Chem 205 Physical Chemistry by zrn20302


									Chem 205 Physical Chemistry
       Section 208, MWF 8:00 am
       Section 210, MWF 10:00 am

    David Chen, Chemistry/Physics A347,
Office Hours: Wednesday 2 pm and Fridays 11 am

      Part I Thermodynamics

      Part II Kinetics

      Part III Spectroscopy
Marking Scheme:

Midterm, Monday Feb. 23rd, 2004, 25%

Quizzes, TBA, 15%

Final, TBA, 60%

Textbook: The Elements of Physical Chemistry with
Applications in Biology, 3rd Ed., Peter Atkins
      Part I Thermodynamics
             Transformations of Energy

    Why do we need to know Thermodynamics?

Thermodynamics is central to chemistry, and central to life.

 It explains why reactions occur (the driving forces of the
 reactions), and the energy a reaction generates or requires.
Question: Is it possible to design a ship that is purely
powered by the heat of the ocean -- take in water from the
ocean, absorb the heat from water and turn water into ice,
then drop the ice balls behind?
What is the origin of life?

Evolution?                Creation?

Will we know everything about life when we graduate?

 What’s the purpose of life?
by means of Natural Selection, or the Preservation of
Favored Races in the Struggle for Life
-- 1859

THE DESENT OF MAN, and Selection in Relation to Sex
-- 1871
Charles Robert Darwin

Concept of Evolution

There is a kinship among all forms of life because all
evolved in an amplitude of time from one common ancestry,
and that there are differences between them because they
have diverged from that ancestry in taking over the earth, its
air and its waters.

Then God said, “Let the land produce vegetation: seed-baring plants and
trees on the land that bear fruit with seed in it, according to their various
--Genesis 1: 11

And God said, “Let the water teem with living creatures, and let birds fly
above the earth across the expanse of the sky.” So God created the great
creatures of the sea and every living and moving thing with which the
water teems, according to their kinds, and every winged bird according
to its kind.
--Genesis 1:20-21

Then God said, “Let us make man in our image, in our likeness, and let
them rule the fish of the sea and the birds of the air, over the livestock,
over all the earth, and over all the creatures that move along the ground.
So God created man in his own image, in the image of God he created
him; male and female he created them.
--Genesis 1: 26-27
All flesh is not the same: Men have one kind of flesh, animals have another,
birds another and fish another. There are also heavenly bodies and there are
earthly bodies; but the splendor of the heavenly bodies is one kind, and splendor
of the earthly bodies is another.
1 Corinthians 15:39-40

So will it be with the resurrection of the dead. The body that is sown is
perishable, it is raised imperishable.
1 Corinthians 15:42

The purpose of human existence: to inherit the kingdom of God.

We have to know the differences between hypotheses, theories,
facts, faith, and truth when we make decisions. Physical
chemistry is an integral part of knowledge that forms a solid
foundation for chemistry and for life.
  Chapter 1 The properties of Gases

Gases form the working substance of many machines
(e.g., heat engines, refrigerators) and it is important to
understand something of their properties. The gas phase
is also the simplest state of matter to treat theoretically,
and it shows limiting behavior that is universal. This
enables us to make a number of useful generalizations.
In the early stages of developing and understanding
thermodynamic concepts we shall deal largely with the
gas phase because of this simplicity and generality.
The state of a system is defined by a particular set of
property numbers. The set of property values (in
particular, P, V and T) describing the state of a system
can sometimes be related by an algebraic expression
called an equation of State.

 For ideal gases, or any gas at a low pressure,
 the state equation is:

            PV = nRT
P: pressure

V: volume

n: number of moles

R: gas constant
0.082 L atm K-1 mol-1
0.08314 L bar K-1 mol-1
                          Chemical Principles: The Quest for Insight
8.314 L kPa K-1 mol-1     Peter Atkins, Loretta Jones, 2nd ed.
8.314 J K-1 mol-1
62.36 L Torr K-1 mol-1

T: Temperature
Chemical Principles: The Quest for Insight
Peter Atkins, Loretta Jones, 2nd ed.
Procedures for using the ideal gas law

To calculate the pressure (or other property) of a given sample

Step 1. Rearrange PV=nRT to give the desired quantity on the
left, and all other quantities on the right.

Step 2. Substitute the data, if necessary, convert the mass of
gas to the amount in moles. Note the T must be in Kelvins.

Step 3. Choose the value of R that matches the units of
pressure and volume you need to use. Alternatively, convert
The pressure units to match the value of R you prefer to use.
                                           PV1 P2V2
Combined Gas Law                            1
                                           T1   T2
To calculate the response of a gas to a change in conditions:

Step 1. Construct a table summarizing the data, which may include changes
in any of the four variables (pressure, volume, amount, and temperature).
Express the temperature in kelvins and the amount in moles.

Step 2. Rearrange the relation so that the quantity required is on the left and
All other quantities are on the right. Cancel any quantities that are unchanged.

Step 3. Substitute the data and check to see whether the answer agrees with
your predictions.
  Do you know the gases around us?

Troposphere: T decreases with increasing altitude.
Tropopause: From 11 to 16 km, constant T (-55˚C)
Stratosphere: From 16 km to 45 km, T rises.
          Ozone formation, releasing heat. Low
          mixing, trapping pollutants.
Stratopause: from 45 km up, T reaches 0˚C.
Mesosphere: T drops again.
Mesopause: About -100˚C
Thermosphere: T rises to over 1000 ˚C at very high
          altitude.                               Chemical Principles: The Quest for Insight
                                                       Peter Atkins, Loretta Jones, 2nd ed.
The kinetic model of gases

1. A gas consists of a collection of molecules (or any
   small particles including atoms and ions) in
   continuous motion.

2. Gas molecules are infinitesimally small points.

3. The molecules move in straight lines until they

4. The molecules do not influence one another expect
   during collisions.
    Relation between Internal Energy and Temperature

                                             Ideal gas exerts pressure on the
                                             walls of its container. Consider a
                                             single molecule of mass m
                                             contained in this box and moving
                                             with velocity v.

                                             v2 = vx2 + vy2 + vz2

Chemical Principles: The Quest for Insight
Peter Atkins, Loretta Jones, 2nd ed.
                                    For the moment we focus attention on
                                    the x- direction only. The momentum of
                                    the molecule in this direction is mvx,
                                    which we take as positive if the molecule
                                    is moving from left to right. When it
                                    strikes the right-hand wall, it is reflected
                                    back elastically and its momentum
                                    changes from +mvx to -mvx, so that the
                                    change in momentum is 2mvx.

The molecule must travel a           Hence the pressure on the wall is:
distance 2l (to the other side of    P1 = mvx2 / l3 = mux2 / V.
the box and back) before it can
strike the right-hand wall again,    If the box contains N molecules, the the
so that the frequency with           pressure is:
which it strikes this wall is        P = NP1 = Nmux2 / l3 = Nmux2 / V.
vx/2l, and the rate of change of
momentum at this wall is:
2mvx(vx / 2l) = mvx2 / l.

   energy/distance = force
if all the molecules are identical, we can use the mean square velocity,
<v2>, instead of vx2. Since the gas is isotropic,
<vx2> = <vy2> = <vz2>, so vx2 = <v2> / 3.
                                         v 2 + v 2 + ...+ v 2 1 / 2
                                     v = 1                 1N 
      Mean square velocity:                      2
                                                              
                                                   N          
Therefore, PV = Nm<v2> / 3.

If we have one mole of gas, N will be Avogadro's number NA, and we
can combine this with the ideal gas law:
PV = RT = NAm<v2> / 3.

This shows that the average translational kinetic energy of one mole
of an ideal gas is:
Etrans = 1/2NAm<v2> =(3/2)RT,

or for each molecule,
etrans = (3/2)kBT, where kB = R/NA is Boltzmann's constant.

The kinetic energy of the ideal gas is a function of temperature only!
According to Principle of Equipartition of
Energy, each degree of freedom contribute
RT/2 of internal molar energy. Therefore,
rigid diatomic molecules has the EKinetic of
(5/2)RT, because the degree of freedom is
5, including 3 translational and 2

The Equation is generally expressed as;

Ekinetic = (f/2)RT, where f is the degree of
freedom of the particles.
Because an ideal gas consists of point particles, the
only form of energy it can have is translational
kinetic energy, which is normally termed the internal
energy of the gas. For real gases, which have a finite
size and exhibit intermolecular forces, this result
does not hold, and it is found that E = E(T,V).

     Equations of State for Real Gases

Two assumptions that lead to deviations from the IGL:

1. Point masses
2. No attractive and repulsive forces between molecules
 Van der Waals Equation
1. Size effect: Since the molecules themselves occupy volume, the actual "free"
volume the molecules have to move in is less than the volume of the container V.
Therefore, replace V in the IGL by V - nb, where b is the volume/mole occupied
by the gas itself.
2. Attractive forces: These will cause molecules to spend more time in the
presence of each other during a collision (which are not now totally elastic),
decreasing the number of collisions with the walls of the container and hence the
observed pressure. The effect that any one molecule has on all the others will be
proportional to the gas density, since the larger the concentration of molecules on
which a given one can act, the greater the effect. But simultaneously, the other
molecules are exerting a similar effect on our given molecule, so the total effect
should be proportional to the square of the density, or proportional to (n/V)2. The
observed pressure will be less than the ideal gas pressure by an amount n2a/V2,
where a is a constant related to the intermolecular forces. We should therefore
replace Pideal in the IGL by P + n2a/V2, where P is the observed pressure.
                n2 
           P + a 2 (V − nb) = nRT
                   
                V 
Pressure increases as an object is submerged
deeper into a body of water. Suppose a balloon
is inflated to a volume of 2.0 L at atmospheric
pressure, attached by a string to a sufficiently
heavy object, and dropped into a fairly deep
lake. If the balloon reaches the bottom of the
lake where the pressure is 3.0 atm, what will be
the volume of the balloon?

a) 1.5 L
b) 6.0 L
c) 0.67 L

What is the final pressure inside a closed
container (initial pressure 1 atm) that is heated
from room temperature (25°C) to 450°F inside a
kitchen oven?

a) 17 atm
b) 0.59 atm
c) 1.7 atm

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