Molecular Formula and Structure

8/3/2019 Molecular Formula and Structure

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Formula and Structure

The Lewis Structure

A Lewis structure represents the connection of atoms and the distribution of valence electrons in

a chemical species. From the distribution of electrons in the Lewis structure, the threedimensional organization of atoms in the species can be predicted using valence shell electronpair repulsion (VSEPR) theory. Additionally the orbitals each atom in the species uses for

bonding can be ascertained from the Lewis structure. A set of rules to follow to obtain a proper

Lewis structure is first provided followed by a more detailed discussion of these rules. Next a

summary of geometry and hybridization is provided followed by a more detailed discussion ofthese items.

Rules for Lewis Structures

A Lewis structure consists of the electron distribution in a compound and the formal charge oneach atom. The following rules will assist you to draw such structures to represent the electronic

structure of compounds.

1. Determine whether the compound is covalent or ionic. If covalent, treat the entiremolecule. If ionic, treat each ion separately.

2. Determine the total number of valence electrons available to the molecule or ion by (a)

summing the valence electrons of all the atoms in the unit and (b) adding one electron for

each net negative charge or subtracting one electron for each net positive charge. Thendivide the total number of available electrons by 2 to obtain the number of electron pairs

(E.P.) available.

3. Organize the atoms so there is a central atom (usually the least electronegative) surrounded

by ligand (outer) atoms. Note that hydrogen is always a ligand atom, never a central atom.

4. Determine a provisional electron distribution by arranging the electron pairs (E.P.) in the

following manner until all available pairs have been distributed:

(a) One pair between the central atom and each ligand atom.

(b) Three more pairs on each outer atom (except hydrogen, which has no additionalpairs), yielding 4 E.P. (i.e., an octet) around each ligand atom when the bonding

pair is included in the count.

(c) Remaining electron pairs (if any) on the central atom.

5. Calculate the formal charge (F.C.) on all atoms in the species.

(a) Count the total number of bonds. Total = BP (bonding pair)

(b) Count the total number of lone pairs. Single electrons count as 1/2. Total = LP(lone pair)

(c) F.C. = [V] - [BP] - 2 [LP ] , where V = number of valence electrons for the atom.

6. Examine the central atom. If the central atom formal charge is zero or equal to the overall

charge on the species, the provisional electron distribution from (4) is correct. If the centralatom formal charge does not meet this criterion, follow rule 7 to convert the provisional


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structure into the correct structure.

7. Examine the central atom again. If the central atom is from the second (n = 2) row of the

periodic table, follow a). If it is not (all other elements), follow b).(a) To obtain the correct structure, form a multiple bond by sharing an electron pair

form the ligand atom that has the most negative formal charge sequentially until the

central atom has 4 EP (an octet).(b) To obtain the correct structure, form a multiple bond by sharing an electron pair

from the ligand atom that has the most negative formal charge sequentially until theformal charge on the central atom is reduced to zero or two double bonds are

formed.

8. Recalculate the formal charge of each atom to complete the Lewis structure. Note that the

overall charge on the species is equal to the sum of the formal charge on each atom.

Summary of Steric Number, Geometry and Hybridization

Steric number is defined as the number of ligands and lone pairs on an atom provided the atom

has a least two ligands. In the following table, A represents the central atom, B represents aligand atom, E represents a lone pair of electrons, SN represents the steric number for A , EG

represents the electron geometry for A, Hyb. represents the hybridization of A, CN represents

the coordination number of A ( number of ligands) and AG represents the compound's atomgeometry, also called its coordination geometry or molecular geometry.

Summary of Steric Number (SN), Geometry and Hybridization

Cpd SN EG Hyb CN AG Examples

AB2 2 Linear sp 2 Linear BeF2, CO2, CN22-

AB2E 3 Trigonal Planar sp2

2 Bent SO2, NO2-, O3

AB3 3 Trigonal Planar sp2

3 Trigonal Planar BF3, NO3-, CH3

+

AB2E2 4 Tetrahedral sp3

2 Bent H2O, SF2, ClO2-

AB3E 4 Tetrahedral sp3

3 Trigonal Pyramidal NH3, PF3, SO32-

AB4 4 Tetrahedral sp3

4 Tetrahedral BF4-, NH4

+, SO4

2-

AB2E3 5 Trig. Bipyramid dsp3

2 Linear XeF2, I3-

AB3E2 5 Trig.Bipyramid dsp3

3 T shaped ClF3AB4E 5 Trig. Bipyramid dsp

34 Butterfly (Seesaw) SF4, IF4

+

AB5 5 Trig. Bipyramid dsp3 5 Trigonal Bipyramidal PF

AB4E2 6 Octahedral d2sp3 4 Square Planar XeF4, ICl4

-

AB5E 6 Octahedral d2sp3 5 Square Pyramidal BrF5, XeOF4

AB6 6 Octahedral d2sp3 6 Octahedral SF6


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A central atom bonded to only one ligand (connected to only one atom) has a steric number of

one regardless of the number of lone pairs it has. For these systems, the central atom is not

hybridized and almost always uses a p orbital for bonding to the ligand. The exception is thegroup 1 elements which use an s orbital and hydrogen which can only use an s orbital for

bonding. Note: Hydrogen is always a ligand except when bonded to itself.

Terminal Atoms (Bonded to only one atom)

Cpd SN EG Hyb. CN AG Examples

ABE3 1 Linear p 1 Linear F2, FCl, HI, O22-

ABE2 1 Linear p 1 Linear O2, SO, NO-

ABE 1 Linear p 1 Linear CO, NO+, CN

-,

AB 1 Linear s 1 Linear LiH, LiF, H2

Note: A ligand atom (F, O, N, Cl, S etc.) bonded only to a central atom is not hybridized and willuse a p orbital (not its s orbital) for bonding. The s orbital will hold the first lone pair of the

ligand atom. The exception is the hydrogen atom which will use its s orbital since it does not

have a valence p orbital. Group 1 metals normally aren't ligands.

Discussion of the Lewis Rules

Covalent and Ionic Compounds

In a covalent compound the atoms are held together in a single unit, a molecule. Apply the Lewis

rules to the molecule as an entity. In ionic compounds there is a cation (positively charged ion)

and an anion (negatively charged ion). Apply the Lewis rules separately to the cation and theanion. Learning to recognize the formula and charge of common cations and anions in order to

identify ionic compounds.

Counting Valence Electrons

Counting valence electrons starts with the chemical formula. The subscript specifies the number

of each atom present in the formula unit. A common error is not counting an atom each time itappears in the formula. Each atom contributes its valence electrons every time it occurs in theformula.

Look at the number at the top of the column of the periodic table in which an atom resides to find

the number of valence electrons it contributes. If the number is a Roman Numeral, that is thenumber of electrons provided. In newer versions of the periodic table, the number is an arabic

number and the last digit specifies the number of electrons contributed.


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For example, P has 5 valence electrons and its column is labeled Group V or Group 15 (newform). Ca in the column labeled Group 2 or Group II has 2 valence electrons while S in Group 16

or Group VI has 6 valence electrons.

For ions the charge also must be taken into account. The superscript specifies the number ofunits of charge. The sign indicates the type of charge, positive or negative.

For each unit of negative charge an electron is added. For each unit of positive charge an electronis subtracted. For example 3- means three electrons have been gained while 2+ means two

electrons have been lost.

SF4 CO32- NH4

+

S 1 6 = 6 C 1 4 = 4 N 1 5 = 5

F 4 7 = 28 O 3 6 = 18 H 4 1 = 4

Charge 0 = 0 Charge 2 1 = 2 Charge 1 1 = -1

Total Electrons 34 Total Electrons 24 Total Electrons 8

Electron Pairs 17 Electrons Pairs 12 Electron Pairs 4

Classifying/Organizing the Atoms in the Formula

A simple distinction can be made between the atoms in any chemical structure. An atom can be

connected to only one other atom, in which case it is called a terminal atom or an atom can beconnected to more than one atom in which case it is called a central atom.

Many chemical formulas can be classified into an ABn format in which a single central atom A

is surrounded by other atoms or groups of atoms labeled B. The surrounding atoms or groups

of atoms are called ligands. The number of ligands n determines the coordination number. Forcommon molecules values of n range from 1 through 6.

Rules which will always identify the correct central atom, ligands and coordination number

(value of n) from a simple formula do not exist; however there are guidelines which produce the

correct result for most compounds treated in general and introductory chemistry.

The central atom is identified either directly or by elimination. Identifying by elimination

requires recognizing atoms which normally are terminal atoms (ligands) and hence not likely to

be the central atom.1. The hydrogen atom is always a ligand (terminal atom) and is never a central atom. For

example, O, N and Cl are the central atoms for the species H2O, NH3 and HCl.

2. The central atom is usually the least electronegative atom and normally is present only


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once in the formula. For example, S, B, P, Cl, O and C respectively are the central atoms

of the following species SCl2, BF3, PCl5, ClO2, OF2.and H2CO

3. The common ligand groups OH, NH2 and CH3 may replace one or more ligand atoms. In aligand group, normally only one of the atoms, the major ligand atom is directly connected

to the central atom; the remaining atoms of the ligand group are in turn connected to that

atom. For example B, N, and P are the central atoms for the following compounds B(OH) 3,N(CH3)3 and P(NH2)3. The O, C and N atoms, which are the major atoms of theirrespective ligand groups, are directly connected to the central atom. The hydrogen atoms

in turn are connected to the O,C and N atoms not the central atom.

4. If the likely central atom is present twice in the formula, use it once as the central atom

and then as a ligand that is directly connected to the central atom. For example chose one Fas the central atom in F2 and the other F as a ligand. In the case of H2NNH2, chose one N

as the central atom and select two hydrogen atoms and the remaining NH2 group as the

ligands. This works as well for the simple organic molecules, HCCH, H2CCH2 and

H3CCH3.

5. The guidelines work for simple formulas and even more effectively when used withformulas which convey information about the ligands, especially ligand groups. For

example sulfuric acid can be represented as H2SO4 or (HO)2SO2. Acetic acid can be

represented as C2H4O2, HC2H3O2, CH3CO2H, CH3COOH, or CH3C(O)OH. Each formula

provides more information about the organization and connections between the atoms. Theparenthesis around the O in the last formula for acetic acid carries special meaning - that

the specific oxygen atom within the parenthesis is directly connected to the proceeding

carbon atom but not connected to the OH that follows it. The last representation makes itclear that there are three ligands connected to the central carbon atom: CH 3, OH and O.

Distributing Electrons

A chemical bond is normally formed by pairs of electrons. Nonbonding electrons also are

generally associated in pairs. The overwhelming majority of chemical species have an evennumber of electrons; only a few have an odd number. For bookkeeping purposes we will divide

the number of valences electrons in a molecule by two to determine the number of electron pairs.

For the odd numbered cases, the electrons are still counted as pairs but the left over electron (thehalf pair) is distributed last.

An electron pair may end up in one of two positions. It may be placed between two atoms, in

which case it holds the atoms together and is called a bond (BP) or it may be placed on a single

atom in which case it is called a lone pair (LP). The term lone pair arises because the atomhas the electron pair to itself alone as opposed to sharing it with another atom as a bond.

The rules for distributing electrons depend on the premise that a terminal atom (ligand) willalways have four electron pairs. These electron pairs may be a combination of bonding or lone

pairs. The hydrogen atom ligand is a special case since it only takes a single bonding pair and

does not receive any lone pairs. The premise of an octet also applies to the major atom of aligand group. Again the electron pairs may be a combination of bonding or lone pairs. In addition


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to the electron pair connecting the central atom, the C atom in CH3 has three bonding pair

connecting the three H atoms, while the N atom in NH2 has a lone pair and two bonding pairconnecting the two H atoms and the O atom in OH has two lone pair and one bonding pair

connecting the H atom. While octet requirement for a terminal atom is almost without exception,

the central atom does not have the same requirement. Compounds in which the central atoms has

an octet are common but in many others the central atom has more than an octet of electrons andin some compounds less.

Electron pairs are distributed until they run out in the following sequence:A. Place one electron pair between the central atom and each ligand atom or between the

central atom and the connecting atom of the ligand group.

B. Except for hydrogen atom, place three more electron pairs around the ligand atom or the

connecting atom of the ligand group. The additional pairs are lone pairs for a ligand atom

and may be either bonding and/or lone pairs for the connecting atom of a ligand group asappropriate. A hydrogen atom ligand receives only the bonding pair with the central atom

(from step A) and does not receive additional pairs.

C. Any remaining electron pairs or a single electron (in the case of odd electron species) areplaced on the central atom.

This distribution of electrons produces what is called a provisional Lewis structure. Theprovisional structure may be the correct Lewis structure or it may need to be modified to obtain

the correct structure. Evaluating the provisional structure depends on the formal charges of the

atoms.

Calculating Formal Charges

The formal charge concept is an attempt to compare the free state of an atom to its condition in a

molecule. In its free state the atom has a certain number of valence electrons, V. The formalcharge equation is designed to determine whether the atom has gained or lost electrons compared

the free state when it is represented in a molecule with a particular distribution of bonding and

lone pair electrons. The formal charge of an atom changes with different bonding and lone pairarrangements. If the formal charge on the atom is positive it has lost some electrons relative to

the free atom and if it is negative it has gained some electrons. Actual relative charges on atoms

in molecules are much smaller than the equation suggests; hence the term formal. Formalcharges are suggestive of trends not actual values. Though simply in concept, formal charges

were one of the first ways of estimating relative charges in molecules.

The evaluation of the provisional Lewis structure depends only on the formal charge of thecentral atom but its modification to arrive at the correct structure may depend on the formal

charge of the ligand atoms; hence the formal charge on each atom is calculated. The formal

charge must be evaluated for each atom in the structure (not just each element) because the same

element may have different arrangements of BP and LP and therefore a different formal charge.The formal charge on an atom depends on the number of valence electrons for that atom and the

number of lone pairs and bonding pairs on the atom in the structure.


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In the formula, V is the number of valence electrons the atom has, LP is the number of lone pairsthe atom has in the Lewis Structure, and BP is the number of bonding pairs the atom has in the

Lewis Structure. A single electron counts as 1/2 pair.

A simple test can be used to determine if this formula has been consistently applied: The sum ofthe formal charges on each of the atoms in the structure should equal the overall charge on the

chemical formula. In the case of neutral compounds this is zero and in the case of ionic species it

is equal to the sign and magnitude of the charge.

Note: This test only tells you if the formal charge equation has been applied properly. It does not

mean the structure is necessarily correct. Even incorrect structures meet this test if the formal

charge equation is properly applied.

Testing the Provisional Structure

The formal charge on the central atom of the provisional structure indicates if the provisionalstructure is the correct Lewis structure or needs to be modified.

The provisional structure is the correct Lewis Structure if either case applies.1. The formal charge on the central atom equals the charge on the formula

2. The formal charge on the central atom is negative.

What correct means is that the electron arrangement has the lowest energy compared to otherpossible electron arrangements.

Modifying The Provisional Structure

If the provisional structure is not correct and has to be modified, the modification procedure

involves making a double bond by sharing a lone electron pair on the ligand atom with the

central atom. The extent to which this step is repeated is determined by the row of the periodictable in which the central atom resides. If the central atom is from the second row of the periodic

table, the correct structure is obtained when the central atom achieves an octet (or a septet for

odd electron species) of electrons. If the central atom is from the third through seventh row of the

periodic table, the correct Lewis Structure is obtained when the central atom formal charge is

zero or if two double bonds are formed.

To obtain the correct Lewis Structure from an incorrect provisional structure for

A. A central atom from the 2nd row of the periodic chart (Li through F)Share an electron pair from the ligand atom with the most negative formal charge to form

a double bond. Continue this process until the central atom achieves an octet (or a septet

in the case of an odd electron species).


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B. A central atom from the other rows of the periodic chart (3rd through 7th rows).

Share an electron pair from the ligand atom with the most negative formal charge to forma double bond. Continue this process until the central atom has a formal charge of zero or

until two double bonds are formed.

Note: The rules used to determine if the correct Lewis Structure is achieved when modifying the

provisional structure are different than the rules used to determine if the provisional structure isthe correct Lewis structure.

The rule that the ligand atom with the largest negative formal charge should be chosen at each

step to share an electron pair with the central atom has important implications. In practice thismeans that multiple bonds normally involve only single ligand atoms. The connecting atom of a

ligand group such as the O in OH or the N in NH2 normally will not take part in a multiple bond

because it does not have the most negative formal charge. Additionally, this guideline favors

forming two double bonds with two equivalent ligands rather than a triple bond with one ofthem. In the formation of the multiple bond the value of the formal charge on the ligand is

increased by one (made less negative i.e. more positive) and the value of the formal charge on

the central atom is decreased by one (made less positive i.e. more negative). As a result, triplebonds normally are observed only in diatomic systems where no other choice exists.

Resonance

For many molecules and ions the actual electron distribution cannot be represented by a singleLewis structure but two or more Lewis structures are needed to represent it. The actual electron

distribution is considered to be a weighted composite of these Lewis structures and is referred to

as resonance hybrid of the contributing Lewis structures that, correspondingly, are called

resonance structures.

Generally, molecules or ions that have Lewis structures which contain multiple bonds are the

ones that require multiple Lewis structures (resonance structures) to represent the actual electrondistribution. The resonance structures arise directly when there is a choice between equivalent

ligands (same atom, same formal charge) to use in carrying out the modification process in step

5.

For example, the provisional structure for CO32-

contains three equivalent oxygen atoms of

minus one formal charge that can be used to form the double bond and yield the correct structure.Consequently three Lewis structures can be generated, each with one carbon oxygen double bond

but with that bond being formed between carbon and each of the three oxygen atoms. These

three structures are energetically equivalent and the actual electron distribution in CO32-

is aresonance hybrid of the three. The carbon oxygen bonds of CO3

2-are not single bonds and have

multiple bond character but also are not true double bonds. They are best represented as a

resonance hybrid of the three contributing resonance structures.

Discussion of VSEPR Theory


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The Lewis structure of a molecule is required to predict its geometry . Valence shell electron pair

repulsion (VSEPR) theory is used with the Lewis structure to predict the geometric arrangementof the bonding pair and lone pair sets of electrons about the central atom. Because electrons are

negatively charged, the bonding and lone pair sets of electrons on the central atom will attempt

to maximize their separation For a given number of electron pair sets, there is only a single

geometric arrangement which maximizes their separation and minimizes their repulsion; hencethere is only a single electron geometry. Knowing the electron geometry allows the prediction of

the molecular geometry - the arrangement of ligands around the central atom - from the choices

that exist for a given coordination number.

Possible Coordination Geometries

In an ABn system for a given value of n, a limited number of coordination geometries have been

observed experimentally. Each is summarized for n from 1 through 6.

A

B

Diatomic systems - systems with only one ligand - must be linear.

AB2

A two ligand system can be linear or angular (bent). Bent systems commonly haveangle values which are near either 120 or 109. A few examples of bent AB2

molecules have angles near 90.

AB3

A three ligand system can have one of three coordination geometries - trigonal planar,trigonal pyramidal or T-shaped. The angles between the ligands for the trigonal planargeometry are 120 while for the trigonal pyramidal geometry they are 109. For the T-

shaped geometry, two angles are 90 and one is 180.


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AB4

A four coordinate system has three possible coordination geometries - tetrahedral,square planar and butterfly. Note the butterfly structure is also called Seesaw. The

bond angles for the tetrahedral geometry are 109 and for the square planar geometry90. The butterfly (Seesaw) geometry has three types of bond angles with values - 90,

120 and 180.

AB5

A five coordinate system can have one of two coordination geometries - trigonalbipyramidal and square pyramidal. The trigonal bipyramidal geometry has three types

of bond angles with values - 90,120 and 180. The square pyramidal geometry has

two values for the bond angles - 90 and 180.


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AB6

Six coordinate systems have one common geometry, octahedral. Bond angles are 90and 180.

Steric Number and Electron Geometry

The steric number (SN) is the number of sets of bonding and lone pair electrons about the central

atom of the Lewis structure. The electron geometry for a given steric number is the arrangement

which maximizes the separation of the sets of electrons and thus minimizes the repulsionbetween the sets.

A lone pair and a bonding pair each are a single set. Double and triple bonds even though they

contain two and three pair of electrons respectively also each act as a single set.


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Because single, double or triple bonds all act as single set and are connected to a ligand, the

simplest way to determine the steric number is to count the ligands connected to the central atomplus the lone pairs on the central atom.

Note: This relationship only applies to atoms that are bonded to more than one atom. An atombonded to only one atom can only have a linear attachment.

The steric number will identify the geometrical arrangement of the sets of electrons about thecentral atom. This is called the electron geometry. Only a single electron geometry exists that

maximizes the separation of the sets of electrons for each steric number.

For a SN of two, the electron sets are directed oppositely and are 180 apart.

For a SN of three the electron sets are directed toward the vertices of a trigonal plane and are

120 apart.

For a SN of four, the electron sets are directed toward the vertices of a tetrahedron and are 109

apart.

For a SN of five, the electron sets are directed toward the vertices of a trigonal bipyramid. The

trigonal bipyramid has two types of vertices, three equatorial vertices and two apical vertices.

The apical sites are 90 apart from the three equatorial sites and 180 apart from each other. Theequatorial sites are 120 apart from the other two equatorial sites and 90 apart from the two

apical sites.

For a SN of six, the electron sets are directed toward the vertices of an octahedron and are 90

apart.

Summary of Electron Geometry

SN Electron Geometries

1 Linear

2 Linear

3 Trigonal planar

4 Tetrahedral

5 Trigonal bipyramidal

6 Octahedral

The Molecular Geometry


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The molecular geometry is the arrangement of the ligands around the central atom. It is derived

from the electron geometry and the number of lone pairs on the central atom. A system thatcontains only two atoms (AB) must be linear regardless of the number of electrons on the central

atom.

For an SN of 2 with two ligands (AB2), the molecular geometry is linear.

For an SN of 3 with three ligands(AB3), the geometry is trigonal planar. For two ligands and a

lone pair(AB2E), the molecular geometry is bent.

For an SN of 4 with four ligands (AB4), the molecular geometry is tetrahedral; for three ligands

and a lone pair (AB3E), the molecular geometry is trigonal pyramidal; and for two ligands andtwo lone pairs (AB2E2), the molecular geometry is bent.


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For an SN of 5 with five ligands (AB5), the molecular geometry is trigonal bipyramidal; for four

ligands and a lone pair (AB4E), the molecular geometry is butterfly (Seesaw); for three ligandsand two long pair (AB3E2), the molecular geometry is T-shaped; for two ligands and three long

pair (AB2E

3), the molecular geometry is linear.

For an SN of 6 with six ligands (AB6), the molecular geometry is octahedral; for five ligands and

a lone pair (AB5E), the molecular geometry is square pyramidal; and for four ligands and twolone pair (AB4E2), the molecular geometry is square planar.


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The size of the electron sets is important in determining the coordination geometry for SN of 5

and 6. The largest electron sets (those that will repel the most) will occupy sites that maximizeseparation. The size or domain of the sets is in the order - lone pair > bond pair. Within bonding

sets the size domain is triple bond > double bond > single bond. Consequently repulsion between

electron sets follows the sequence - lone pair - lone pair > lone pair - bond pair > bond pair -bond pair. Lone pair electrons will occupy sites that first maximize their separation and secondly

their separation from multiple bonds.

Of the two sites for an SN of 5, the equatorial site is the one that minimizes repulsion. Lone pairsets will reside at the equatorial position in preference to the apical position. Up to three lone pair

electrons will occupy the equatorial positions. The butterfly (Seesaw), T-shaped and lineargeometries result for the AB4E, AB3E2 and AB2E3 cases respectively.

For an SN of six with two lone pair sets, these sets will attempt to maximize separation and will

orient themselves oppositely or trans with an angle of 180. Analogously a multiple bond and

lone pair or two multiple bonds will have the same trans orientation.

Distortion of structures and angles from ideal also can be deduced using the size of the respective

electron sets. As a broad rule whenever possible, the electron geometry (and hence moleculargeometry) will distort slightly to maximize electron set separation (minimize repulsion). For

example, the bond angles for AB3E and AB2E2 systems are usually less than the ideal angle of

109 in order to minimize repulsions between the lone pair and the bond pairs.

Copyright 2007 John Wiley & Sons, Inc. All rights reserved.

Molecular Formula and Structure

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