Unit 7
States of Matter
A phase is a homogeneous part of the system in
contact with other parts of the system but
separated from them by a well-defined boundary.
2 Phases
Solid phase - ice
Liquid phase - water
11.1
Studying Solids, Liquids and Gases
• The study of solids, liquids, and
gases require an understanding of:
–The kinetic molecular theory
–The arrangement of atoms within
a molecule.
–The intermolecular forces of
attraction between particles.
Kinetic Molecular Theory
1. Particles of matter are ALWAYS in motion
2. A gas is composed of molecules that are
separated from each other by distances far
greater than their own dimensions. The
molecules can be considered to be points; that
is, they possess mass but have negligible
volume.
3. Collisions of particles with container walls are
elastic collisions (no loss of kinetic energy).
4. Particles of a gas exert no forces on each other.
5. Average kinetic energy  Kelvin
temperature of a gas.
Kinetic Energy of Gas Particles
At the same conditions of temperature,
all gases have the same average kinetic
energy, but not the same speed.
1 2
KE  mv
2
If each of these containers contain gas as the same temperature,
which gas has the slowest average velocity? Which gas has the
fastest average velocity?
Two factors determine whether a
substance is a solid, a liquid, or a gas.
1. The kinetic energies of the particles (atoms,
molecules, or ions) that make up a substance.
Kinetic energy tends to keep the particles
moving apart.
2. The attractive intermolecular forces between
particles that tend to draw the particles
together.
– If the average kinetic energy is greater than the
attractive forces between the particles, a substance
will not condense to form a liquid or a solid.
– If the kinetic energy is less than the attractive
forces, a liquid or solid will form.
The average kinetic energy
of the particles in a gas is
great enough to overcome
the forces of attraction
between them. The
molecules of a gas move
apart when they collide.
The average kinetic energy
of the particles in a liquid (or
solid) is small enough that
the forces of attraction
between them is sufficient to
hold the particles close
together. The molecules in a
liquid (or solid) do not move
apart.
Intermolecular Forces
Intermolecular forces are attractive forces between molecules.
Intramolecular forces hold atoms together in a molecule.
Intermolecular vs Intramolecular
•
41 kJ to vaporize 1 mole of water
•
930 kJ to break all O-H bonds in 1 mole of water
“Measure” of intermolecular force
Generally,
intermolecular
forces are much
weaker than
intramolecular
forces.
boiling point
melting point
ΔHvap
Δ Hfus
Δ Hsub
11.2
Types of Intermolecular Forces
Dipole-Dipole Forces
Attractive forces between polar molecules
Orientation of Polar Molecules in a Solid
11.2
Dipole
Forces
dipole-dipole
attraction:
molecules with
dipoles orient
themselves so
that “+” and “-”
ends of the
dipoles are close
to each other.
Types of Intermolecular Forces
Ion-Dipole Forces
Attractive forces between an ion and a polar molecule
Ion-Dipole Interaction
11.2
11.2
Types of Intermolecular Forces
Hydrogen Bond (strongest)
The hydrogen bond is a special dipole-dipole interaction
between the hydrogen atom in a polar N-H, O-H, or F-H bond
and an electronegative O, N, or F atom. IT IS NOT A BOND.
11.2
Hydrogen Bonding in Water
hydrogen
bonds: dipoledipole attraction
in which hydrogen
is bound to a
highly
electronegative
atom. (F, O, N)
Why is the hydrogen bond considered a
“special” dipole-dipole interaction?
Talk about hydrides and electron increasing.
Decreasing molar mass
Decreasing boiling point
11.2
Types of Intermolecular Forces
Dispersion Forces – van der Walls forces/London forces
(weakest)
Attractive forces that arise as a result of temporary
dipoles induced in atoms or molecules
ion-induced dipole interaction
dipole-induced dipole interaction
11.2
Induced-Dipole Forces
• Induced dipole forces result when an ion or a dipole
induces a dipole in an atom or a molecule with no
dipole. These are weak forces. Ion-Induced Dipole Forces
Dipole-Induced Dipole Forces
A weak attraction that
results when the
approach of an ion
induces a dipole in an
atom or in a nonpolar
molecule by disturbing
the arrangement of
electrons in the
nonpolar species.
A weak attraction that
results when a polar
molecule induces a
dipole in an atom or in
a nonpolar molecule
by disturbing the
arrangement of
electrons in the
nonpolar species.
Because of the constant motion of the electrons, an atom or
molecule can develop a temporary (instantaneous) dipole when
its electrons are distributed unsymmetrically about the nucleus.
A second atom or molecule, in turn, can be distorted by the
appearance of the dipole in the first atom or molecule
(because electrons repel one another) which leads to an
electrostatic attraction between the two atoms or molecules.
Intermolecular Forces
Dispersion Forces Continued
Dispersion forces are present between all molecules, whether they are
polar or nonpolar.
Polarizability is the ease with which the electron distribution in the atom or
molecule can be distorted.
Polarizability increases with:
•
greater number of electrons
•
more diffuse electron cloud
Dispersion forces
usually increase
with molar mass.
11.2
Physical Consequences of Hydrogen
Bonding
• At 25oC, nitrosyl fluoride (ONF) is
a gas whereas water is a liquid.
Why?
– ONF and water have about the
same shape.
– ONF has a higher molecular weight
(49 amu) than water (18 amu).
• Conclusion: London dispersion forces
not responsible for the difference
between these two compounds.
– ONF and water have the same
dipole moment.
• Conclusion: dipole-dipole forces not
responsible for the difference between
these two compounds.
– ONF cannot form hydrogen bonds;
water can form hydrogen bonds.
What type(s) of intermolecular forces exist between each of the
following molecules?
HBr
HBr is a polar molecule: dipole-dipole forces. There are also dispersion
forces between HBr molecules.
CH4
CH4 is nonpolar: dispersion forces.
S
SO2
SO2 is a polar molecule: dipole-dipole forces. There are also
dispersion forces between SO2 molecules.
11.2
Types of Intermolecular ForcesSolutions
What intermolecular forces are present in each of
the following?
1. Water
6. Nitrogen (N2)
2. Carbon tetrachloride
7. Ethane (C2H6)
3. Ammonia
8. Acetone (CH2O)
4. Carbon dioxide
9. Methanol (CH3OH)
5. Phosphorus trichloride 10. Borane (BH3)
Properties of Liquids
Surface tension is the amount of energy required to stretch
or increase the surface of a liquid by a unit area.
Strong
intermolecular
forces
High
surface
tension
11.3
Properties of Liquids
Cohesion is the intermolecular attraction between like molecules
Adhesion is an attraction between unlike molecules
Adhesion
attracted to glass
Cohesion
attracted to each other
11.3
Properties of Liquids
Viscosity is a measure of a fluid’s resistance to flow.
Strong
intermolecular
forces
High
viscosity
11.3
Types of Crystals
Ionic Crystals – Ion-Ion interactions are the strongest
(including the “intermolecular forces” (H bonding, etc.)
• Lattice points occupied by cations and anions
• Held together by electrostatic attraction
• Hard, brittle, high melting point
• Poor conductor of heat and electricity
CsCl
ZnS
CaF2
11.6
Types of Crystals
Covalent Network Solid – Stronger than intermolecular forces but generally
weaker than ion-ion
• Lattice points occupied by atoms
• Held together by covalent bonds
• Hard, high melting point
• Poor conductor of heat and electricity
carbon
atoms
diamond
graphite
11.6
Diamond
Graphite
Types of Crystals
Metallic Crystals – Typically weaker than covalent, but can be in the low
end of covalent
•
•
•
•
Lattice points occupied by metal atoms
Held together by metallic bonds
Soft to hard, low to high melting point
Good conductors of heat and electricity
Cross Section of a Metallic Crystal
nucleus &
inner shell e-
mobile “sea”
of e-
11.6
Types of Crystals
11.6
Strong to weak
Let’s list all the intermolecular forces in order
from strongest to weakest…
Practice-States of Matter HW 2
Three States of Matter
Volume
T2 > T1
Condensation
Evaporation
Least
Order
Greatest
Order
11.8
Practice—States of Matter HW1
The equilibrium vapor pressure is the vapor pressure
measured when a dynamic equilibrium exists between
condensation and evaporation
H2O (l)
H2O (g)
Dynamic Equilibrium
Rate of
= Rate of
condensation evaporation
11.8
Gas-Liquid Equilibration
Copyright 1999,
PRENTICE HALL
Chapter 11
44
Molar heat of vaporization (DHvap) is the energy required to vaporize 1 mole of a
liquid.
Clausius-Clapeyron Equation
ln P = -
ΔHvap
P = (equilibrium) vapor pressure
+C
RT
C = constant (depends on P & T)
T = temperature (K)
R = gas constant (8.314 J/K•mol)
11.8
The boiling point is the temperature at which the (equilibrium) vapor
pressure of a liquid is equal to the external pressure.
The normal boiling point is the temperature at which a liquid boils when
the external pressure is 1 atm.
11.8
The critical temperature (Tc) is the temperature above which
the gas cannot be made to liquefy, no matter how great the
applied pressure.
The critical pressure
(Pc) is the minimum
pressure that must be
applied to bring about
liquefaction at the
critical temperature.
11.8
Critical Temperature, Tc
Copyright 1999,
PRENTICE HALL
Chapter 11
48
The melting point of a solid or
the freezing point of a liquid is
the temperature at which the
solid and liquid phases coexist
in equilibrium
Freezing
H2O (l)
Melting
H2O (s)
11.8
Molar heat of fusion (ΔHfus) is the energy required to melt
1 mole of a solid substance.
11.8
11.8
Heating Curve Illustrated q=mCΔT
Copyright 1999,
PRENTICE HALL
Chapter 11
52
Practice-Heating Curve WS
Molar heat of sublimation
(ΔHsub) is the energy required to
sublime 1 mole of a solid.
Deposition
H2O (g)
Sublimation
H2O (s)
ΔHsub = ΔHfus + ΔHvap
( Hess’s Law)
11.8
A phase diagram summarizes the conditions at which a substance exists
as a solid, liquid, or gas.
The triple point is where all 3 phases meet.
Phase Diagram of Water
11.9
11.9
Can you find…
Where’s Waldo?
The Triple Point?
Critical pressure?
Critical temperature?
Where fusion occurs?
Where vaporization
occurs?
Melting point
(at 1 atm)?
Boiling point
(at 6 atm)?
Carbon Dioxide
11.9
Practice-Phase Diagram WS
Gases
Elements that exist as gases at 250C and 1 atmosphere
5.1
5.1
Physical Characteristics of Gases
•
Gases assume the volume and shape of their containers.
•
Gases are the most compressible state of matter.
•
Gases will mix evenly and completely when confined to the
same container.
•
Gases have much lower densities than liquids and solids.
5.1
Pressure =
Force
Area
(force = mass x acceleration)
Units of Pressure
1 pascal (Pa) = 1 N/m2
1 atm = 760 mm Hg = 760 torr
= 101,325 Pa (101.325 kPa)
= 14.7 psi
= 29.92 in. Hg
Barometer
5.2
10 miles
4 miles
Sea level
0.2 atm
0.5 atm
1 atm
5.2
Converting Celsius to Kelvin
Gas law problems involving
temperature require that the
temperature be in KELVINS!
Kelvins = C + 273
°C = Kelvins - 273
Boyle’s Law
P α 1/V
This means Pressure and
Volume are INVERSELY
PROPORTIONAL if moles
and temperature are
constant (do not change).
For example, P goes up as
V goes down.
P1V1 = P2 V2
Robert Boyle
(1627-1691). Son
of Earl of Cork,
Ireland.
Charles’s Law
If n and P are constant,
then V α T
V and T are directly
proportional.
V1
V2
=
T1
T2
• If one temperature goes up, the
volume goes up!
Jacques Charles (17461823). Isolated boron and
studied gases. Balloonist.
Gay-Lussac’s Law
If n and V are
constant,
then P α T
P and T are directly
proportional.
P1
P2
=
T1
T2
If one temperature goes up,
the pressure goes up!
Joseph Louis Gay-Lussac
(1778-1850)
Combined Gas Law
• The good news is that you don’t
have to remember all three gas
laws! Since they are all related to
each other, we can combine them
into a single equation. BE SURE
YOU KNOW THIS EQUATION!
P1 V1
P2 V2
=
T1
T2
No, it’s not related to R2D2
And now, we pause for this
commercial message from STP
OK, so it’s really not THIS kind of
STP…
STP in chemistry stands for
Standard Temperature and
Pressure
Standard Pressure =
1 atm
(or an equivalent)
Standard Temperature =
0 deg C (273 K)
STP allows us to compare
amounts of gases between
different pressures and
temperatures
Avogadro’s Law
V a number of moles (n)
V = constant x n
Constant temperature
Constant pressure
V1/n1 = V2/n2
5.3
Ideal Gas Equation
Boyle’s law: V a 1 (at constant n and T)
P
Charles’ law: V a T (at constant n and P)
Avogadro’s law: V a n (at constant P and T)
Va
nT
P
V = constant x
nT
=R
P
nT
P
R is the gas constant
PV = nRT
5.4
Ideal Gases
Ideal gases are imaginary gases
that perfectly fit all of the
assumptions of the kinetic
molecular theory.
Best observed at high
temperatures, low pressures, with
few molecules. This lessens the
intermolecular forces of attraction
Deviation of Real Gases from
Ideal Behavior
 Real Gases
 A gas that does not behave
completely according to the
assumptions of the kinetic-molecular
theory
 Kinetic-molecular theory holds
true for noble gases.
The conditions 0 0C and 1 atm are called standard
temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal gas
occupies 22.414 L.
PV = nRT
(1 atm)(22.414L)
PV
R=
=
nT
(1 mol)(273.15 K)
R = 0.082057 L • atm / (mol • K)
5.4
Density (d) Calculations
PM
m
d=
=
V
RT
m is the mass of the gas in g
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
Solve for n, which =
mass/molar mass
Or,
dRT
M=
P
d is the density of the gas in g/L
5.4
A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and
27.00C. What is the molar mass of the gas?
PV = nRT
2.10 L x 1 atm
n=
L•atm
0.0821 mol•K
x 300.15 K
n = 0.0852 mol
n=
g
M
M = 54.6 g/mol
5.3
Gas Stoichiometry
What is the volume of CO2 produced at 370 C and 1.00 atm
when 5.60 g of glucose are used up in the reaction:
C6H12O6 (s) + 6O2 (g)
g C6H12O6
5.60 g C6H12O6
V=
mol C6H12O6
x
nRT
=
P
6CO2 (g) + 6H2O (l)
mol CO2
V CO2
6 mol CO2
1 mol C6H12O6
x
= 0.187 mol CO2
180 g C6H12O6
1 mol C6H12O6
L•atm
x 310.15 K
mol•K
1.00 atm
0.187 mol x 0.0821
= 4.76 L
5.5
Dalton’s Law of Partial Pressures
V and T
are
constant
P1
P2
Ptotal = P1 + P2
5.6
Consider a case in which two gases, A and B, are in a container of
volume V.
nART
PA =
V
nA is the number of moles of A
nBRT
PB =
V
nB is the number of moles of B
PT = PA + PB
PA = XA PT
nA
XA =
nA + nB
nB
XB =
nA + nB
PB = XB PT
Pi = Xi PT
mole fraction (Xi) =
ni
nT
5.6
A sample of natural gas contains 8.24 moles of CH4, 0.421
moles of C2H6, and 0.116 moles of C3H8. If the total
pressure of the gases is 1.37 atm, what is the partial pressure
of propane (C3H8)?
Pi = Xi PT
PT = 1.37 atm
Xpropane =
0.116
8.24 + 0.421 + 0.116
Ppropane = 0.0132 x 1.37 atm
= 0.0132
= 0.0181 atm
5.6
Bottle full of oxygen gas
and water vapor
2KClO3 (s)
2KCl (s) + 3O2 (g)
PT = PO2 + PH2 O
5.6
5.6
Chemistry in Action:
Scuba Diving and the Gas Laws
P
Depth (ft)
Pressure
(atm)
0
1
33
2
66
3
V
5.6
Kinetic theory of gases and …
• Compressibility of Gases
• Boyle’s Law
P a collision rate with wall
Collision rate a number density
Number density a 1/V
P a 1/V
• Charles’ Law
P a collision rate with wall
Collision rate a average kinetic energy of gas molecules
Average kinetic energy a T
PaT
5.7
Kinetic theory of gases and …
• Avogadro’s Law
P a collision rate with wall
Collision rate a number density
Number density a n
Pan
• Dalton’s Law of Partial Pressures
Molecules do not attract or repel one another
P exerted by one type of molecule is unaffected by the
presence of another gas
Ptotal = SPi
5.7
Deviations from Ideal Behavior
1 mole of ideal gas
PV = nRT
PV = 1.0
n=
RT
Repulsive Forces
Attractive Forces
5.8
Effect of intermolecular forces on the pressure exerted by a gas.
5.8
Van der Waals equation
nonideal gas
(
2)
an
P + 2 (V – nb) = nRT
V
}
}
corrected
pressure
corrected
volume
5.8
Velocity of a Gas
The distribution of speeds
of three different gases
at the same temperature
The distribution of speeds
for nitrogen gas molecules
at three different temperatures
urms =
M
3RT
5.7
Gas diffusion is the gradual mixing of molecules of one gas with
molecules of another by virtue of their kinetic properties.
NH4Cl
NH3
17 g/mol
HCl
36 g/mol
5.7
GAS DIFFUSION AND
EFFUSION
• diffusion is the
gradual mixing of
molecules of
different gases.
• effusion is the
movement of
molecules through
a small hole into an
empty container.
GAS DIFFUSION AND
EFFUSION
Graham’s law governs
effusion and diffusion
of gas molecules.
KE=1/2 mv2
Rate for A
Rate for B
M of B
M of A
Rate of effusion is
inversely proportional to
its molar mass.
Thomas Graham, 1805-1869. Professor in
Glasgow and London.
GAS DIFFUSION AND
EFFUSION
Molecules effuse thru holes in a
rubber balloon, for example, at
a rate (= moles/time) that is
• proportional to T
• inversely proportional to M.
Therefore, He effuses more
rapidly than O2 at same T.
He
Gas Diffusion
relation of mass to rate of diffusion
• HCl and NH3 diffuse
from opposite ends of
tube.
• Gases meet to form
NH4Cl
• HCl heavier than NH3
• Therefore, NH4Cl
forms closer to HCl
end of tube.
Graham’s Law Problem 1
1 mole of oxygen gas and 2 moles of ammonia are
placed in a container and allowed to react at 850
degrees celsius according to the equation:
4 NH3(g) + 5 O2(g) --> 4 NO(g) + 6 H2O(g)
Using Graham's Law, what is the ratio of the
effusion rates of NH3(g) to O2(g)?
Graham’s Law Problem 2
What is the rate of effusion for H2 if 15.00 ml
of CO2 takes 4.55 sec to effuse out of a
container?
Graham’s Law Problem 3
What is the molar mass of gas X if it effuses
0.876 times as rapidly as N2(g)?