Chapter 12
Intermolecular Forces:
Liquids, Solids, and Phase Changes
If you are doing this lecture “online” then print the lecture notes
available as a word document, go through this ppt lecture, and do all
the example and practice assignments for discussion time.
Why do gases differ from liquids & solids?
Gases are tiny particles far apart with no attraction for each
other (ideally) and they are moving rapidly in random
directions
Gases obey a set of laws: Ideal Gas Laws
But liquids & solids don't have a set of "laws" because....
Liquids: - condensed from gases
- not compressible therefore not much space
between molecules
-moving randomly but more slowly, are attracted
to each other!
Solids: - ordered fixed in place particles
- close together
- strong forces of attraction!
Interparticle Forces
Interparticle forces of attraction between "particles" that
affect physical state & physical behavior
Note: particles can be ions, atoms or molecules
True chemical bonding forces are intra-particle forces:
within a chemical substance
They are atom to atom or ion to ion, not molecule to
molecule: ionic bonding, metallic bonding, covalent
bonding, and (new to us) network covalent bonding
Interparticle forces are between particles, not within them
Special group of interparticle forces between molecules and
atoms:
- called intermolecular forces
- affect behavior of covalent compounds
Next slide is table from your packet of handouts
SUMMARY OF INTERPARTICLE FORCES
INTERPARTICLE
FORCE
STRENGTH
kJ/mol
PREDICTED
MP/BP
EXAMPLES
PARTICLES
DESCRIPTION
Covalent
Bonding
atoms
sharing of e-s
between two atoms
strong
high/high
H2O (0,100)
Network Covalent
Bonding
atoms
sharing of e-s
betw two atoms extended
very strong
very high
diamond (35530,?)
Metallic Bonding
atoms
sharing of e-s in a sea
Between all atoms
strong
high
iron (1555, 3000)
Ionic Bonding
cations &
anions
electrostatic attraction
between opposite charges
400-4000
high
NaCl (804, 1413)
Hydrogen Bonding*
polar molecules
with H bonded to
F, O or N
attraction between H on
one molecule to F, O or N
on other molecules
15-40
medium
H2O
Dipole-Dipole
Attraction
polar molecules
attraction between slightly
opposite charges
5-25
low/medium
(CH3)2C=O (-95, 56)
London Dispersion
Forces
all atoms, ions
and molecules
attraction between induced
dipole opposite charges
0.05-40
low/medium
I2 (114, 183)
Ion-Dipole
Attraction
ions and polar
molecules
attraction between
opposite charges
40-600
na
NaCl(aq)
Dipole-Induced
Dipole Attraction
polar and nonpolar
molecules
attraction between dipole
and induced dipole
2-10
na
O2 in H2O
*Not really bonding, just an unfortunate choice for naming this intermolecular force of attraction. Italics indicate the three Intermolecular Forces.
Properties
High MP,
brittle solid
Low MP,
soft when
solid
Range of
MPs,
malleable
ADD:
Network Covalent
Atom-Atom like cov bond
500+
Diamond Very high MP,
very hard solid
Network Covalent Bonding
Make special note of the network covalent
solids that I added to Table 12.2:
- covalent bonds are extended throughout
the crystal solid
- diamond and SiC, also SiO2
Diamond is fcc with 4 C's in "holes" in unit
cell, which we see later in chapter
Graphite has unique structure (see diagram)
**
**
**
**“True” Intermolecular Forces in pure substances
Ion-Dipole Attraction:
Interparticle forces involved in dissolving ionic
solids in water or other polar solvents:
Ion-dipole attraction has to overcome ion-ion
attraction in a solid’s crystal lattice
This is why some compounds are soluble and
some are not
Called Hydration of an ion: typically endothermic takes energy to pull ions apart
Some energy is gained back as Heat of Hydration polar water molecules orient themselves and
surround the individual ions
More detail coming soon in Chapter 13
The Major InterMolecular
(IM) Forces
The three major IM Forces are very weak to
moderate forces of attraction between molecules
(or atoms)
- London (dispersion) forces (LDF)
- Dipole-dipole attractions
- Special case of enhanced dipole attraction
called Hydrogen-bonding
- Dipole-induced dipole attraction, between
different types of molecules or atoms
London Dispersion Forces (LDF)
"Instantaneous dipole" causes neighboring electron clouds
to also move to one side, inducing a dipole in them
Leads to a small force of attraction between slight positive
and slight negative ends of two different particles –
these attractions are called London dispersion forces
Strength of LDF depends on: (1) size of electron cloud in
atom and/or (2) number of atoms in a molecule
Polarizability increases down a group
Polarizability decreases left to right across a period
Look at the elemental halogens: fluorine and chlorine are
gases; bromine is liquid and iodine is solid because of
size of e- cloud around each molecule
Figure 12.14
Dispersion forces among nonpolar molecules.
instantaneous
dipoles
separated Cl2 molecules
An instantaneous dipole
in one Cl2 molecule will
induce a dipole in a
nearby Cl2 molecule.
The partial charges
attract the molecules
together. This process
takes place with the
particles throughout the
container.
Figure 12.15
Molar mass and boiling point.
The strength of LDF increases with the
number of electrons, which correlates
with molar mass. Therefore, LDF
increases down a group in the Periodic
Table, which can be verified by the
increase in boiling points.
Figure 12.16
Molecular shape and boiling point.
fewer points for
dispersion
forces to act
more points for
dispersion
forces to act
(It’s just Pentane.)
Spherical molecular shapes
make less contact with each
other than do cyllindrical
shapes, so they have a lower
boiling point.
2,2-dimethylpropane
I have corrected the organic names – compare to your textbook, which is using
Figure 12.11
Polar molecules and dipole-dipole forces.
solid
In a solid or a liquid, polar
molecules are close enough for
the attraction to hold.
Orientation is more orderly in a
solid because the average KE
of the particles is lower.
liquid
Dipole-dipole Attraction
Dipoles involve polar molecules which are
attracted to each other because of the
slight positive and slight negative "poles"
to the molecules
Compare molecules of F2, HF, HCl, HBr, HI
Boiling points: F2<HCl<HBr<HI<HF
Data for IM Forces
F2
Tot # e-s 18
MM
38
DEN
0
Dip Mom 0
% Disp 100
% Dipole 0
BP, K
85
DHvap
6.86
HF
10
20
1.8
1.4
Low
High
291
High
HCl
18
36.5
1.0
1.1
81.4
18.6
188
16
HBr
36
81
0.8
0.8
94.5
5.5
206
18
HI
54
128
0.5
0.4
99.5
0.5
238
20
Enhanced Dipole-Dipole or
Hydrogen-Bonding?
Dipole forces are decreasing down the
hydrohalogen group because DEN is decreasing
WHY is HF so very different in boiling point?
HF represents a special case of dipole-dipole
attraction called Hydrogen-bonding
Occurs when H is bonded to a highly EN atom that
is also very small: H to F, O or N
Size of EN atom is important also, allows H to get
very close, as seen with radius in pm below:
N-70
O-73
F-72
Cl-100 (no H-bond)
SAMPLE PROBLEM 12.3
PROBLEM:
Which of the following substances exhibits H bonding? For
those that do, draw two molecules of the substance with the H
bonds between them.
O
C2H6
(a)
PLAN:
(b) CH3OH
(c) CH3C
NH2
Find molecules in which H is bonded to N, O or F. Draw H
bonds in the format -B:
H-A-.
SOLUTION:
(b)
Drawing Hydrogen Bonds Between Molecules
of a Substance
(a) C2H6 has no H bonding sites.
H
H C O H
H
H
H O C H
H
(c)
H
O
H N CH3C CH C
3
N H
O
CH3C N H
H N
CH3C
O
H
O
H
H
The N-H is also attracted to the N-H.
Figure 12.13
Hydrogen bonding and boiling point.
Boiling points of
the binary covalent
hydrides of Groups
14 – 17 plotted
agains Period digit.
Shows that H2O,
HF and NH3 do not
follow the
downward trend,
as shown by the
dashed line for
group 16.
Dipole-Induced Dipole: between
two different compounds’ particles
Dipole-induced dipole forces account for
limited solubility of oxygen in water
Ability to do this = function of polarizability
of molecule
Compare H2 to I2: bigger molecule
polarizes, soluble in water, which is
demonstrated by the much greater
solubility of I2 in water
SAMPLE PROBLEM 12.4
PROBLEM:
Predicting the Type and Relative Strength of
Intermolecular Forces
For each pair of substances, identify the dominant interparticle
forces affecting the physical properties of each substance, and
then select the substance with the higher boiling point.
(a) MgCl2 or PCl3
(b) CH3NH2 or CH3F
(c) CH3OH or CH3CH2OH
CH3
(d) Hexane (CH3CH2CH2CH2CH2CH3)
CH3CCH2CH3
or 2,2-dimethylbutane
CH3
•Bonding forces are stronger than nonbonding(intermolecular) forces.
•Hydrogen bonding is a strong type of dipole-dipole force.
•Dispersion forces are decisive when the difference is molar mass or
molecular shape.
SAMPLE PROBLEM 12.4
Predicting the Type and Relative Strength of
Intermolecular Forces
continued
SOLUTION:
(a) Mg2+ and Cl- are held together by ionic bonds while PCl3 is covalently
bonded and the molecules are held together by dipole-dipole interactions. Ionic
bonds are stronger than dipole interactions and so MgCl2 has the higher boiling
point.
(b) CH3NH2 and CH3F are both covalent compounds and have bonds which are
polar. The dipole in CH3NH2 can H-bond while CH3F is just dipole-dipole.
Therefore CH3NH2 has the stronger interactions and the higher boiling point.
(c) Both CH3OH and CH3CH2OH can H bond but CH3CH2OH has more CH for
more London dispersion force interaction. Therefore CH3CH2OH has the higher
boiling point.
(d) Hexane and 2,2-dimethylbutane are both nonpolar with only London
dispersion forces to hold the molecules together. Hexane has the larger surface
area, thereby the greater dispersion forces and the higher boiling point.
Practice with Intermolecular
Forces: explain the forces behind
this data:
1. Butane (CH3CH2CH2CH3) melts at -138oC and boils at
0.5oC, while acetone (CH3C=OCH3) melts at -95oc and
boils at +56oC, yet both weigh 58 g/mol. Draw Lewis
structures and explain the differences in MPs and BPs.
2. Guess BP order for CCl4, N2, Cl2, ClNO (chlorinenitrogen-oxygen).
Figure 12.17 modified
Summary diagram for analyzing the interparticle forces in a sample.
ions present
ions only
IONIC BONDING
(Section 9.2)
Metal atoms only
INTERACTING PARTICLES
METALLIC
(atoms, molecules, ions)
BONDING
ions not present
polar molecules only
DIPOLE-DIPOLE
FORCES
ion + polar molecule
ION-DIPOLE FORCES
H bonded to
N, O, or F
HYDROGEN
BONDING
nonpolar
molecules or atoms
Only, LONDON
DISPERSION
FORCES
polar + nonpolar
molecules
DIPOLEINDUCED DIPOLE
FORCES
LONDON DISPERSION FORCES ALSO PRESENT IN ALL OF ABOVE.
NETWORK COVALENT BONDING POSSIBLE FOR VERY FEW ATOMS.
Practice
See handouts
Also chapter problems: 2, 29, 31, 33, 37,
39, 43, 45
4th ed. #119: What forces are overcome
when the following events occur: (a) NaCl
dissolves in water, (b) krypton boils, (c)
water boils, (d) CO2 sublimes?
QUESTIONS TO ASK IN PREDICTING THE
KINDS OF INTERPARTICLE FORCES THAT
WILL BE PRESENT IN A SOLID OR A LIQUID
Start at the top with the first question, “Is it metallic?”. When you can answer yes, you are done. If the answer is no, keep
going down the list. The “it” refers to whatever substance you are working with.
Question
Is it metallic? (ONLY metal present)
If yes, this force is present* MP & BP Examples (MP, BP)
Metallic bonding
High
Iron (1555, 3000)
Is it ionic? (cation & anion present)
Ionic bonding
High
NaCl(804, not defined)
Is it network covalent compound?
Network covalent bonding
High
Diamond (3550, not def), SiC, SiO2
In the molecule, is H attached by a covalent Hydrogen bonding
bond to F, O or N?
Medium
Water (0.100)
Does the molecule have a dipole moment?
Low
HCl (-114, -85)
Very low
Hydrogen (-257, -253)
Iodine (114, 183)
Is the substance molecular?
(covalent bonds present)
Is it a molecule with no dipole moment?
Dipole-dipole attraction
Only London Forces
Does the substance consist of atoms with no
covalent bonds between them?
Only London Forces
Extremely low
Neon (-249, -246)
*Remember – London forces are present in all liquids and solids.
Practice with these, supposing all to be in liquid or solid phase: methane, ethanol, sucrose (look up structure), NaOH, SiC, F2O,
Cl2O, octane, radon, uranium, hydrobromic acid.
PROPERTIES OF LIQUIDS & INTERPARTICLE FORCES:
Why would a metal object with higher density than
water float on water?
Why can we fill a glass of water above its rim?
Surface tension is related to strength of
attractive forces in liquid: the stronger the
attractive forces the greater the surface tension
Surface tension is the energy required to increase
surface area by a unit amount; units are J/m2
Figure 12.18
The molecular basis of surface tension.
hydrogen bonding
occurs across the
surface
and below the surface
hydrogen bonding
occurs in three
dimensions
the net vector
for attractive
forces is downward
Molecules in the interior
of a liquid experience
IM forces in all
directions. Molecules at
the surface experience
a net attraction
downward, causing the
liquid to minimize the
number of molecules at
the surface, ergo
surface tension.
Table 12.3
Surface Tension and Forces Between Particles
Surface Tension
Substance
Formula
(J/m2) at 200C
diethyl ether
CH3CH2OCH2CH3
1.7x10-2
dipole-dipole; dispersion
CH3CH2OH
2.3x10-2
H bonding
CH3CH2CH2CH2OH
2.5x10-2
H bonding; dispersion
H2O
7.3x10-2
H bonding
Hg
48x10-2
metallic bonding
ethanol
1-butanol
water
mercury
Major Force(s)
Figure 12.19
Shape of water or mercury meniscus in glass.
capillarity
stronger
cohesive forces
adhesive forces
H 2O
Hg
See note in box below or look in textbook.
Properties of Liquids
Capillary action: rising of a liquid through a
narrow space against the force of gravity
Viscosity: resistance to flow, units in
Newton-seconds/m2
Table 12.4 Viscosity of Water at Several Temperatures
viscosity - resistance to flow
Temperature(0C)
Viscosity
(N*s/m2)*
20
1.00x10-3
40
0.65x10-3
60
0.47x10-3
80
0.35x10-3
*The units of viscosity are Newton-seconds per square meter.
Why water is special:
Water molecules are 80% H-bonded at normal conditions
Molecules are so close together that you cannot tell which
H's belong to which O in each molecule
This is important to life on earth (& possibly elsewhere)
Ice floats on liquid water because the solid (ice) is less
dense than the liquid (good for fishies)
Ice forms a crystal structure in tetrahedral arrangement
Hydrogen-bonding also accounts for other physical
properties:
Lower weight alcohols are very soluble in water because
of the -OH functional group
Great solvent properties because water is so polar
Very high specific heat as noted back in Chapter 6
High surface tension
Figure 12.20
The H-bonding ability of the water molecule.
hydrogen bond donor
hydrogen bond acceptor
Because it has two O-H
bonds and two lone pairs,
one water molecule can
engage in as many as four
hydrogen-bonding attractions
to surrounding water
molecules, which are
arranged tetrahedrally.
Figure 12.21
The hexagonal structure of ice.
A. The geometric arrangement of the
hydrogen-bonding in water leads to
open, hexagonally shaped crystal
structure of ice. Thus, when water
freezes, the volume increases.
B. The delicate six-pointed beauty
of snowflakes reflects the
hexagonal crystal structure of ice.
SOLIDS & CRYSTAL STRUCTURES
SOLIDS: fixed particles that cannot move with
velocity, but do vibrate and rotate in position, so
they do have KE
Generally have long-range order - crystals have
well-defined regular shapes, or if short-range
order they are amorphous - no regular shape,
like asphalt, wax, glass
Crystal structure includes the four types of solids
ionic (all cation-anion units)
metallic (Cu, Zn, U, etc.)
molecular/atomic (ice, I2, etc.)
network covalent (diamond, SiC, SiO2)
General Properties of the Four
Types of Crystalline Solids
1. Ionic (KNO3, MgO): high MP/BP; some watersolb, brittle, conduct only when molten or
aqueous
2. Molecular (C10H8, I2): low MP/BP; more solb in
nonpolar; nonconductors
3. Network Covalent (Cdiamond, SiC, SiO2): very
high MP/BP; insolb, brittle, non- or semiconductor
4. Metallic (Cu, Fe, U): wide range of MPs; insolb,
malleable, ductile, elec conductor
Figure 12.22
celestite
The striking beauty of crystalline solids.
pyrite
amethyst
halite
Figure 12.22 in current 2nd edition has wulfanite, barite, calcite,
quartz as amethyst, and beryl (emerald)
Crystal Structures
Crystals have a crystal lattice arrangement of which
smallest pieces are unit cell in 3-D, containing > one
formula unit
Seven basic types: cubic, tetragonal, orthorhombic,
monoclinic, hexagonal, rhombohedral, triclinic
See packet of handouts and Dry Lab VI(?) in Lab Manual
for “Crystal Structures and Characteristics”
Simplest are the cubic, of which there are three types
Simple cubic (sc): metals and ionic cmpds
Body-centered cubic (bcc): metals
Face-centered cubic (fcc): metals and ionic cmpds
Figure 12.23
The crystal lattice and the unit cell.
lattice point
unit
cell
unit
cell
portion of a 3-D lattice
A. The lattice is an array of points that defines the
positions of the particles in a crystal structure. It is
shown here as points connected by lines. One unit cell is
highlighted.
portion of a 2-D lattice
A checkerboard is a twodimensional analogy for a lattice.
Figure 12.24 (1 of 3)
The three cubic unit cells.
Simple Cubic
1/8 atom at
8 corners
Atoms touch
along edge
of cube
Atoms/unit cell = 1/8 * 8 = 1
coordination number = 6
Cell length = 2r
See notes box below slide.
Figure 12.24 (2 of 3)
The three cubic unit cells.
Body-centered
Cubic
Atoms touch
along main
diagonal.
1/8 atom at
8 corners
1 atom at
center
Atoms/unit cell = (1/8*8) + 1 = 2
coordination number = 8
See notes box below slide.
Cell length = 4r/(3)1/2
Figure 12.24 (3 of 3)
The three cubic unit cells.
Face-centered
Cubic
1/8 atom at
8 corners
Atoms touch
along face
diagonal.
coordination number = 12
See notes box below slide.
1/2 atom at
6 faces
Atoms/unit cell = (1/8*8)+(1/2*6) = 4
Cell length = 4r/(2)1/2
Cell length and cell volume
See figure 12.28 for derivation of cell length based
on which cubic structure makes up the unit cell.
For metals cell length is: sc length = 2r; bcc
length = 4r/(3)1/2; fcc length = 4r/(2)1/2
Cell length determination is different for ionic
compounds, which are simple cubic or facecentered cubic: sc length = 2(r+R)/(3)1/2; fcc
length = 2(r+R)
Volume of any cube = (length)3
Crystal Structures Practice
See handouts and practice problems
Also chapter problems: 61, 64, 67, 73, 75
4th ed. #98: Polonium is a rare
radioactive metal that is the only element
with a crystal structure based on the
simple cubic unit cell. If its density is
9.142 g/cm3, calculate an atomic radius
for a polonium atom.
Crystal Structures Practice
4th ed. #101: Tantalum, with D = 16.634
g/cm3, has a bcc structure with an edge
length of 3.3058 Angstroms. Use its
molar mass and this data to prove
Avogadro’s number.
Phase Changes
exothermic
sublimination
vaporizing
melting
solid
liquid
condensing
freezing
deposition
endothermic
gas
Vapor Pressure
Evaporation/vaporization: small fraction of
molecules have high enough velocity to escape
force of attraction at surface
RATE OF EVAPORATION: will increase with
increasing T, since fraction of molecules with
escape vel will increase
In a closed system, a dynamic equilibrium will be
reached:
Rate of evaporation = rate of condensation
Vapor pressure: vapor molecules exert a partial
pressure called vapor pressure
Figure 12.4
Liquid-gas equilibrium.
A. In a closed flask at const T, with
air removed, Pi = 0. As molecules
escape surface to become vapor, P
increases. B. At equilibrium, # of
molecules escaping liquid = # of
molecules condensing, P is constant.
C. Plot of P vs. time shows P
becomes constant.
Figure 12.5
The effect of temperature on the distribution of
molecular speed in a liquid.
With T1 lower than T2, most probable molecular speed, u1, is less than u2.
Fraction of molecules with “escape velocity” is greater at the higher
temperature. At higher T, equilibrium is reached with more molecules in
the vapor phase, therefore at a higher P.
Vapor Pressure Practice
If 1.00 L of water is placed in 2.30x104 L
closed room, will all the water evaporate?
Given D = 0.997 g/mL, Vapor Pressure =
23.8 torr at 25.0oC.
Water will evap till room is at 23.8 torr
partial pressure of water vapor.
See how many moles at that point:
n = PV/RT = 29.4 mol
How many moles in 1.0 L beaker? About 55
moles - won't all evaporate
Vapor Pressure vs. Temperature
Boiling point: occurs when you see bubbles
of gas forming in the liquid and coming to
surface
Any pure liquid remains at constant T while
boiling, since this is a change of state
Definition:
BP is the Temperature at which VP =
barometric P
Why does water boil at 100oC in Fairfield
and at 95oC in Denver?
Figures 12.6 and 12.7
Figure 12.7
Vapor pressure as a function of
temperature and intermolecular forces.
A linear plot of vapor
pressure- temperature
relationship.
The Clausius-Clapeyron equation comes
from this graph: y = mx + b
You practice drawing and
labelling a generic VP curve
Vapor pressure curves:
Initial "phase diagrams" incorporated into
P/T diagrams that will include solid phase
later
Why can NH3 be condensed from gas to
liquid at Room T by compression, but N2
can't?
Relative Humidity
NOT IN TEXT:
Relative humidity as reported by weather
forecasters:
%water evap=actual partial P/equil vapor P * 100
If actual is 12.8 and VP for given T is 21.1,
relative humidity is 61%
VP and DHvap
DHvap is related to VP and T thru the
Clausius-Clapeyron equation
ln P = (-DHvap/RT) + C (where R = 8.314
J/mol-K, T in K)
If plotted on a graph, the slope is:
=(ln p2 – ln p1)/(1/T2 – 1/T1)= -DHvap/R
Rearranges to Clausius-Clapeyron
Equation (next slide)
The Clausius-Clapeyron Equation
ln P =
MEMORIZE!
-DHvap1 
   C
R
T 
P2
-DHvap 1
1 
ln
=
  
R T2 T 
P1
1
Alternately, if you don’t want to use
the negative sign:
ln (P2/P1) = DHvap/R(1/T1-1/T2)
Clausius-Clapeyron equation
examples
Look at Sample Problem 12.2 in text.
My Example: hexane has DHvap = 30.1 kJ/mol and
at 25.0oC, VP = 148 torr. What will VP be at
50.0oC?
ln (P2/148) = (-30.1x103J/8.314 J/mol-K)(1/323.15 – 1/298.15)
ln (P2/148) = 0.9394 (take antilog of both sides)
P2/148 = e0.9394 = 2.55
P2 = 379 torr
Practice:
Chapter problems: 17 & 18
17: A liquid has DHovap of 35.5 kJ/mol and a
BP of 122oC at 1.00 atm. What is its VP at
113oC?
18: What is the DHovap of a liquid that has a
VP of 641 torr at 85.2oC and a BP of
95.6oC at 1.00 atm?
Figure 12.8 4th ed.,
not in principles
Iodine subliming.
test tube with ice
iodine solid
iodine vapor
iodine solid
Simple Phase Diagrams
Are P vs. T diagrams showing three phases for
pure elements or compounds, incorporates the
VP curve
Critical Point is where liquid and gas cannot be
distinguished from each other
Triple Point is where solid, liquid and gas phases
meet and all three are present
Example: For water the Triple Point is 0.01oC and
4.58 torr
For CO2 Triple Point is at -56.7oC and 5.1 atm
Figure 12.8
Phase diagrams for CO2 and H2O.
CO2
H 2O
Each region depicts the T & P under which the phase is stable. Lines between regions show
conditions at which two phases exist in equilibrium. The Critical Point shows conditions beyond
which liquid and gas cannot be distinguished from each other. At the triple point, three phases
exist is equilibrium. CO2 phase diagram is typical with forward sloping solid-liquid line; solid is
more dense than liquid. H2O phase diagram is sloping backward; solid is less dense than liquid.
Phase Diagrams
You must draw and label phase diagrams
based on data given to you and determine
the physical state of a substance from its
placement on a phase diagram.
Work on problems 20 & 22