Strand 1  Matter and Chemical Bonding
SCH 3U Strand 1  Matter and Chemical Bonding:  Bonding Title

Lewis Symbols or Diagrams

    Chemical identity is determined by the number of protons within the nucleus of an atom, atomic mass is determined by the number of protons and neutrons within the nucleus and chemical bonding is largely determined by the number of outermost or valence electrons within the atom.  Thus, electrons in completely filled energy levels are mostly ignored when considering chemical properties.  Simplified Bohr diagrams which only consider electrons in outer energy levels are called Lewis Symbols.  A Lewis Symbol consists of the element symbol surrounded by "dots" to represent the number of electrons in the outer energy level as represented by a Bohr Diagram.  In a Lewis symbol, the inner closed shells of electrons can be considered as included in chemical symbol for the element, and the outer shell or valence electrons are represented by dots.  The dots are placed in four groups of one or two electrons each, with 8 electrons representing a closed shell or noble gas configuration. Lewis diagrams are useful for visualizing both ionic and covalent bonds.  The number of valence electrons for an atom is often, but not always, determined from the position of that element on the periodic table. Consider the following examples:

Bohr-Rutherford to Lewis

    Thus, we would see that each family has the same Lewis Symbols configuration and each element in a period has one more electron/dot than the previous element for representative elements.

Period 2

Representative Lewis Atoms

    As you can see this correlates with the Bohr-Rutherford diagrams and electronic configurations as well.

Electronic Configurations

    However, we must notice that the ground state of some of the elements (Be, B, C) is not the same as the bonding state.  In other words, the element in free space in it's minimum energy configuration (ground state) is not necessarily the same as the element in a molecule.  To reconfigure an atom into its 'normal valence' state, we can split the non-bonding pair (lone pair) of electrons into two unpaired electrons.  In the case of Be, we split the two 2s electrons into two unpaired electrons (into orbitals not necessarily called 2s and 2p but we'll get to that later).  Similarly, we can expand the valence of B and C by splitting their lone pairs into single electrons.  In each of these cases, we increase the "valence" by 2 for each lone pair we split up. We can do this because there are a maximum of 4 orbitals at the n=2 quantum level into which we can put electrons with minimal expense energy-wise.  If we tried to split the lone pair on Nitrogen into two unpaired electrons we would run into the limit of the number of orbitals.  N, has only 4 orbitals (places) to hold electrons.  The normal ground state of N already has at least 1 electron in each of the four orbitals.  If we tried splitting the lone pair we would have no place to put the extra electron without moving it to an n=3 orbital.  That would cost too much energy.

    Thus, we represent the ground state in a unique manner to convey the precise orbital placement of valence electrons.

Ground State Lewis Configuarion

    Note that the actual order beyond the s orbital is arbitrary other than electrons must be placed singly before pairing.  So the order of 3, 4 and 5 does not matter as long as 6,7 and 8 are not filled before 5.  Once at atom enters into bonding, these positions are not followed as hybridization and promotions have priority not to mention that atoms re-orientate themselves to align properly for bonding.

    Lewis diagrams are much more convenient to demonstrate bonding than electronic configurations or orbital box diagrams.  Consider the orbital box diagrams for the following bonded atoms:

CH4 (more on this configuration later).




    As you can see these, diagrams convey a lot of information, but are rather cumbersome and most of the electrons are not involved in the bonding.  Lewis diagrams simplify and focus attention of the relevant atomic interactions.  There are two types of bonds to consider, one involving electron transfer (loss and gain) and the other involving a compromise or sharing of electrons.

Ionic Bonding

    Typically this involves that bonding of a metal with a non-metal atom.  Since metals have very low attraction for their outer electrons while non-metals have such a high affinity for outer electrons, the non-metals successfully steal outer electrons from metal atoms.  Thus, there is a transfer of electrons from one atom to another resulting in the formation of positive and negative charges.  The conditions for bonds are that the total charge is zero and that each atom must have a noble gas electron configuration.  Consider some examples:

Ionic Bonding

    In order to illustrate the actual bonding that took place, electron transfers are usually conveyed. 

Bohr-Rutherford Electron Transfer

Lewis Bonding of NaCl

    Likewise, other bonds could be shown:

Lewis Bonding of Mg and O

    The only force acting within this chemical bond is the force of attraction between charged particles.  This attraction lacks definitive direction in that it acts in every direction.  As a result ionic solids tend to be crystals of numerous ions and when placed in water, the ions easily attract to the polar water molecules and the solid breaks apart or dissolves.  Notice that for each ion, the result is a full, stable octet, that is the atoms have not obtained the electronic configuration of a noble gas.  Typically this means 8 outer electrons, but actually it means full outer orbitals.

Covalent  Bonding

    In the idealized covalent bond, two atoms share a pair of electrons, closing the shell for each of them.  The atoms share a pair of electrons, and that pair is referred to as a bonding pair.  The pairs of electrons which do not participate in the bond have traditionally been called "lone pairs".  A single bond can be represented by the two dots of the bonding pair, or by a single line which represents that pair.  The single line representation for a bond is commonly used in drawing Lewis structures for molecules. 

Covalent Bonding

    Sometimes it is easier to visualize how the bonding took place if the bonding pairs of electrons are joined.

Lewis Bonding of H and Cl

    The actual chemical bond formed is a permanent connection resulting in a new particle.  The shape of the molecule is determined by the number of valence electrons present (more on that later).

Single Lewis Bonds

    The actual bond itself is really due to an overlap of the valence electrons resulting in a new orbital configuration.

Overlapping Orbitals

    The relative strength of the nucleus of each atom involved in the bonding determines how far apart the atoms remain once the overlap has taken place.  This distance is referred to as the bond length.

Bond Length

    The formation of the bond is determined by the interplay of the attractive forces expressed between the nucleus of one atom and the outer electrons of the other.  However, as the atoms approach one another, the forces of repulsion between the outer electrons and nuclei of each atom start to force the atoms apart.  When the force of repulsion equals the force of attraction, the bond forms.

Energy of Bonding

    Or a simpler version would be:

Bonding Forces

    Lewis symbols and Lewis diagrams can be used to describe multiple bonds,.

Multiple Lewis Bonds

    Electrons are typically not shared equally within a covalent bond as one atom may have a stronger hold on the shared pair of electrons than the other atom causing the shared pair of electrons to orbit closer to that stronger atom for a larger percentage of time.  Electronegativity is a measure of the tendency of an atom to attract a bonding pair of electrons.  The Pauling scale is the most commonly used. Fluorine (the most electronegative element) is assigned a value of 4.0, and values range down to cesium and francium which are the least electronegative at 0.7.  The most electronegative element is fluorine.  If you remember that fact, everything becomes easy, because electronegativity must always increase towards fluorine in the Periodic Table.  This simplification ignores the noble gases. Historically this is because they were believed not to form bonds - and if they don't form bonds, they can't have an electronegativity value.  Even now that we know that some of them do form bonds, data sources still don't quote electronegativity values for them.

Electronegativity Trends

    The attraction that a bonding pair of electrons feels for a particular nucleus depends on the number of protons in the nucleus; the distance from the nucleus; and the amount of screening by inner electrons.  As you go across a period the electronegativity increases because the number of charges on the nucleus increases. That attracts the bonding pair of electrons more strongly.  As you go down a group, electronegativity decreases because the bonding pair of electrons is increasingly distant from the attraction of the nucleus. 

    Consider a bond between two atoms, A and B. 

    Each atom may be forming other bonds as well as the one shown - but these are irrelevant to the argument.  If the atoms are equally electronegative, both have the same tendency to attract the bonding pair of electrons, and so it will be found on average half way between the two atoms.  In actuality, the shared pair of electrons move back and forth to some degree, but on average they are equally distributed.  To get a bond like this, A and B would usually have to be the same atom. You will find this sort of bond in, for example, H2 or Cl2 molecules.  This sort of bond could be thought of as being a "pure" covalent bond - where the electrons are shared evenly between the two atoms.

    Consider now, what happens if B is slightly more electronegative than A.  B will attract the electron pair rather more than A does.

    That means that the B end of the bond has more than its fair share of electron density and so becomes slightly negative.  At the same time, the A end (rather short of electrons) becomes slightly positive. In the diagram, "" (read as "delta") means "slightly" - so + means "slightly positive".

    The implication of all this is that there is no clear-cut division between covalent and ionic bonds. I n a pure covalent bond, the electrons are held on average exactly half way between the atoms.  In a polar bond, the electrons have been dragged slightly towards one end.  How far does this dragging have to go before the bond counts as ionic?  There is no real answer to that. You normally think of sodium chloride as being a typically ionic solid, but even here the sodium hasn't completely lost control of its electron.  Because of the properties of sodium chloride, however, we tend to count it as if it were purely ionic.

      For atoms that share electrons equally, there is no percent ionic character to the bond.  In other words, the percent ionic character is 0.  This means that the shared pair of electrons is not distributed closer to one atom on average.  Atoms that share an electron pair unequally will have a certain degree of ionic character to its bond.  To determine the percent ionic character of a bond, you will need to know the electronegativities of the atoms involved.  Then calculate the difference in the electronegativities. This difference is then translated to a percent ionic character by using a chart or graph as a reference.  For example, an electronegativity difference of 1.7 is said to be 51% ionic.  Thus any difference in electronegativity between two atoms exceeding 1.7 is considered enough ionic character to indicate that one of the atoms is likely to hold the shared pair more often than 50% of the time making this bond ionic greater than n50% of the time.  Some texts state 2.0 is the critical division between polar covalent and ionic.  This inconsistency should be understandable since numerous bonds have electronegativity differences greater than 1.7 yet remain polar instead of ionic due to other factors.  The key factor is that this scale represents the likelihood of acting ionically, not that actuality.   It is a predictive scale only.  Obviously bonds with electronegativity differences around 1.5 to 2.0 are going to sway back and forth from ionic to polar covalent.

Percent Ionic Character

    When the electronegativity difference is only 0.4, the bond is only 4% ionic in character which means that there is only a 4% chance that the stronger atom will have the electrons closer to itself than the other atom on average.  Worded another way, 4% of the time, the electrons are not equally distributed.  Many texts state that an electronegativity difference of 0 between atoms is the only pure covalent bond.  However, common sense would indicate that this is a gross assumption.  Many pure covalent bonds exist that have slight ionic character so numerous sources identify any electronegativity under 0.4 as being pure covalent because there is still a 96% chance of the electrons being shared equally.  In science 95% is considered an excellent confidence level.  That is, this is the mark that someone can be sure is essentially the same as 100% since chance will vary results slightly.  Thus polar covalent sharing of electrons is considered when the electronegativity difference exceeds 0.4 and is under 1.7.

Intermolecular Bonding

    Intramolecular forces of attraction act within a compound or molecule to hold that molecule together.  These forces of attraction result in the typical bonds identified in chemistry: ionic, covalent and polar covalent.  It has been found that compounds and molecules exist more readily as solids and liquids, than as gases indicating that there must be a force of attraction between the particles.  These intermolecular forces of attraction account for a considerably array of chemical and physical properties of these substances. There are two types of intermolecular forces of attraction.

1. Ionic Forces of Attraction

    In ionic compounds, the ions do not direct their force of attraction between each other, but rather attract other ions in all directions.  For example Na+ is actually surrounded by six chloride ions.  Each chloride ion is likewise surrounded by six sodium ions.  Due to this strong intermolecular bond, ionic solids have the following properties which all become more pronounced as the ionic bond becomes stronger and/or the ions involved become smaller in size.

  • They have a high melting point since it is very difficult to pull one atom away from another. 
  • Solid ionic compounds do not conduct electricity since there are no free ions to pass along electrons.
  • Liquid ionic compounds conduct electricity because the ions are attracted to polar water which then separates and frees the ions from the lattice collective.
  • Solid ionic compounds are typically odourless since the numerous attractions prevent any ions from leaving the lattice collective.
  • Solid ionic compounds tend to fracture when struck since it takes considerable force to separate ions from the lattice structure. to conduct electricity. To show electrical conductivity, the ions in the mixture would need to be free to move. Without dissolving in water, the ions are still fixed in their crystal lattice positions. 
2. Van der Waals Forces of Attraction

    These forces of attraction are typically only 1% of the strength of a covalent bond, but they can range from 0.001-15% of the strength of a covalent bond.   Individually they are weak, but because they usually so numerous, they are collectively strong. 

   Water is the only substance we routinely encounter as a solid, a liquid, and a gas. At low temperatures, it is a solid in which the individual molecules are locked into a rigid structure.  As we raise the temperature, the average kinetic energy of the molecules increases, which increases the rate at which these molecules move.  The intramolecular bonds that hold the atoms in H2O molecules together are almost 25 times as strong as the intermolecular bonds between water molecules.  (It takes 464 kJ/mol to break the H--O bonds within a water molecule and only 19 kJ/mol to break the bonds between water molecules.)

    All motion disrupt the bonds between water molecules.  As the system becomes warmer, the thermal energy of the water molecules eventually becomes too large to allow these molecules to be locked into the rigid structure of ice.  At this point, the solid melts to form a liquid in which intermolecular bonds are constantly broken and reformed as the molecules move through the liquid.  Eventually, the thermal energy of the water molecules becomes so large that they move too rapidly to form intermolecular bonds and the liquid boils to form a gas in which each particle moves more or less randomly through space.  The difference between solids and liquids, or liquids and gases, is therefore based on a competition between the strength of intermolecular bonds and the thermal energy of the system.  At a given temperature, substances that contain strong intermolecular bonds are more likely to be solids.  For a given intermolecular bond strength, the higher the temperature, the more likely the substance will be a gas.  The kinetic theory assumes that there is no force of attraction between the particles in a gas.  If this assumption were correct, gases would never condense to form liquids and solids at low temperatures.  In 1873 the Dutch physicist Johannes van der Waals derived an equation that not only included the force of attraction between gas particles but also corrected for the fact that the volume of these particles becomes a significant fraction of the total volume of the gas at high pressures.  The van der Waals equation is used today to give a better fit to the experimental data of real gases than can be obtained with the ideal gas equation. But that wasn't van der Waals's goal.  He was trying to develop a model that would explain the behavior of liquids by including terms that reflected the size of the atoms or molecules in the liquid and the strength of the bonds between these atoms or molecules.  The weak intermolecular bonds in liquids and solids are therefore often called van der Waals forces. 

There are two main types of Van der Waals forces. 

a) London Dispersion Forces (LDF) 

    These are extremely weak forces of attraction between instantaneous dipoles called an inductive dipole which is created by a momentary unequal distribution of electrons within one atom of a molecule.  Thus, due to the random motion of electrons around atoms, atoms can have very slight partial charges.  Imagine if more electrons are orbiting on one side of an atom than another, this would create slight partial charges.  This force of attraction is present in all molecules but is the only force in effect with nonpolar molecules.  The duration or strength of the force increases with the number of electrons and the size of the atoms involved.  These fluctuations in electron density occur constantly, creating an induced dipole-induced dipole force of attraction between pairs of atoms. As might be expected, this force is relatively weak in helium -- only 0.076 kJ/mol.  This explains the fact that helium becomes a liquid at temperatures below 4.2 K.  By itself, a helium atom is perfectly symmetrical.  But movement of the electrons around the nuclei of a pair of neighboring helium atoms can become synchronized so that each atom simultaneously obtains an induced dipole moment. As atoms become larger and/or have more electrons, the number of inductive dipoles increases.

Helium LDF

    As you can see below, the larger atoms have more LDF's and as a result have higher boiling points.

Increasing LDF
    The same trend can be seen below, except HF is an exception since this molecule has hydrogen bonding resulting in a very strong intermolecular attraction.
b) Dipole - Dipole Forces:

    Many molecules contain bonds that fall between the extremes of ionic and covalent bonds.  The difference between the electronegativities of the atoms in these molecules is large enough that the electrons aren't shared equally, and yet small enough that the electrons aren't drawn exclusively to one of the atoms to form positive and negative ions.  The bonds in these molecules are said to be polar, because they have positive and negative ends, or poles, and the molecules are often said to have a dipole moment.  HCl molecules, for example, have a dipole moment because the hydrogen atom has a slight positive charge and the chlorine atom has a slight negative charge.  Because of the force of attraction between appositely charged particles, there is a small dipole-dipole force of attraction between adjacent HCl molecules. 

HCl Dipole-dipole

    The dipole-dipole interaction in HCl is relatively weak; only 3.3 kJ/mol. (The covalent bonds between the hydrogen and chlorine atoms in HCl are 130 times as strong.)  The force of attraction between HCl molecules is so small that hydrogen chloride boils at -85oC. 

    This dipole-dipole interaction is the attraction of a partial charge of an atom in one molecule for the opposite partial charge on an atom in another molecule.  These forces of attraction are stronger than LDFs because they are permanent and found with polar molecules.  The stronger the dipole the greater the dipole force of attraction. 

    Dipole - dipole forces involving hydrides of F, O, and N appear to be stronger than anticipated.  As a result, this particular dipole-dipole force of attraction is specifically called a hydrogen bond.  Keep in mind that this is not really a bond but the force is collectively strong as there is so many of them that it acts like a bond.  Without hydrogen bonding, water would not be a liquid at room temperature as it would boil at - 80°C.  It also accounts for why ice floats rather than sinking as the water molecules cool they eventually spread out more due to the extensive network of hydrogen bonding. 

Hydrogen Bonding in WaterLattice of Water

    Hydrogen bonding is of extreme importance in biochemistry, i.e. proteins, DNA etc.  People with naturally curly hair have disulphide linkages (S-S between the protein strands), but people with straight hair who blow dry it with a curl are creating curls due to hydrogen bonding and that is why it flattens when it gets wet.

   What would happen if we mixed HCl with argon, which has no dipole moment?  The electrons on an argon atom are distributed homogeneously around the nucleus of the atom.  But these electrons are in constant motion. When an argon atom comes close to a polar HCl molecule, the electrons can shift to one side of the nucleus to produce a very small dipole moment that lasts for only an instant.  By distorting the distribution of electrons around the argon atom, the polar HCl molecule induces a small dipole moment on this atom, which creates a weak dipole-induced dipole force of attraction between the HCl molecule and the Ar atom.  This force is very weak, with a bond energy of about 1 kJ/mol.

    Since all van der Waals attractions are considerably weaker than ionic intermolecular forces of attraction, the properties of non-ionic solids varies and is the pretty much the opposite to those with ionic intermolecular bonds.

  • Low melting points and boiling points because a relatively small amount of energy is required to overcome the weak attractions between covalent molecules, so these compounds melt and boil at much lower temperatures than metallic and ionic compounds do.  In fact, many compounds in this class are liquids or gases at room temperature. 
  • Low enthalpies of fusion and vaporization since less energy is needed to organize the molecules and hold them in a lattice structure.  These properties are usually one or two orders of magnitude smaller than they are for ionic compounds. 
  • Soft or brittle solid forms since it is easy to break their weak intermolecular forces.  This makes the solid form of covalent molecular compounds easy to distort or break and makes them volatile.
  • Poor electrical and thermal conductivity due to the lack of ion formation.
Coordinate Covalent Bonding

    Coordinate covalent or dative bonding is often described in a simple fashion by saying that it involves one atom donating or giving a pair of electrons to another, so that this bonding partner can have a full outer shell.  When electrons are counted up in an electronic dot diagram, this coordinate covalent pair is counted with each of the atoms.  It is similar to borrowing a pair of books from the public library in that the books are given to you and you treat them essentially as if they belonged to you; yet at the same time the books are counted as being part of the library collection.

    If these colourless gases are allowed to mix, a thick white smoke of solid ammonium chloride is formed.

    Ammonium ions, NH4+, are formed by the transfer of a hydrogen ion from the hydrogen chloride to the lone pair of electrons on the ammonia molecule.

Coordinate Bonding

    When the ammonium ion, NH4+, is formed, the fourth hydrogen is attached by a dative covalent bond, because only the hydrogen's nucleus is transferred from the chlorine to the nitrogen. The hydrogen's electron is left behind on the chlorine to form a negative chloride ion.  Once the ammonium ion has been formed it is impossible to tell any difference between the dative covalent and the ordinary covalent bonds. Although the electrons are shown differently in the diagram, there is no difference between them in reality.

    In simple diagrams, a co-ordinate bond is shown by an arrow.  The arrow points from the atom donating the lone pair to the atom accepting it.

Identifying the Coordinate Bond

    However, since the bond is identical to all the other covalent bonds (this is known by comparing the lengths of the bonds), it can be treated as a regular bond and the charge (if any) of the molecule is "experienced" by the entire molecule.  Often, square brackets are drawn around the molecule and the charge is placed outside the brackets.

    Basically, a coordinate covalent bond can occur if there is an atom with lone paris of electrons and another atom with an empty orbital to accept this lone pair of electrons.  Consider the following bonding:

Coordinate Covalent Bonding

    Consider HNO3.  In this case, one of the oxygen atoms can be thought of as attaching to the nitrogen via a co-ordinate bond using the lone pair on the nitrogen atom. 

Coordinate Bonding With Delocalization

    In fact this structure is misleading because it suggests that the two oxygen atoms on the right-hand side of the diagram are joined to the nitrogen in different ways.  Both bonds are actually identical in length and strength, and so the arrangement of the electrons must be identical.  There is no way of showing this using a dots-and-crosses picture.  The bonding involves delocalisation in that the oxygen atom at the top relocated its electrons to create a completely free orbital to allow coordinate covalent bonding.    In a similar fashion carbon monoxide can be thought of as having two ordinary covalent bonds between the carbon and the oxygen plus a co-ordinate bond using a lone pair on the oxygen atom.

Coordinate Covalent Bonding in a Multiple Bond

Molecular Shape

    We use VSEPR theory (Valence Shell Electron Pair Repulsion) to predict the shapes of molecules.  This theory predicts that bonding and non-bonding electron pairs in a molecule will adopt a geometry in which the distance between the electron pairs is maximized from one another in order to minimize the repulsions.  This will result in a molecular geometry with the lowest possible energy.  The theory also allows us to predict which hybridization the central atom takes in bonding to other atoms.

    To start, we need to know the Lewis structure of a molecule.  Then we count how many pairs of electrons (triple bonds are counted as one pair) are around the central atom.  If there are two pairs of electrons, they must be positioned 180° apart from each other and the shape is therefore linear.  Three pairs are best positioned 120° apart and the shape is thus trigonal planar.  Here the shape is referred to include the non-bonding electron pairs.  For the shape of a molecule without counting non-bonding electron pairs, make a normal prediction then look at the molecule without non-bonding electrons showing.  Four pairs of electrons are best positioned as tetrahedral shape. 

Basic VSEPR Shapes

    Handling lone pairs is not as tricky as it might sound since molecular geometries are really just special cases of the parent electronic geometry.  Since the molecular geometry is determined by how many bonding and non-bonding electron groups surround the central atom, the first thing one needs to do is count how many of each there are.  There is a notation that simplifies this bookkeeping: ABxEy.  The A represents the central atom, B represents the electron groups that form bonds to other atoms, and E represents the non-bonding electron groups.  The subscripts, x and y, indicate how many of each kind are present. 

bonding groups: 4
non-bonding groups: 0
bonding groups: 3
non-bonding groups: 1
bonding groups: 2
non-bonding groups: 2
e.g. CH4 methane
e.g. NH3 ammonia
e.g. H2O water

    Depending upon the number of non-bonding electron pairs, the shape of the molecule not counting non-bonding electron pairs can be: a) tetrahedral (no non-bonding pairs); b) trigonal pyramidal (one non-bonding pair); or c) "bent" or "V" (two non-bonding pairs).  However, these are all derivatives of the tetrahedral design. 

    Only single bonds contribute to shape so the second bond of a double bond or second and third bond of a triple bond can be ignored and not counted as a bonding pair.  Thus carbon dioxide is a linear molecule.  AB2 , bonding groups: 2, non-bonding groups: 0, 

carbon dioxide
Vector Cancellation

    Once the shape of a molecule is determined, the question arises as to what happens with polar bonds within this molecule.  If the molecule is made up of 2 atoms only, the polarity of the bond makes the entire molecule polar.  Likewise, a non-polar bond makes the entire molecule nonpolar.  However, what if the molecule has more than 2 atoms?  A non-polar molecule has no net dipole by definition.  That is, the molecule has no distinctive poles of differing polarity.  This can be achieved by the molecule having only non-polar bonds or polar bonds arranged symmetrically so that the dipoles cancel out. 

    In the first case, a molecule such as H-H or Cl-Cl would be non-polar because the bonds are not polar.  If we consider CCl4, the bonds are polar due to the high electronegativity of Cl and the shared electrons are pulled closer to Cl on average making Cl partially negative and C partially positive.  However, the entire molecule is not polar since the vectors of the bond polarity cancel or do not sum in any net direction. 

Non Polar Molecule

    Each C-H bond is polar since carbon is more electronegative than hydrogen (although technically not polar due to an electronegativity under 0.4), however, each C-H bond in CH4 is arranged symmetrically (all angles are 109.5 degrees) so that the dipoles cancel out resulting in no net dipole for the molecule. 

Vector Cancellation

    If we consider NCl3, the electronegativities of N and Cl are similar such that the electronegativity difference is under 0.4 as well, but more on this later and the result is a non-polar molecule as there are no polar bonds present.


A polar molecule has a net dipole.  This is achieved     in the molecule by the molecule being made up of polar bonds arranged unsymmetrically     so that the dipoles do not cancel out.  Consider HCN:    

Vector Summation

Both the C-H and the C-N bonds are polar.  Nitrogen is more electronegative than carbon which is more electronegative than hydrogen.  So that the hydrogen takes on a partial positive charge and the nitrogen takes on a partial negative charge.  This results in an unequal sharing of the bonding electrons resulting in a net dipole for molecule since the two dipoles do not cancel out.

    Consider some more examples:

Vector Summation

    CH3Cl is a polar molecule with a net vector pointing up to the Cl atom.  The next question that arises deals with what would happen if all of the atoms had the same general electronegativity but differ in strength.  If you know physics, you know that vectors have two components:  direction and magnitude.  So far we have not dealt with the magnitude of the bond vectors as we have only been using predicted electronegativities based on periodic table positioning or we have been using simple bond polarities.  Consider the case where the H's in the above diagram were replaced with bromine atoms.  Bromine is more electronegative than C and would have a partial negative charge.  However, the magnitude of the vector pointing toward Cl (C-Cl) would be larger than the magnitude of the a single C-Br vector.  It becomes difficult to rectify how all the vectors sum, but they do not cancel so although it may seem that this molecule would be non-polar it would in fact be slightly polar as there is a difference in the relative strength of the poles within the molecule.  Most books do not consider the actually electronegativities, but rather avoid the entire issue.  Consider a simple example: A--B--C, where both A and C are more electronegative than B.  Thus, A and C would be partially negative and have a vector pointing from B to them.  However, what if A was more electronegative than C, then the magnitude of the B-A vector would be larger than the B-C vector and they would not cancel even thought they are pointing in opposite directions.  Thus, the molecule would be polar as one side is slightly more partial positive (less partial negative) than the other side.