CHEM 121
Introduction to Fundamental Chemistry
Summer Quarter 2008 SCCC
Lecture 10
http://seattlecentral.edu/faculty/lcwest/CHE121
The States of Matter
ƒ Observed Properties of Matter
ƒThe Kinetic Molecular Theory of Matter
ƒ The Solid, Liquid and Gaseous States of Matter
ƒ The Gas Laws
ƒ Pressure, Temperature and Volume Relationships
ƒ The Ideal Gas Laws
ƒ Dalton’s Law
ƒ Grahams Law
Matter exists in three common states:
ƒ Solid
ƒ Liquid
ƒ Gas
At 250C and 1 atmosphere all elements are solids, except:
ƒ The group 8 elements are all gases.
ƒ H2, N2, O2, F2 and Cl2 are gases.
ƒ Hg and Br2 are liquids.
We can define a kinetic theory of matter based on the following
postulates:
1. Matter is composed of small particles called molecules
2. The particles are in constant random motion
ƒ
They possess kinetic energy
3. There are repulsive and attractive forces between
particles.
ƒ
They posses potential energy
4. Average particle speed increases with temperature
5. No energy is lost when the particles collide
The kinetic energy of a particle is given by the equation:
1
KE = mv 2
2
Where:
m = particle mass and
v = particle velocity
According to postulate 4 of our kinetic theory particle velocity
increases with temperature. This means as temperature
increases our theory says the kinetic energy increases.
Potential energy is the sum of the attractive and repulsive
forces between particles.
Examples of these types of forces are the gravitational attractive
forces between objects and the repulsive forces between the
same poles of magnets.
Alternatively we can say forces between particles may be either
cohesive or disruptive.
Cohesive forces are of the type we described in chapter 4 and
include dipole-dipole interactions, dispersion forces, attraction
between oppositely charged ions.
Cohesive forces are largely temperature independent.
e.g. magnets and gravity function the same way at different
temperature.
Disruptive forces are those forces that make particles move
away from each other.
These forces result predominately from the particle motion.
Disruptive forces increase with temperature in agreement with
postulate 4.
We can conclude that as we increase the temperature particles
will become further apart from each other.
Gases are characterized by:
ƒ Being easily compressible
ƒ Variable shape
ƒ Shape adapts to that of the container.
ƒDensity is lowest in this phase and is variable (d = m/V)
ƒ Fill whatever container they are placed in
ƒThe largest thermal expansion of all phases.
ƒGases rapidly expand when heated.
The shape, density and volume of a gas depends on the
container!!
The particles in gases are well separated from each other, move
in rapid random motion and do not have fixed positions.
ƒ Gases fill whatever container they are
placed in.
ƒ This means their density, volume and
shape is dependent on the container they
are in.
ƒ Gases are easily compressed.
The attractive forces between particles of a gas are relatively
weak.
In the liquid state the particles are randomly arranged (like in a
gas).
The particles are closer to each other than in gases so the
density of liquids is greater than that of gases.
Liquids adopt the shape of the container into which they are
placed.
Unlike gases liquids have a fixed volume and density. This is
because they have greater attractive forces between particles.
As the particles in liquids are very close to one another they have
small compressability.
When particles of a liquid are heated the particles will move
around more rapidly.
As they have many close neighbours they may only travel a
short distant before undergoing a collision and bouncing back in
the opposite direction. For this reason liquids have little thermal
expansion.
Liquid state
Gaseous state
ƒParticles are close together
ƒParticles are far apart
ƒNot held in fixed positions
ƒCompletely fill container
ƒTake the shape of container
ƒEasily compressed
ƒHave fixed volume
ƒModerate thermal expansion
ƒLittle compressability
ƒSmall thermal expansion
In the solid state particles are held in fixed lattice positions.
Cohesive forces are much more dominant for solids than
dispersive forces.
Unlike gases solids have fixed shape, volume and density.
The particles may only move a small amount around their fixed
positions so solids have little thermal expansion.
In solids the particles are close together and so they have high
density.
ƒ Strong cohesive forces
ƒ Particles in fixed lattice positions
ƒ Constant shape
ƒ Constant density
ƒ Constant volume
ƒ Minimal compressability
ƒ Little thermal expansion
The mathematical relationships between pressure,
temperature, volume and amount of gases are called gas laws.
The development of the gas laws were developed around the time
of the industrial revolution and contributed greatly to the
development of the steam and internal combustion engine.
When performing calculations with the gas laws we use the
Kelvin temperature scale.
The Kelvin temperature scale has the same size increments as
the Celcius temperature scale but has its zero set at the
temperature at which all motion stops (kinetic energy = 0).
This temperature is called absolute zero and is equal to
-273oC.
K = oC + 273
The relationship between pressure and volume at constant
temperature is given by Boyles law.
Boyles law states that at constant temperature pressure is
inversely proportional to volume.
Intuitvely this makes sense
What does this mean mathematically?
Working through from the original relationship:
1
V
k
P=
V
Pα
Pi =
where k is a constant for a given temperatur e
k
Vi
Pi Vi = k
Pf V f = k
Pi Vi = P f V f
Charles law states that at constant pressure the volume of a
gas is proportional to its temperature.
i.e. as we heat a gas up it expands and as we cool a gas it
contracts.
Mathematically Charles law can be expressed:
VαT
V = k' T
where k' is a constant for a given pressure
V
= k'
T
Vi
= k'
Ti
Vf
Tf
= k'
Vi V f
=
Ti
Tf
Boyles law and Charles law can be combined to give the
combined gas law.
The combined gas law is expressed mathematically as:
PV
= k' ' where k' ' is a constant
T
Pi Vi
= k' '
Ti
Pf V f
= k' '
Tf
Pi Vi P f V f
=
Ti
Tf
Boyles law states that at constant temperature:
Pα
1
V
P=
k
V
where k is a constant for a given temperatur e
Pi Vi = P f V f
If we know three of the parameters Pi, Vi, Pf and Vf
we can determine the unknown parameter.
Charles law states that at constant pressure:
VαT
V = k' T
where k' is a constant for a given pressure
Vi V f
=
Ti
Tf
If we know three of the parameters Ti, Vi, Tf and Vf
we can determine the unknown parameter.
Boyles law and Charles law can be combined to give the
combined gas law:
PV
= k' ' where k' ' is a constant
T
Pi Vi P f V f
=
Ti
Tf
If we know five of the parameters Pi, Ti, Vi, Pf, Tf and Vf
we can determine the unknown parameter.
All of the gas laws we have discuss so far have not considered
variations in the amount of gas.
i.e. they are for a fixed quantity of gas.
The Italian scientist Amadeo Avagadro investigated how the
pressure, temperature and volume of a gas varies with the
amount of gas.
Avogadro proposed that:
“equal volumes of gases at the same pressure and
temperature contain equal numbers of gas molecules”
This was found to be true and became known as Avogadro’s
law.
If a gas cylinder containing 1 mole of H2 gas has a pressure
of 1 atm and a temperature of 298K and I then empty this
cylinder and fill it with CO2 to the same pressure while
maintaining the temperature at 298K how many moles of CO2
would the cylinder contain ?
1 mole of CO2
Combining Boyle’s, Charles’s and Avogadro’s Laws we can obtain
the “ideal gas law”.
PV = nRT where R is a constant
R is called the universal gas constant:
R = 0. 0821 L atm mol-1 K-1
Using the ideal gas equation if we are given any three of P, V, n
or T we can determine the unkown parameter.
The gas laws we have discussed so far work well for “ideal
gases”.
Ideal gases are defined to have no interparticle interactions.
This is mostly true for the noble gases it is certainly not the
case for highly polar molecules.
For gases with significant interparticle interactions deviation
from ideal behaviour will be observed, particularly at extremes
of pressure and temperature.
Dalton’s law states:
“the total pressure exerted by a mixture of gases at constant
volume and temperature is equal to the sum of the partial
pressures”
or mathematically:
Ptotal = ∑ Pi
i
Our text book has an excellent explanation of this on page 183.
Consider three same sized gas cylinders containing three
different gases at three different pressures.
What would the
pressure be if we put
all this gas into a
fourth cylinder of the
same size?
Ptotal = PU + Po + P †
Consider a box full of gas. If I put a hole in this box the gas will
begin to leak out.
This process is called effusion.
The rate of effusion depends upon
the molecular mass of the gas
according to Graham’s law.
effusion rate of A
=
effusion rate of B
molecular mass of B
molecular mass of A
Consider two boxes of different gases.
If these boxes are brought
A
B
together and the wall between
them removed they will
spontaneously mix. This
process is called diffusion.
diffusion rate of A
=
diffusion rate of B
molecular mass of B
molecular mass of A
When matter takes energy from its surroundings (endothermic
processes) the kinetic energy of the particles increases
resulting in greater dispersive forces and the particles moving
away from each other.
i.e. Processes in which particles move away from each other
(solid to liquid change of state) are endothermic.
When matter releases energy to its surroundings (exothermic
processes) the kinetic energy of the particles decreases
resulting in greater cohesive forces and the particles moving
closer to each other.
i.e. Processes in which particles move closer to each other (liquid
to solid change of state) are exothermic.
Evaporation is the name of the process by which a liquid
becomes a gas.
Considering our previous discussion would you expect
evaporation to be endothermic or exothermic?
Evaporation takes place from the surface of a liquid.
How do you expect the rate of evaporation to be affected by
the surface area of the liquid?
We can define the vapor pressure of a liquid as:
“the pressure exerted by a vapor that is in equilibrium with its
liquid.”
This is a little confusing so lets take sometime to explain.
If we place a liquid in a sealed
conatiner with some empty space
above the liquid initially there will be
no vapor or gas above that liquid.
Those molecules at the surface of
the liquid with sufficient energy will
leave the liquid and enter the gas
phase. Some of the vapor molecules
will strike the surface of the liquid
and return to the liquid phase.
When the rate at which the liquid is entering the gas phase
equals the rate at which the vapor is returning to the liquid phase
we say the system is at equilibrium. After this time the liquid
level will remain constant. The pressure exerted by the vapor at
this time is called the vapor pressure.
The vapor pressure of a liquid decreases with molecular mass.
The vapor pressure of a increases with temperature.
The vapor pressure of a liquid depends upon the chemical nature
of the liquid.
Those molecules that have strong intermolecular attractive
forces have lower vapor pressures than expected for their
molecular mass.
What easily recognised characteristic will lead to strong
intermolecular attractive forces?
Lets consider some examples:
At 20oC H2O (MW = 18 gmol-1) has a vapor pressure of 17.5 torr !!
This due to strong hydrogen bonds between water molecules.
As we increase the temperature the vapor pressure of a liquid
increases.
The temperature at which the vapor pressure equals the external
pressure (atmospheric pressure) is called the boiling point.
Bubbles of vapor with atmospheric pressure may form anywhere
in the liquid and rise to the surface at the boiling point of a liquid.
What is the effect of lowering the atmospheric pressure on
the boiling point?
We will skip sections 6.14 and 6.15
Midterm Tuesday will cover material from Chapter 4, Chapter
5 and Sections 6.1-6.13
Next Tuesday is a BIG day you have a lab to hand
in and prepare for as well as the midterm.
Don’t leave everything to the last minute !!