Solutions and States of Matter 6
A solid, based on the type of force which holds it together, will belong to one of several categories.
1. Ionic Solids
Ionic solids, the first category we will discuss, are made of ions held
together in a crystal lattice by electrostatic attractions. As described in
the bonding chapter, ionic solids are made of ions which, because of the
large electronegativity difference between them, exist as cations and
anions. Thus compounds of (very electropositive) alkali metals are almost
always ionic. Because ionic bonds are strong, ionic solids are normally
hard, high melting and high boiling. Because of the rigidity of the lattice
structure associated with ionic bonding, ionic solids are normally rather
brittle. When ionic solids dissolve in water, as many do, the lattices break Figure 1. An ionic lattice
apart to form ions. For example:
Na2SO4(s) 2 Na+(aq) + SO4-2(aq)
When an ionic solid is dissolved or melted, the ions are capable of movement, causing the melt or solution
to conduct electricity. In the solid, however, the ions are immobilized by the lattice. Thus solid ionic
compounds do not conduct electricity.
While it is difficult to make generalizations, changes which increase the forces in the lattice will cause an
ionic solid to have a higher boiling or melting point. Lithium fluoride, with its smaller ions, and
magnesium oxide, with its higher charges, both have melting and boiling temperatures which are higher
than those of sodium chloride.
2. Network and Amorphous Solids
Like ionic solids, the particles in a network solid are arranged to form a crystal lattice. Often network
solids contain anions and cations. However, unlike ionic solids network solid are held together by covalent
bonds. How can we distinguish between network and ionic solids?
In some cases, for example diamond, it is obvious that the bonding between
atoms is covalent. Since diamond is made entirely of carbon, there is no
electronegativity difference between the atoms and, hence, no reason for
electrons to be shared unequally. Other cases, however, are less obvious. As
we have discussed, large electronegativity differences lead to ionic
bonding. But how large must the difference be? It is difficult to find a rule
that works and, in any case, most of us have not memorized an
electronegativity table. So we will use other methods for differentiating
between network and ionic solids.
Figure 2. The structure of
First, there are several network solids which you should remember — diamond
diamond, graphite, silicon dioxide (also known as quartz or silica) and
aluminum oxide (also known as sapphire or alumina.) It is also possible to recognize network solids by
their properties. While ionic solids are hard, network solids are even harder. Anything used as an abrasive
will be a network solid. Diamond, silica (in sand paper) and alumina (the "grit" used in polishing almost
anything) come to mind. Silicon carbide (SiC, Carborundum) and tungsten carbide (WC, used in carbide
drill bits) are other abrasives with network structures.
Graphite, a form of carbon, has a network structure which is
sufficiently unusual that it is worthy of comment. Unlike most
lattice structures, which extend in 3 dimensions, graphite consists
of 2-dimensional sheets of carbon atoms. It is the ability of these
sheets to slide across one another which makes graphite soft and
An amorphous solid is one which has no regular (crystalline)
structure. Glass is the only amorphous solid you are expected
to know. Although silicon dioxide is the principal component Figure 3. The structure of graphite
of glass, it is not glass. Silicon dioxide is a network solid and
3. Metallic solids
These are held together by metallic bonds — bonds which are neither ionic nor covalent. We recognize
metallic solids by their properties. Metallic solids have the following characteristics:
- they are strong
- they are high melting (generally)
- they are conductive of heat
- they are conductive of electricity
- they are malleable (can be made into thin sheets)
- they are ductile (can be drawn into thin wires)
- they have what is known as "metallic luster"
Actually defining what is meant by "metallic luster" is difficult, but we know it when we see it.
Not surprisingly metallic solids are generally metals — but not always. At low temperatures tin converts
from its metallic form to a form called "grey tin," which has a diamond structure and is definitely
There are two models used to explain metallic bonding. One of these — the "sea of electrons" model — is
very simple but doesn't explain much. The other model — the band model — explains things well, but
with a complexity that is beyond the scope of this course.
In the "sea of electrons" model a metal's valence electrons are removed, leaving the metal cations (e.g. Na+
or Al+3) surrounded and held together by a "sea" of valence electrons. These loosely-held electrons move
through the metal, making it electrically conductive. Also the non-directionality of the bonding in this
model makes it easy to deform the structure, leading to the observed malleability and ductility. Finally the
fact that the alkali metals share only a single electron per atom is consistent with their observed softness.
However, the sea of electrons model does not lead to quantitative predictions, nor does it explain
phenomena such as semi-conduction. The band model does all of these. It is based on the fact that
electrons in a metal are allowed to have certain energies and that this range of allowed energies is called a
"band." However, further discussion of the band model is not warranted at this time.
4. Molecular solids
These are made of molecules which, as you know, are held together by covalent bonds. Molecular solids,
however, are not held together by covalent bonds. The covalent bonds occur within the molecules not
between them. Molecular solids are, therefore, held together by bonds which are much weaker than
covalent bonds. This has consequences. In most cases molecular solids are soft and exhibit low melting
and boiling points. They are also poor conductors of heat and electricity.
Examples of molecular solids include virtually all organic compounds and compounds which are liquids
or gases at room temperature. Molecular solids include the solid forms of water, benzene, acetone, aspirin,
DNA, nitrogen and carbon dioxide. It is often difficult to predict what will be a molecular solid without
knowing something about its properties. It is easy to see that carbon dioxide is molecular while silicon
dioxide is a network solid; but why this happens is less obvious. Although the noble gases do not form
molecules, we will consider their solid forms to be molecular solids.
The (intermolecular) forces which hold molecular solids together are of several varieties. You should
know something about them.
Dipole-dipole forces exist between molecules which are aligned so that the positive end of one molecule is
near the negative end of another. Dipole-dipole forces are important in holding together HBr and acetone.
Despite containing polar bonds, molecules such as CO2 and CCl4 are not polar and therefore are not
affected by dipole-dipole forces.
A very important case which resembles the dipole-dipole interactions
is the hydrogen bond. A hydrogen bond exists between a very
electronegative element (usually F, O or N) and a hydrogen atom
which is bonded to a very electronegative element. (Remember —
chemistry is FON.) Examples of molecules held together by hydrogen
bonds are HF, H2O and NH3. Acetonitrile (H3C-CN) does not exhibit
hydrogen bonding because, although it contains an electronegative
nitrogen atom, none of its hydrogens is bonded to nitrogen. Hydrogen
bonding is enormously important in biochemistry, with protein and
nucleic acid structures being largely determined by the formation of
Figure 4. Hydrogen bonding
A common example of the effect of hydrogen bonding is
seen in the boiling points on the left. Plotting the boiling
points of H2S, H2Se, and H2Te against molecular weight
gives a straight line, consistent with the effect of London
forces (discussed in the next paragraph). Water, because of
its ability to form hydrogen bonds, has a much higher
boiling point than predicted. If a similar graph were drawn
for the second and third row elements, you would see that
hydrogen fluoride and ammonia behave like water.
Methane, however, does not hydrogen bond and, as shown
in Figure 5, does not deviate from the expected trend.
Figure 5. The effect of hydrogen bonding
A third type of intermolecular force, known as London Dispersion Forces (LDF), exists between all
molecules. It is caused by the attraction between temporary dipoles. This is because from time to time the
electrons in a molecule find themselves mostly on one side of the molecule, producing a temporary or
instantaneous dipole. This temporary dipole attracts or repels electrons in nearby molecules, inducing
dipoles. The induced dipoles on adjoining molecules then attract
or repel electrons in the original molecule, reinforcing the
instantaneous dipole. This phenomenon causes an attraction Formula Name Melt Pt.
between molecules which grows larger as the molecule grows CH4 Natural gas -60 C
larger. There are many examples of this. As halogens grow C3H8 Propane -20 C
heavier, their melting and boiling points increase. Thus fluorine C4H10 Butane 15 C
and chlorine are gases, bromine is a liquid, and iodine is a solid. ~C7H16 Gasoline 50 C
Similarly the melting points of hydrocarbons grow higher as the ~C10H22 Kerosene 120 C
molecules grow larger. Small London forces explain why liquid
Figure 6. Hydrocarbon melting points
helium is the coldest known liquid.
What are the forces which hold together a solid (or liquid)? For network, ionic or metallic solids the
answer is obvious — covalent, ionic or metallic bonds. However, liquids and molecular solids pose more
of a problem. Where hydrogen bonding occurs, it tends to be a major factor in holding the molecules
together. When molecules are large, LDF's are important. Dipole-dipole forces are seldom the major force
holding together a solid or liquid, but in a small molecule where there is no H-bonding (e.g. acetonitrile),
the dipole-dipole force can be important. Where there is neither a dipole nor a hydrogen bond, LDF's are
all that is left to hold together the condensed phase — no matter how weak they are. Thus dry ice and
liquid nitrogen are held together by weak LDF's and are easily vaporized.
5. Phase Changes
If heated sufficiently, a solid becomes a liquid and a liquid becomes a gas.
However the process is not a smooth one. As a solid is heated, the
temperature rises until the solid melts. The temperature then remains
constant. When all the solid has melted, the temperature of the liquid rises
until it reaches its boiling point. At the boiling point, the temperature
levels off until the liquid has vaporized. The temperature of the gas then
rises. (The heat added at these transition temperatures is used to melt or
boil the substance, not to raise its temperature. The leveling of the
temperature during melting and boiling assumes the mixture is
well-stirred and homogeneous. The graph shown here is referred to as a
"heating curve." The opposite graph, in which a gas becomes liquid and
then solid, is referred to as a cooling curve. Recall that (at 1 atm.) liquid Figure 7. A heating curve
water exists between 0 - 100 C, but ice/water exists only at 0 C.
6. Phase Diagrams
Pure substances have definite, reproducible transitions between phases only if the pressure remains
constant. The pressure dependence of these processes is shown by the diagram below. This diagram,
known as a phase diagram, allows us to predict the phase in which a given substance will exist at any
temperature and pressure. At this point it is useful to define what is meant by a phase. A phase is a region
of uniform properties surrounded by an interface. Although there are some who will tell you that a plasma
is a fourth phase of matter, it does not fit this definition.
Systems which lie exactly on one of the lines are common, since they
correspond to a mixture of two phases. When a solid at point (a) is
heated, the system moves along the dashed line until it reaches point
(b), where it melts. Once all of the solid has melted, still at point (b), the
system moves along the line until it reaches point (c).
Beyond point (d), known as the critical point, liquid and gas phases
are the same. The single phase which exists beyond the critical point
is called a "supercritical fluid." The critical point is defined by the
critical temperature (TC) and the critical pressure (PC).
TC is the temperature above which a substance cannot be Figure 8. A typical phase
PC is the pressure needed to liquefy a substance at its critical
Notice that the critical pressure is defined in terms of the critical temperature. Keep this straight, because
multiple choice questions will sometimes try to confuse you.
Point (e) in Figure 8, known as the triple point, is the one and only
Vaporization Liquid to gas
point at which the three phases coexist. One of the ways in which you
Melting Solid to liquid
will use the triple point is illustrated by the carbon dioxide phase
Condensation Gas to liquid
diagram, show in Figure 10. Since the triple point, (b), is at 5.11 atm,
Freezing Liquid to solid
liquid carbon dioxide does not exist below 5.11 atm. Hence at normal
Sublimation Solid to gas
pressure carbon dioxide goes directly from the solid phase to the gas
Deposition Gas to solid
phase — it sublimes.
Figure 9. Types of phase transitions
Curve a-b in Figure 10 is known as the "sublimation curve." It gives the
vapor pressure of solid carbon dioxide at any temperature or it can give
the sublimation temperature of carbon dioxide at any pressure. A
particularly important point on the curve is the "normal sublimation
temperature." This is the temperature at which carbon dioxide sublimes
at normal pressure (1 atm.) As you can see, the normal sublimation
temperature of carbon dioxide is -78.5 C.
Figure 10. The carbon
dioxide phase diagram
The water phase diagram (Figure 11) is interesting because the
solid/liquid line slopes to the left. This is unusual and indicates that the
solid phase is less dense than the liquid phase. (It floats!) To help
remember which slope this is, consider solid water at point (a). Increasing
the pressure converts the solid (a) to a liquid (b). According to Le
Chatelier's Principle, this happens if the liquid phase occupies less
volume than the solid — if the solid is less dense than the liquid. As can
Figure 11. The water phase
be seen from the diagram, water has a normal melting point of 0 C and a normal boiling point of 100 C.
Note that in both cases the pressure scale is logarithmic and the slope of the solid/liquid line is
A possible question is whether a given solute will dissolve in a certain solvent. While this can be difficult
to answer, the general rule is that "like dissolves like." This means that ionic solutes (e.g. NaCl) or very
polar solutes (e.g. ethanol) will dissolve in a very polar solvent such as water. Non polar solutes (e.g. fat)
dissolve in non-polar solvents such as hexane or carbon tetrachloride. However sodium chloride does not
dissolve in hexane and fat does not dissolve in water.
In order to deal with the properties of solutions, we must introduce some new units of concentration in
addition to reviewing the old ones. Molarity, which you already know, is moles per liter of solution. The
difference between measuring the solution and measuring the solvent is significant for all but very dilute
solutions. This is why in making solutions of precise molarity, chemists measure the volume of the
solution after the solute is dissolved.
Molality is represented by a lower case "m" and is equal to moles per kilogram of solvent.
m = kg solvent
Mole fraction, χ, is what it sounds like — the fraction of the moles of one compound in a mixture. Note
that the symbol is a Greek "chi" and not an "x." If one mole of A is mixed with two moles of B, the mole
fraction of A, χA, is 1/3.
Consider a 10% (by mass) solution of sodium chloride. A kilogram of this solution, which has a density of
1.09 g/mL, contains 100 g of NaCl and 900 g of water. Let us calculate the molarity, the molality and the
9. Colligative Properties
Many solution properties, referred to as "colligative properties," depend on the concentration of the solute.
Some very important ones, e.g. osmotic pressure, are not included in the AP syllabus. If you understand
those which we cover, you will be able to learn the others.
First are two closely related phenomena, freezing point depression and boiling point elevation. The
formulas, which are given on the AP formula sheet, are:
ΔT = m KF i and ΔT = m KB i
Here ΔT is change in temperature (in degrees Celsius) and m is the molality. KF is the freezing point
depression constant and KB is the boiling point elevation constant. These are experimentally determined
and not numbers which you are expected to know. Finally i is the van't Hoff factor, the number of particles
into which the solute breaks upon dissolving. When potassium sulfate dissolves, it reacts:
K2SO4 2 K+ + SO4
Therefore it has a van't Hoff factor of 3. Because they are electrically non-conductive, molecules which do
not break into ions are referred to as "non-electrolytes." Compounds in this category, which includes all
organic molecules, have a van't Hoff factor of 1.
What is the freezing point of a 10% zinc chloride (ZnCl2) solution? A 10% solution corresponds to 100 g
of zinc chloride dissolved in 900 g of water. Since ZnCl2 has a molecular weight of 136.28, this gives a
molality of 0.815. The freezing point depression constant for water is 1.86 K/m, so:
ΔT = KF m i = 1.86 0.815 3 = 4.5
Since 10% has two significant digits, the answer must have two significant digits.
Since the freezing point of water is 0 C, the answer is 0 - 4.5 = -4.5 C. This can be a problem in solvents
other than water, since students occasionally calculate ΔT and then forget to subtract it from the freezing
point. Boiling point elevation problems are identical but, of course, have a different constant and increase
the temperature rather than decreasing it.
Raoult's Law says that the partial pressure exerted by a volatile liquid is proportional to its mole fraction in
a mixture. If the vapor pressure in equilibrium with pure A is PA, then the vapor pressure of the liquid in
a solution is:
PA = χ PA
The vapor pressure of pure water is 3.17 kPa. What is the vapor pressure of a 20.0% glucose solution? The
molar mass of glucose is 180 g/mol; so the mole fraction of water is:
The vapor pressure of the solution is, then:
PA = χ PA = 0.9756 3.17 = 3.09 kPa
Where a solution has two volatile components, the vapor pressure is the sum of the two partial pressures.
Suppose we have a 50/50 (w/w) mixture of ethanol (MW = 46.08; P = 45 kPa) and methanol (MW =
32.05; P = 81 kPa). What is the vapor pressure of the mixture? We assume 100 g of mixture.
χethanol = 1.09 + 1.56 = 0.411
χmethanol = 1.09 + 1.56 = 0.589
P Pethanol ethanol Pm ethanol m ethanol
P = 0.411 45.0 kPa + 0.589 81.0 kPa = 66.0 kPa
As always, the sum of the mole fractions is one. This is important in certain types of problems.
10. Exceptions to Ideal Behavior
Solutions which obey the laws described above are called "ideal solutions." Not all solutions are ideal.
While you will not need to do calculations on non-ideal solutions, you should understand them well
enough to be able to explain their behavior.
At high concentrations of ionic solute, the van't Hoff factor is often less than expected. For example, at a
suitably high concentration the van't Hoff factor for sodium chloride will be 1.9. This happens because
although sodium and chloride don't react in solution, they do attract one another. At high concentrations,
when there is a sodium ion near every chloride ion, this attraction becomes important. The technical term
used to describe this interaction is "ion pairing." Remember it!
Deviations from Raoult's Law can be of two types. Positive deviations,
where the actual vapor pressure is higher than the calculated value,
occur when the forces of attraction between dissimilar molecules are
weaker than the forces between identical molecules. In such a case, for
example a mixture of ethanol and water, the intermolecular forces are
weakened due to the mixing. Although this makes it easier for the
solution to evaporate, the weakening of bonds does cost energy. The
mixing of water with ethanol is endothermic.
A negative deviation occurs when the force between dissimilar Figure 12. A positive deviation
molecules is greater than the force between identical molecules. In from Raoult’s Law
such a case, for example the mixing of nitric acid and water, the
mixing process is exothermic. Often this stronger interaction occurs because of a chemical reaction
between the components, e.g:
HNO3 + H2O H3O+ + NO3 .
While nitric acid cannot protonate another HNO3 molecule, it readily protonates a water molecule.