Intermolecular Forces of Attraction
METALLIC BONDING
What is a metallic bond?
Metallic bonding in sodium
Metals tend to have high melting points and boiling points suggesting strong bonds
between the atoms. Even a metal like sodium (melting point 97.8°C) melts at a
considerably higher temperature than the element (neon) which precedes it in the Periodic
Table.
Sodium has the electronic structure 1s22s22p63s1. When sodium atoms come together, the
electron in the 3s atomic orbital of one sodium atom shares space with the corresponding
electron on a neighbouring atom to form a molecular orbital - in much the same sort of
way that a covalent bond is formed.
The difference, however, is that each sodium atom is being touched by eight other
sodium atoms - and the sharing occurs between the central atom and the 3s orbitals on all
of the eight other atoms. And each of these eight is in turn being touched by eight sodium
atoms, which in turn are touched by eight atoms - and so on and so on, until you have
taken in all the atoms in that lump of sodium.
All of the 3s orbitals on all of the atoms overlap to give a vast number of molecular
orbitals which extend over the whole piece of metal. There have to be huge numbers of
molecular orbitals, of course, because any orbital can only hold two electrons.
The electrons can move freely within these molecular orbitals, and so each electron
becomes detached from its parent atom. The electrons are said to be delocalized. The
metal is held together by the strong forces of attraction between the positive nuclei and
the delocalised electrons.
This is sometimes described as "an array of positive ions in a sea of electrons".
If you are going to use this view, beware! Is a metal made up of atoms or ions? It is made
of atoms.
Each positive centre in the diagram represents all the rest of the atom apart from the outer
electron, but that electron hasn't been lost - it may no longer have an attachment to a
particular atom, but it's still there in the structure. Sodium metal is therefore written as Na
- not Na+.
Metallic bonding in magnesium
If you work through the same argument with magnesium, you end up with stronger bonds
and so a higher melting point.
Magnesium has the outer electronic structure 3s2. Both of these electrons become
delocalized, so the "sea" has twice the electron density as it does in sodium. The
remaining "ions" also have twice the charge (if you are going to use this particular view
of the metal bond) and so there will be more attraction between "ions" and "sea".
More realistically, each magnesium atom has one more proton in the nucleus than a
sodium atom has, and so not only will there be a greater number of delocalized electrons,
but there will also be a greater attraction for them.
Magnesium atoms have a slightly smaller radius than sodium atoms, and so the
delocalized electrons are closer to the nuclei. Each magnesium atom also has twelve near
neighbours rather than sodium's eight. Both of these factors increase the strength of the
bond still further.
Metallic bonding in transition elements
Transition metals tend to have particularly high melting points and boiling points. The
reason is that they can involve the 3d electrons in the delocalization as well as the 4s. The
more electrons you can involve, the stronger the attractions tend to be.
The metallic bond in molten metals
In a molten metal, the metallic bond is still present, although the ordered structure has
been broken down. The metallic bond isn't fully broken until the metal boils. That means
that boiling point is actually a better guide to the strength of the metallic bond than
melting point is. On melting, the bond is loosened, not broken.
INTERMOLECULAR BONDING - VAN DER WAALS FORCES
What are intermolecular attractions?
Intermolecular versus intramolecular bonds
Intermolecular attractions are attractions between one molecule and a neighbouring
molecule. The forces of attraction which hold an individual molecule together (for
example, the covalent bonds) are known as intramolecular attractions. These two words
are so confusingly similar that it is safer to abandon one of them and never use it. The
term "intramolecular" won't be used again on this site.
All molecules experience intermolecular attractions, although in some cases those
attractions are very weak. Even in a gas like hydrogen, H2, if you slow the molecules
down by cooling the gas, the attractions are large enough for the molecules to stick
together eventually to form a liquid and then a solid.
In hydrogen's case the attractions are so weak that the molecules have to be cooled to 21
K (-252°C) before the attractions are enough to condense the hydrogen as a liquid.
Helium's intermolecular attractions are even weaker - the molecules won't stick together
to form a liquid until the temperature drops to 4 K (-269°C).
van der Waals forces: dispersion forces
Dispersion forces (one of the two types of van der Waals force we are dealing with on
this page) are also known as "London forces" (named after Fritz London who first
suggested how they might arise).
The origin of van der Waals dispersion forces
Temporary fluctuating dipoles
Attractions are electrical in nature. In a symmetrical molecule like hydrogen, however,
there doesn't seem to be any electrical distortion to produce positive or negative parts.
But that's only true on average.
The lozenge-shaped diagram represents a small symmetrical molecule - H2, perhaps, or
Br2. The even shading shows that on average there is no electrical distortion.
But the electrons are mobile, and at any one instant they might find themselves towards
one end of the molecule, making that end -. The other end will be temporarily short of
electrons and so becomes +.
An instant later the electrons may well have moved up to the other end, reversing the
polarity of the molecule.
This constant "sloshing around" of the electrons in the molecule causes rapidly
fluctuating dipoles even in the most symmetrical molecule. It even happens in monatomic
molecules - molecules of noble gases, like helium, which consist of a single atom.
If both the helium electrons happen to be on one side of the atom at the same time, the
nucleus is no longer properly covered by electrons for that instant.
How temporary dipoles give rise to intermolecular attractions
I'm going to use the same lozenge-shaped diagram now to represent any molecule which
could, in fact, be a much more complicated shape. Shape does matter (see below), but
keeping the shape simple makes it a lot easier to both draw the diagrams and understand
what is going on.
Imagine a molecule which has a temporary polarity being approached by one which
happens to be entirely non-polar just at that moment. (A pretty unlikely event, but it
makes the diagrams much easier to draw! In reality, one of the molecules is likely to have
a greater polarity than the other at that time - and so will be the dominant one.)
As the right hand molecule approaches, its electrons will tend to be attracted by the
slightly positive end of the left hand one.
This sets up an induced dipole in the approaching molecule, which is orientated in such a
way that the + end of one is attracted to the - end of the other.
An instant later the electrons in the left hand molecule may well have moved up the other
end. In doing so, they will repel the electrons in the right hand one.
The polarity of both molecules reverses, but you still have + attracting -. As long as the
molecules stay close to each other the polarities will continue to fluctuate in
synchronization so that the attraction is always maintained.
There is no reason why this has to be restricted to two molecules. As long as the
molecules are close together this synchronized movement of the electrons can occur over
huge numbers of molecules.
This diagram shows how a whole lattice of molecules could be held together in a solid
using van der Waals dispersion forces. An instant later, of course, you would have to
draw a quite different arrangement of the distribution of the electrons as they shifted
around - but always in synchronization.
The strength of dispersion forces
Dispersion forces between molecules are much weaker than the covalent bonds within
molecules. It isn't possible to give any exact value, because the size of the attraction
varies considerably with the size of the molecule and its shape.
How molecular size affects the strength of the dispersion forces
The boiling points of the noble gases are
helium
-269°C
neon
-246°C
argon
-186°C
krypton
-152°C
xenon
-108°C
radon
-62°C
All of these elements have monatomic molecules.
The reason that the boiling points increase as you go down the group is that the number
of electrons increases, and so also does the radius of the atom. The more electrons you
have, and the more distance over which they can move, the bigger the possible temporary
dipoles and therefore the bigger the dispersion forces.
Because of the greater temporary dipoles, xenon molecules are "stickier" than neon
molecules. Neon molecules will break away from each other at much lower temperatures
than xenon molecules - hence neon has the lower boiling point.
This is the reason that (all other things being equal) bigger molecules have higher boiling
points than small ones. Bigger molecules have more electrons and more distance over
which temporary dipoles can develop - and so the bigger molecules are "stickier".
How molecular shape affects the strength of the dispersion forces
The shapes of the molecules also matter. Long thin molecules can develop bigger
temporary dipoles due to electron movement than short fat ones containing the same
numbers of electrons.
Long thin molecules can also lie closer together - these attractions are at their most
effective if the molecules are really close.
For example, the hydrocarbon molecules butane and 2-methylpropane both have a
molecular formula C4H10, but the atoms are arranged differently. In butane the carbon
atoms are arranged in a single chain, but 2-methylpropane is a shorter chain with a
branch.
Butane has a higher boiling point because the dispersion forces are greater. The
molecules are longer (and so set up bigger temporary dipoles) and can lie closer together
than the shorter, fatter 2-methylpropane molecules.
van der Waals forces: dipole-dipole interactions
A molecule like HCl has a permanent dipole because chlorine is more electronegative
than hydrogen. These permanent, in-built dipoles will cause the molecules to attract each
other rather more than they otherwise would if they had to rely only on dispersion forces.
It's important to realize that all molecules experience dispersion forces. Dipole-dipole
interactions are not an alternative to dispersion forces - they occur in addition to them.
Molecules which have permanent dipoles will therefore have boiling points rather higher
than molecules which only have temporary fluctuating dipoles.
Surprisingly dipole-dipole attractions are fairly minor compared with dispersion forces,
and their effect can only really be seen if you compare two molecules with the same
number of electrons and the same size. For example, the boiling points of ethane,
CH3CH3, and fluoromethane, CH3F, are:
Why choose these two molecules to compare? Both have identical numbers of electrons,
and if you made models you would find that the sizes were similar - as you can see in the
diagrams. That means that the dispersion forces in both molecules should be much the
same.
The higher boiling point of fluoromethane is due to the large permanent dipole on the
molecule because of the high electronegativity of fluorine. However, even given the large
permanent polarity of the molecule, the boiling point has only been increased by some
10°.
Here is another example showing the dominance of the
dispersion forces. Trichloromethane, CHCl3, is a highly
polar molecule because of the electronegativity of the three
chlorines. There will be quite strong dipole-dipole attractions
between one molecule and its neighbours.
On the other hand, tetrachloromethane, CCl4, is non-polar. The
outside of the molecule is uniformly - in all directions. CCl4
has to rely only on dispersion forces.
So which has the highest boiling point? CCl4 does, because it is a bigger molecule with
more electrons. The increase in the dispersion forces more than compensates for the loss
of dipole-dipole interactions.
The boiling points are:
CHCl3
CCl4
61.2°C
76.8°C
INTERMOLECULAR BONDING - HYDROGEN BONDS
The evidence for hydrogen bonding
Many elements form compounds with hydrogen - referred to as "hydrides". If you plot
the boiling points of the hydrides of the Group 4 elements, you find that the boiling
points increase as you go down the group.
The increase in boiling point happens because the molecules are getting larger with more
electrons, and so van der Waals dispersion forces become greater.
If you repeat this exercise with the hydrides of elements in Groups 5, 6 and 7, something
odd happens.
Although for the most part the trend is exactly the same as in group 4 (for exactly the
same reasons), the boiling point of the hydride of the first element in each group is
abnormally high.
In the cases of NH3, H2O and HF there must be some additional intermolecular forces of
attraction, requiring significantly more heat energy to break. These relatively powerful
intermolecular forces are described as hydrogen bonds.
The origin of hydrogen bonding
The molecules which have this extra bonding are:
Note: The solid line represents a bond in the plane of the screen or paper. Dotted bonds
are going back into the screen or paper away from you, and wedge-shaped ones are
coming out towards you.
Notice that in each of these molecules:
 The hydrogen is attached directly to one of the most electronegative elements,
causing the hydrogen to acquire a significant amount of positive charge.
 Each of the elements to which the hydrogen is attached is not only significantly
negative, but also has at least one "active" lone pair.
Lone pairs at the 2-level have the electrons contained in a relatively small volume of
space which therefore has a high density of negative charge. Lone pairs at higher levels
are more diffuse and not so attractive to positive things.
Consider two water molecules coming close together.
The + hydrogen is so strongly attracted to the lone pair that it is almost as if you were
beginning to form a co-ordinate (dative covalent) bond. It doesn't go that far, but the
attraction is significantly stronger than an ordinary dipole-dipole interaction.
Hydrogen bonds have about a tenth of the strength of an average covalent bond, and are
being constantly broken and reformed in liquid water. If you liken the covalent bond
between the oxygen and hydrogen to a stable marriage, the hydrogen bond has "just good
friends" status. On the same scale, van der Waals attractions represent mere passing
acquaintances!
Water as a "perfect" example of hydrogen bonding
Notice that each water molecule can potentially form four hydrogen bonds with
surrounding water molecules. There are exactly the right numbers of + hydrogens and
lone pairs so that every one of them can be involved in hydrogen bonding.
This is why the boiling point of water is higher than that of ammonia or hydrogen
fluoride. In the case of ammonia, the amount of hydrogen bonding is limited by the fact
that each nitrogen only has one lone pair. In a group of ammonia molecules, there aren't
enough lone pairs to go around to satisfy all the hydrogens.
In hydrogen fluoride, the problem is a shortage of hydrogens. In water, there is exactly
the right number of each. Water could be considered as the "perfect" hydrogen bonded
system.
More complex examples of hydrogen bonding
The hydration of negative ions
When an ionic substance dissolves in water, water molecules cluster around the separated
ions. This process is called hydration.
Water frequently attaches to positive ions by co-ordinate (dative covalent) bonds. It
bonds to negative ions using hydrogen bonds.
The diagram shows the potential hydrogen bonds formed to a chloride ion, Cl-. Although
the lone pairs in the chloride ion are at the 3-level and wouldn't normally be active
enough to form hydrogen bonds, in this case they are made more attractive by the full
negative charge on the chlorine.
However complicated the negative ion, there will always be lone pairs that the hydrogen
atoms from the water molecules can hydrogen bond to.
Hydrogen bonding in alcohols
An alcohol is an organic molecule containing an -O-H group.
Any molecule which has a hydrogen atom attached directly to an oxygen or a nitrogen is
capable of hydrogen bonding. Such molecules will always have higher boiling points
than similarly sized molecules which don't have an -O-H or an -N-H group. The
hydrogen bonding makes the molecules "stickier", and more heat is necessary to separate
them.
Ethanol, CH3CH2-O-H, and methoxymethane, CH3-O-CH3, both have the same
molecular formula, C2H6O.
They have the same number of electrons, and a similar length to the molecule. The van
der Waals attractions (both dispersion forces and dipole-dipole attractions) in each will be
much the same.
However, ethanol has a hydrogen atom attached directly to an oxygen - and that oxygen
still has exactly the same two lone pairs as in a water molecule. Hydrogen bonding can
occur between ethanol molecules, although not as effectively as in water. The hydrogen
bonding is limited by the fact that there is only one hydrogen in each ethanol molecule
with sufficient + charge.
In methoxymethane, the lone pairs on the oxygen are still there, but the hydrogens aren't
sufficiently + for hydrogen bonds to form. Except in some rather unusual cases, the
hydrogen atom has to be attached directly to the very electronegative element for
hydrogen bonding to occur.
The boiling points of ethanol and methoxymethane show the dramatic effect that the
hydrogen bonding has on the stickiness of the ethanol molecules:
ethanol (with hydrogen bonding)
78.5°C
methoxymethane (without hydrogen bonding)
-24.8°C
The hydrogen bonding in the ethanol has lifted its boiling point about 100°C.
It is important to realise that hydrogen bonding exists in addition to van der Waals
attractions. For example, all the following molecules contain the same number of
electrons, and the first two are much the same length. The higher boiling point of the
butan-1-ol is due to the additional hydrogen bonding.
Comparing the two alcohols (containing -OH groups), both boiling points are high
because of the additional hydrogen bonding due to the hydrogen attached directly to the
oxygen - but they aren't the same.
The boiling point of the 2-methylpropan-1-ol isn't as high as the butan-1-ol because the
branching in the molecule makes the van der Waals attractions less effective than in the
longer butan-1-ol.
Hydrogen bonding in organic molecules containing nitrogen
Hydrogen bonding also occurs in organic molecules containing N-H groups - in the same
sort of way that it occurs in ammonia. Examples range from simple molecules like
CH3NH2 (methylamine) to large molecules like proteins and DNA.
The two strands of the famous double helix in DNA are held together by hydrogen bonds
between hydrogen atoms attached to nitrogen on one strand, and lone pairs on another
nitrogen or an oxygen on the other one strand.