Bond Angles and Shapes of Molecules

VSEPR(ValenceShellElectronPairRepulsion) Model

Coordination Number:
     6
     5
     4
     3
     2


A chemical formula indicates the number(s) of atoms that will be connected by bonds in the simplest form of a molecule or ion.  Thus, the formula H2O indicates that the molecule contains two hydrogen atoms and one oxygen atom, but gives no information regarding the spatial arrangement of the atoms, nor any information regarding the bonding between the atoms.  Lewis electron-dot structures provide considerable information about these arrangements, though the original Lewis octet rules are limited to fairly simple molecules.  The expanded rules allow two - dimensional representation of complex molecules with a system of symbols for the atoms, dashes (-) for bonds, and dots (:) for a pair of unshared electrons.

The Valence Shell Electron Pair Repulsion model was developed to translate these 2-dimensional drawings into 3-dimensional shapes which illustrate the bond angles within the molecule, and the general spatial arrangement of the atoms.  The process begins with a count of the atoms and unshared pairs of electrons around a central atom.  The number of atoms around the central atom is called the coordination number.  For want of a better word, and being of the Southern persuasion, I call the sum of the atoms and the unshared pairs of electrons thangs.  In the drawing above, there are 4 thangs around the O-atom in water:  2 H-atoms and 2 unshared pairs of electrons.  There are also 4 thangs around the N-atom in ammonia: 3 H-atoms and 1 unshared pair of electrons.  There are 3  thangs around the B-atom in boron trifluoride, and 3 thangs around the N-atom in the nitrate ion.  It is important to note that the pair of unshared electrons counts as 1 thang, and that an atom counts as 1 thang, whether it has a single, double, or triple bond.  In the drawing above, the O-atom in water has coordination number = 2.  In the other three molecules, the central atom has coordination number = 3.

The number of thangs determines the basic spatial arrangement of the atoms around the central atom, since the thangs try to get as far from each other as possible, while remaining as close as possible to the central atom.  This leads to fairly symmetric arrangements of the thangs.  However, when we determine the structure of the molecules with X-ray or Spectrometric Methods, we see the locations of the atoms but not the electrons.  This leads to a variety of shapes of molecules, and different sets of bond angles around the central atom.

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Coordination Number = 6:
    Coordination numbers greater  than 6 are rarely encountered, so this is the largest number we will consider here.  Placement of six atoms symmetrically about a central atom results in an octahedral arrangement.  The bond between each atom and the central atom is at a 90° angle to the bonds between the central atom and four of the other atoms.
 
 

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Coordination Number = 5
    When there are five atoms and no unshared pairs of electrons around the central atom, they are arranged with three of the atoms in a plane with their bonds at 120° angles, one atom above this plane, and one below it.  The bonds of the last two form 90° angles with those of the first three.  This shape is called a trigonal bipyramid.
 

The coordination number of 5 may also occur if there are 5 atoms and 1 unshared pair of electrons about the central atom.  These six thangs form an octahedral arrangement, but one of the atoms has been replaced by the (invisible) electron pair.  This arrangement is called a square pyramid.  All of the bond angles are 90°.

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Coodination Number = 4
    Four atoms around a central atom with no unshared pairs of electrons are arranged in the shape of a tetrahedron, with all of the bonds forming 109° angles with each other.  This is a difficult shape to visualize, but it is like three of the atoms form a tripod for the central atom and the fourth atom sticks straight up.

    If there are 4 atoms and 1 unshared pair of electrons around the central atom, these five thangs form the shape of a trigonal bipyramid in which one of the atoms has been replaced by the (invisible) electron pair.  One of the positions in the plane of three atoms generally has the least repulsion from the other positions, and this is favored by the electron pair.  This results in a seesaw arrangement with the bonds of two of the atoms at a 120° angle, and the other two atoms at 90° to these.

    If there are 4 atoms and 2 unshared pairs of electrons around the central atom, these six thangs form the shape of a octahedron in which two of the atoms have been replaced by the (invisible) electron pairs, at 180° to each other.  This gives a square planar arrangement with the bonds forming 90° angles.

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Coodination Number = 3
    Three atoms around a central atom with no unshared pairs of electrons gives a flat triangular shape, a trigonal planar arrangement, with all of the bonds forming angles of 120°.  Note that there are four bonds (a double bond and two single bonds) around the S-atom in sulfur trioxide, but only three thangs.

    In ammonia, there are 3 atoms and 1 unshared pair of electrons around the central atom, and these four thangs form the shape of a tetrahedron in which one of the atoms has been replaced by the (invisible) electron pair.  One of the positions in the plane of three atoms generally has the least repulsion from the other positions, and this is favored by the electron pair.  This results in a trigonal pyramid arrangement with the bonds approximately 109° to each other.

    If there are 3 atoms and 2 unshared pairs of electrons around the central atom, these five thangs form the shape of a trigonal bipyramid in which two of the atoms have been replaced by the (invisible) electron pairs at 120° to each other.  This gives a T-shape arrangement with the bonds forming 90° angles.

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Coodination Number = 2
    If there are no unshared electrons, two atoms and a central atom line up linearly with a 180° bond angle as in the carbon dioxide molecule.  If there is one unshared pair of electrons, the three thangs take the trigonal planar arrangement so the molecule has a bent shape with a 120° bond angle as in the ozone molecule.  Two unshared pairs and two atoms give the tetrahedral arrangement of four thangs, so the water molecule has a bent shape with a 109° bond angle.
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