular geometry
• Trigonal pyramidal (e.g. ammonia, NH₃)
  • valence electrons = 5 + 3x1= 8
  • only 4 pairs, single bonds because only have H's bound to N, 3 bonds, since only 3 H's
  • LS: from symmetry N will be central atom, therefore=
  • Considering N as the central atom, have 3 bonded atoms and one lone-pair, therefore
  • steric number = 4, so tetrahedral electronic geometry, but only 3 atoms so
  • trigonal pyramidal molecular geometry
• Bent (e.g. water, H₂O)
  • valence electrons = 6 + 2x1= 8
  • only 4 pairs, single bonds because only have H's bound to O, 2 bonds, since only 2 H's
  • LS: from symmetry O will be central atom, therefore=
  • Considering O as the central atom, have 2 bonded atoms and 2 lone-pairs, therefore
  • steric number = 4, so tetrahedral electronic geometry, but only 2 atoms so
  • bent molecular geometry

Small atoms:

• Linear with angles of 180° ( BeCl₂) Note that this is an example where the "hi-lo" rules will lead us astray. The "1.7 rule" for electronegativities on the other hand predict covalent bonding. Also, the extreme small size of Be also leads to a prediction of greater covalent bond character than expected for other alkaline earth elements.
  • valence electrons = 2 + 2x7 = 16
  • from symmetry Be will be central atom, therefore only two pairs on Be with single bonds to Cl
  • LS:
  • steric number = 2, so linear electronic geometry, so
  • linear molecular geometry
• Trigonal planar with angles of 120° ( BCl₃)
  • valence electrons = 3 + 3x7 = 24
  • from symmetry B will be central atom, therefore only three pairs on B with single bonds to Cl
  • LS:
  • steric number = 3, so trigonal planar electronic geometry, & three bonded atoms so
  • trigonal planar molecular geometry

Representative atoms with empty d-shells can also have what are sometimes referred to as expanded valence shells. In these cases the d-orbitals also participate in bonding enabling more bonds to be formed. Thus two additional electronic geometries are possible:

• Trigonal bipyramidal with angles of 90° & 120° results when the valance shell is expanded to accommodate 10 electrons in five pairs.
• Octahedral with angles of 90° results when the valance shell is expanded to accommodate 12 electrons in six pairs.

These two electron pair geometries can lead to six new molecular geometries in addition to another way to make a linear molecule:

• Trigonal bipyramidal with angles of 90° & 120° (PCl₅)
  • valence electrons = 5 + 5x7 = 40
  • 40 > 6y + 2 = 38, D = 2 therefore expanded valence with one extra pair
  • from symmetry P is central atom
  • valence electrons around P = P electrons + one from each Cl = 5 + 5
  • LS:
  • steric number = 5, so trigonal bipyramidal electronic geometry
  • 5 bonded atoms so Trigonal bipyramidal molecular geometry
• Seesaw with angles of 90° & 120° (SF₄)
  • valence electrons = 6 + 4x7 = 34
  • 34 > 6y + 2 = 32, D = 2 therefore expanded valence with one extra pair
  • from symmetry S is central atom
  • valence electrons around S = S electrons + one from each F = 6 + 4
  • LS:
  • steric number = 5, so trigonal bipyramidal electronic geometry
  • 4 bonded atoms so Seesaw molecular geometry
• T-shaped with angles of 90° (ClF₃)
  • valence electrons = 7 + 3x7 = 28
  • 28 > 6y + 2 = 26, D = 2 therefore expanded valence with one extra pair
  • from symmetry Cl is central atom
  • valence electrons around Cl = Cl electrons + one from each F = 7 + 3
  • LS:
  • steric number = 5, so trigonal bipyramidal electronic geometry
  • 3 bonded atoms so T-shaped molecular geometry
• Linear with angles of 180° (I₃^-)
  • valence electrons = 7 + 2x7 + 1 = 22
  • 22 > 6y + 2 = 20, D = 2 therefore expanded valence with one extra pair
  • from symmetry I is central atom
  • valence electrons around I = I electrons + one from each I + 1 = 7 + 2 +1
  • LS:
  • steric number = 5, so trigonal bipyramidal electronic geometry
  • 2 bonded atoms so Linear molecular geometry
• Octahedral with angles of 90° (AsF₆^-)
  • valence electrons = 5 + 6x7 + 1 = 48
  • 48 > 6y + 2 = 44, D = 4 therefore expanded valence with two extra pairs
  • LS:
  • from symmetry Cl is central atom
  • valence electrons around Cl = Cl electrons + one from each F = 7 + 3
  • steric number = 5, so trigonal bipyramidal electronic geometry
  • 3 bonded atoms so Octahedral molecular geometry
• Tetragonal pyramidal with angles of 90° (ICl₅)
  • valence electrons = 7 + 5x7 = 42
  • 42 > 6y + 2 = 38, D = 4 therefore expanded valence with two extra pairs
  • from symmetry Br is central atom
  • valence electrons around I = I electrons + one from each F = 7 + 5
  • LS:
  • steric number = 6, so trigonal bipyramidal electronic geometry
  • 5 bonded atoms so Tetragonal pyramidal molecular geometry
• Square planar with angles of 90° (XeF₄)
  • valence electrons = 8 + 4x7 = 36
  • 36 > 6y + 2 = 32, D = 4 therefore expanded valence with two extra pairs
  • from symmetry Xe is central atom
  • valence electrons around Xe = Xe electrons + one from each F = 8 + 4
  • LS:
  • steric number = 6, so trigonal bipyramidal electronic geometry

• 5 bonded atoms so Square planar molecular geometry.

 

Polarity in Covalent Molecules

Polarity: So now we can predict bonding and shape in representative group molecules (and thus most biomolecules), how about electron density and thus charge distribution? Need two bits of information:

• Shape (based on VSEPR Theory)
• Electron distribution within a bond (based on electronegativity)

Examples:

Molecule Geometry Structure Electronegativities Bond Dipoles Molecular Dipole Carbon monoxide  linear    ENC= 2.5, ENO= 3.5     Carbon dioxide  linear   ENC= 2.5, ENO= 3.5    None: two dipoles are of equal magnitude, but opposite in direction and cancel.  Water  bent      ENH= 2.1, ENO= 3.5      Ammonia  trigonal pyramidal     ENH= 2.1, ENN= 3.0     Ammonium ion tetrahedral      ENH= 2.1, ENN= 3.0  None: four dipoles are symmetrically arranged to cancel each other out and give a spherically charged but non-polar ion.

© R A Paselk

Last modified 9 October 2003