Download 1st Set of Notes - Idaho State University

1st Set of Notes
Physical Chemistry: Science
Understanding of Nature/Natural Processes ..... Take seemingly unrelated phenomena,
reduce to more fundamental level, devise hypothesis for these fundamental processes
(often in a mathematical language), show that the phenomena are governed by these
hypothesis. Test hypothesis by applying to other natural phenomena and predict
processes that have not been previously attempted. REFINE INTO THEORY.
Information gained through observation. Observations are made concise through
measurement tools. Observations are made universal through internationally defined
units.
In Science and Technology, future work often is built from earlier studies.
IMPORTANT TO PHYSICAL CHEMISTRY Definition of Units:
Definitions of the SI base units
Unit of length
meter
The meter is the length of the path
travelled by light in vacuum during a time
interval of 1/299 792 458 of a second.
Unit of mass
kilogram
The kilogram is the unit of mass; it is
equal to the mass of the international
prototype of the kilogram.
Unit of time
Unit of
electric current
second
The second is the duration of 9 192 631
770 periods of the radiation
corresponding to the transition between
the two hyperfine levels of the ground state of the
cesium 133 atom.
ampere
The ampere is that constant current
which, if maintained in two straight
parallel conductors of infinite length, of
negligible circular cross-section, and placed 1
meter apart in vacuum, would produce between
these conductors a force equal to2 x 107 newton per meter of length.
Unit of
kelvin
thermodynamic
temperature
Unit of
amount of
substance
mole
The kelvin, unit of thermodynamic
temperature, is the fraction 1/273.16 of
the thermodynamic temperature of the
triple point of water.
1. The mole is the amount of substance
of a system which contains as many
elementary entities as there are atoms in
0.012 kilogram of carbon 12; its symbol is "mol."
2. When the mole is used, the elementary entities
must be specified and may be atoms, molecules,
ions, electrons, other particles, or specified
groups of such particles.
Unit of
luminous
intensity
candela
The candela is the luminous intensity, in
a given direction, of a source that emits
monochromatic radiation of frequency540
x 1012 hertz and that has a radiant intensity in that
direction of 1/683 watt per steradian.
............................................. FUNDAMENTAL UNITS
..................................... SI Unit ........................ Definition ............................ English Units
length ...............................................................
mass ......................................................................
time
temperature
amount of Substance
current
luminosity ..................... candela
............................................DERIVED UNITS
UNITS contain more information, Often help to give mathematical formula
Density
Volume
Acceleration
Energy (KE vs PE)
Force
Pressure
Measurement of these Quantities will help us define natural processes (Macroscopic
vs Microscopic)
GASES - Simple type of system to study based on molecular interactions.
Let us consider Temp, Volume, and Pressure:
Does measurement of these help us?
....................................................Lets look at PRESSURE
In the 1800s, Boyle made a series of measurements on Pressure and Volume while
holding temp and amount of gas constant:
At least for moderate Pressures at constant ....................., found that P * V =
...........................................................TEMP
Celcius and Fahrenheit are arbitrary scales
o
C
o
F
ABSOLUTE TEMPERATURE IS BASED ON CHARLES’ LAW (IDEAL GAS)
Spend a minute reviewing Ideal Gases.
GASES - Simple type of system to study based on molecular interactions.
IDEAL GAS is even simpler:
IDEAL GAS - Theory describing it is called the Kinetic Theory of Gases
Basic Assumptions about IDEAL GAS Model:
1. Molecules are in constant random motion.
2. Molecules basically have no volume (at least compared to total volume).
3. Molecules have no attractive or repulsive forces. (Have elastic collisions).
4. The kinetic energy of any molecule is equal at the same temperature.
Also the idea that pressure is a result of molecules colliding with the wall
Charles made some observations using a thermometer and an apparatus calibrated to read
volume.
Found the following:
A plot of V vs T(oC) yielded:
A straight line of form V = aT + b or y = mx + b
Now for ideal gas it is assumed that the kinetic energy and thus the pressure depend on
Temp, so
if there is an absolute zero, all motion stops there and the volume should shrink to
nothing.
OR another way of saying this: As V=> 0, T => absolute zero. so plot gives absolute
zero scale.
On absolute zero scale V=  T or V/T is constant:
One can derive a root mean square speed for an ideal gas molecule
s = (3RT/M)1/2
s = root mean square speed, ........ T = Temp. in ........................, M = ........................, R =
..
All molecules at the same Temp have the same K.E., but do they have the same root
mean square speed?
Consider Hydrogen gas and Argon gas at T = 25oC?
s(H2)
s(Ar)
s is the root mean square speed. There is in fact not just one speed for all gas molecules
in a container. There is a DISTRIBUTION of speeds.
MAXWELL Boltzmann Distribution
................................................f(s) = 4 (M/2RT)3/2 s2 exp(-Ms2/(2RT))
f(s) is the number or fraction of molecules with a particular speed
M is ................................., s is .............................................., R is ......................, T is ......
avg speed or mean speed is calculated in a similar way as averaging grades. For each
grade,
1) Take fraction that have a particular grade, f(g)
2) Multiply by the grade “g”.
3) Then add the values derived from 1 & 2 together ............. ∑ all grades g * f(g)
The speed distribution is continuous, not discrete like the grades, so average using an
integral rather than a summation.
average or mean speed .......... 0∫inf s f(s) ds
root mean square speed is ........ [ 0∫inf s2 f(s) ds ]1/2
Relates to a couple of quantities:
1. Effusion
2. Pressure
3. Mean free path
Thermo applies to everything from huge systems like a Diesel engine in a Kenworth
semi-trailer truck to the molecules involved in gluconeogenesis. First developed based
on observations on large systems MACROSCOPIC, but has its basis in the
MICROSCOPIC world.
Remember that Thermodynamics is concerned with ______________ __ _____
_________ ________ ____ _Energy .
How do we transfer energy into a system or out of a system? What is the result of this
transfer or energy?
Basically, the system will often move from one Thermodynamic State to another
thermodynamic state. How is a thermodynamic state defined? Need to employ the
Phase Rule.
1) First Look at the different forms of energy transfer and how it can be exchanged and
then we’ll discuss more thoroughly what is meant by a thermodynamic state?
Need to distinguish between the system and the surroundings.
Three ways to exchange energy include WORK, ________, and ___________.
How do we know each of these represent exchanges of energy.
Work: Consider taking a motor and lifting up to a height that it can be pulled out of a
truck. Work must be done to lift the engine. The result is a change in the potential
energy of the engine. So energy has increased.
Most generally, Work = Force * displacement or ∫ F * dx
Use the convention that WORK INTO THE SYSTEM is POSITIVE.
Consider a Spring:
Consider a Piston Arrangement (PV Work)
The (PV) Work will (in general) depend on what the pressure does while the work is
done. Thus it is said to be Path Dependent.
Heat (Associated with a change in the temperature of the system)
An experiment carried out by Joule in the early 1800s consisted of a weight tied to a
string and a paddle. The paddle stirred the water raising its temperature.
Thus since the paddle stirring resulted from a change in the height of a weight, it must be
a form of ______________ _______________.
Adding Matter
Increasing the matter in a system increases the chemical energy of the system. Or
moreover if nuclear processes are occurring the amount of mass is directly related to the
available energy.
In general a particular system can do work, or work can be done on the system.
Very important! Need to focus on a particular system. Define the system.
Nomenclature for defining a system
......... Open system
......... Closed
......... Isolated
2) If our system is a gas (take the case of an ideal gas), how many thermodynamic
variables need to be defined to specify the thermodynamic state of the system?
That is: how many variables need to be specified such that the state of the system,
meaning its density, its refractive index, its molar internal energy, its viscosity, and all
other variables are specified?
Need definitions
Extensive Variable - a variable which is dependent on the amount of material present
(such as the mass)
Intensive Variable - that which is independent of the amount of material present (such as
the density, the color, the molar internal energy, etc.)
Phase Rule:
The number of degrees of freedom necessary to specify the thermodynamic state of a
system is:
...............................F = C - P + 2
where C is the number of independent components
P is the number of phases present
As an example: Consider Argon (an ideal gas) in a vessel. How many intensive
variables need to be defined to fix the thermodynamic state of the system?
F=C-P+2
C = ?, ......................P = ? .........................
Thus F = 2, so two intensive variables. That means if I fix the Temp. and Pressure for
instance, then the thermodynamic state of the system is fixed, so I know the density, the
molar internal energy, the index of refraction, the viscosity, etc. for the system in that
state.
The eqn. of state that describes the system is PV = nRT (two indep. intensive variables?
What about a non-ideal or (real) gas. What Eqns. describe this system
Compressibility Factor PV =
Van der Waals Expression
Virial Expansion
The transfer of energy into a system will likely change the state of that system.
AND THE 1st Law of Thermodynamics Defines how Energy Transfer is related to the
Thermodynamic state if the system.
More definitions.
State Variables are variables that are unaffected by the path used to move between two
thermodynamic states, where the difference in that variable State Variable) depends
upon the values of that variable in the final and initial states.
Variables like the temp, pressure, molar internal energy are state variables.
WORK AND HEAT ARE TWO non-state variables.
In the 1st Law, the energy of the system and surroundings must be conserved. Thus
Energy for system plus surrounding must be equal to zero.
Energysys + Energysurr = 0
We can set Energysurr equal to the heat and energy transferred from the surroundings to
the system making sure that energy transferred into the system is positive for the system
value.
What energy changes in the system are allowed? Change in potential energy of the whole
system, change in the kinetic energy of the whole system, and change in the internal
energy, the vibrations, rotations, translational, and bonding energy associated with the
individual molecules..
So if heat and work are the only methods of energy transfer from the surroundings to a
closed system then:
sys + PEsys + Usys = Q + W ........... (closed system)
And if the kinetic and potential energies of the system as a whole are constant, then
Usys = Q(in) + W(in) .......................(closed system)
U, the internal energy is a property of the system in a particular state and it is in fact a
state property like the density and viscosity.
One can define a similar property called the enthalpy in this w
H = U + PV
or H = U + PV)
then substituting what Eis for a closed system
one obtains:
and if we only have PV type work then
Work = -PV
So
Q + VP
whereas
U = Q - PV
When we change the state of a system we can do so in many different ways or by many
different paths.
Two paths could be:
1) a constant volume path or isochoric case:
Here the value of the heat is just equal to the ____________ ____________ __________.
Another path could involve:
2) a constant pressure path or isobaric case:
Here the value of the heat is just equal to the _______________ _________________ .
In fact the enthalpy was defined the way it was for this reason.
Q is also related to the temperature change involved during the heat transfer process
For a closed system, the transfer of a small quantity of heat dQ into or out of a system,
will result in a change dT in the system.
dQ/dT is in fact called the heat capacity of the system and is given the symbol C.
C is different for different _________ and C varies with ___________.
For the purest then:
Q=
T1
∫ T2 C dT
Example
but if C is constant in the temp range then Q = _____
In the case of a constant pressure process over a small temp range:
Qp = H = Cp T
And in the case of a constant volume process over a small temp range:
Qv = U = Cv T
(HOW does this change for a larger temp. range?)
IT IS A SPECIAL FEATURE OF IDEAL GASES, THAT THE ABOVE
RELATIONSHIPS HOLD, WHETHER OR NOT THE PROCESS IS CONST.
PRESSURE OR CONSTANT VOLUME.
FOR OTHER SYSTEMS, H IS NOT always Cp T and U is NOT always CvT BUT
only for the constant pressure or constant volume cases respectively.
There are other paths connecting different states.
Nomenclature and Examples:
Reversible Path vs. Irreversible Path
Isothermal
Isothermal Reversible