CHEM 301 Physical Chemistry I

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CHEM 301 Physical Chemistry I

• Dr. Robert E. Barletta
• rbarletta_at_jaguar1.usouthal.edu
• Phone [phone]
• Tuesday and Thursday, 930 a.m. - 1045 a.m.
  Room 107
• Text Physical Chemistry, 7th Edition, Peter
  Atkins and J. de Paula

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Rules of the Road

• Attendance encouraged, not mandatory
• Except for exams(see below)
• Responsible for any supplemental material covered
  in lectures
• Cell phones/pagers off during class
• Students are expected to remain in class
  throughout period
• Disabilities
• Certify through Office of Special Student
  Services
• Help
• Office Room 133
• Hours Tues. Thurs. 11-noon
• Other - by appointment
• Homework Problems assigned at the start of each
  chapter
• Due the day after the test on material
• To received credit for an assignment all work
  must be shown

• Exams - A non-programmable calculator only may be
  used
• 3 Hour Exams
• Exam 1 After Chapter 4 covering Chapters 1,
  24a, 2,3, and 4
• Exam 2 After Chapter 8 covering Chapters 5-8
• Exam 3 After Chapter 26 covering Chapters 9, 10,
  24b, 25, and 26
• 1 Final comprehensive, Ch. 27 and portion to
  include ACS Thermodynamics test
• Make-up exams given only for documented excused
  absences
• Grading
• Homework - 5
• Hour exams - 15 each
• Laboratory Grade - 25
• Final Exam - 25

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Physical Chemistry

• Application of physics to the study of chemistry
• Develops rigorous and detailed explanations of
  central, unifying concepts in chemistry
• Contains mathematical models that provide
  quantitative predictions.
• Mathematical underpinning to concepts applied in
  analytical, inorganic, organic, and biochemistry
• Includes essential concepts for studying advanced
  courses in chemistry
• Source American Chemical Society

4
Divisions of Physical Chemistry

• Main Problems
• Position of Chemical Equilibrium
• A B ltgt C D
• Rate of Chemical Reactions - Kinetics
• Other special topics
• Approaches
• Top down (Traditional/Analytical/Historical
  Approach)
• Begin with things we observe in the
  world/laboratory
• Examine how those observables relate to the
  underlying structure of matter
• Bottom up (Synthetic/Molecular Approach)
• Consider the underlying structure of matter
• Derive observables

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Chapter 1 Properties of Gases

• Homework
• Exercises (a only) 1.4,6, 9, 11, 14, 16, 17,
  18, 21
• Problems 1.1, 3, 12(a b only), 20, 32

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Equations of State

• Gases are the simplest state of matter
• Completely fills any container it occupies
• Pure gases (single component) or mixtures of
  components
• Equation of state - equation that relates the
  variables defining its physical properties
• Equation of state for gas p f (T,V,n)
• Gases (pure) Properties - four, however, three
  specifies system
• Pressure, p, force per unit area, N/m2 Pa
  (pascal)
• Standard pressure pø 105 Pa 1bar
• Measured by manometer (open or closed tube), p
  pexternal rgh
• g gravitational acceleration 9.81 m/s-2
• Mechanical equilibrium - pressure on either side
  of movable wall will equalize
• Volume, V
• Amount of substance (number of moles), n
• Temperature, T, indicates direction of flow of
  energy (heat) between two bodies change results
  in change of physical state of object
• Boundaries between objects
• Diathermic - heat flows between bodies. Change
  of state occurs when bodies of different temp.
  brought into contact
• Adiabatic - heat flows between bodies. No change
  of state occurs when bodies of different temp
  brought into contact

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Heat Flow and Thermal Equilibrium
TA TB
High Temp.
Low Temp.
A
B
A
B
A
B
No Heat
Heat
No Heat
Diathermic Wall
Diathermic Wall
Adiabatic Wall

• Thermal equilibrium - no change of state occurs
  when two objects are in contact through a
  diathermic boundary
• Zeroth Law of Thermodynamics - If A is in thermal
  equilibrium with B and B is in thermal
  equilibrium with C then A is in thermal
  equilibrium with C
• Justifies use of thermometer
• Temperature scales
• Celsius scale, Q, (C) degree defined by ice
  point and B.P. of water
• Absolute scale, thermodynamic scale , (K notK)
• T (K) Q 273.15

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Equation of State for Gases ( p f(V,T,N) Ideal
(Perfect) Gas Law

• Approximate equation of state for any gas
• Product of pressure and volume is proportional
  to product of amount and temperature
• PV nRT
• R, gas constant, 8.31447 JK-1mol -1
• R same for all gases, if not gas is not behaving
  ideally
• Increasingly exact as P 0 a limiting law
• For fixed n and V, as T 0, P 0 linearly
• Special cases (historical precident) Boyles Law
  (1661), CharlesLaw Gay-Lussacs Law (1802-08)
  Avogodros principle (1811)
• Used to derive a range of relations in
  thermodynamics
• Practically important, e.g., at STP (T 298.15, P
  pø 1bar), V/n (molar volume) 24.789 L/mol
• For a fixed amount of gas (n, constant) plot of
  properties of gas give surface
• Isobar - pressure constant - line, V a T
• Isotherm - temperature constant, hyperbola, PV
  constant
• Isochor - volume constant - line P a T

http//www.chem1.com/acad/webtext/gas/gas_2.htmlP
VT
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Ideal (Perfect) Gas Law - Mixtures

• Daltons Law Pressure exerted by a mixture of
  gases is sum of partial pressures of the gases
• Partial pressure is pressure component would
  exhibit if it were in a container of the same
  volume alone
• ptotal pA pB pC pD . (A, B, C, D are
  individual gases in mixture)
• pJ V nJRT
• This becomes
• If xJ is the fraction of the molecule, J, in
  mixture xJ nJ / nTotal ), then S xJ 1
• If xJ is the partial pressure of component J in
  the mixture, pJ xJ p, where p is the total
  pressure
• Component J need not be ideal
• p S pJ S xJ p this is true of all gases,
  not just ideal gases

p pA pB
pB xBp
P
pA xAp
0
1
Mole Fraction B, xB
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Real Gases - General Observations

• Deviations from ideal gas law are particularly
  important at high pressures and low temperatures
  (rel. to condensation point of gas)
• Real gases differ from ideal gases in that there
  can be interactions between molecules in the gas
  state
• Repulsive forces important only when molecules
  are nearly in contact, i.e. very high pressures
• Gases at high pressures (spn small), gases less
  compressible
• Attractive forces operate at relatively long
  range (several molecular diameters)
• Gases at moderate pressures (spn few molecular
  dia.) are more compressible since attractive
  forces dominate
• At low pressures, neither repulsive or attractive
  forces dominate - ideal behavior

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Compression Factor, Z

• Compression factor, Z, is ratio of the actual
  molar volume of a gas to the molar volume of an
  ideal gas at the same T P
• Z Vm/ Vm, where Vm V/n
• Using ideal gas law, p Vm RTZ
• The compression factor of a gas is a measure of
  its deviation from ideality
• Depends on pressure (influence of repulsive or
  attractive forces)
• z 1, ideal behavior
• z lt 1 attractive forces dominate, moderate
  pressures
• z gt 1 repulsive forces dominate, high pressures

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Real Gases - Other Equations of StateVirial
Equation

• Consider carbon dioxide
• At high temperatures (gt50C) and high molar
  volumes (Vm gt 0.3 L/mol), isotherm looks close to
  ideal
• Suggests that behavior of real gases can be
  approximated using a power series (virial)
  expansion in n/V (1/Vm) Kammerlingh-Onnes, 1911
• Virial expansions common in physical chemistry

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Virial Equation (continued)

• Coefficients experimentally determined (see
  Atkins, Table 1.3)
• 3rd coefficient less impt than 2nd, etc.
• B/Vm gtgt C/Vm2
• For mixtures, coeff. depend on mole fractions
• B x12B11 2 x1x2B12 x22B22
• x1x2B12 represents interaction between gases
• The compressibility factor, Z, is a function of p
  (see earlier figure) and T
• For ideal gas dZ/dp (slope of graph) 0
• Why?
• For real gas, dZ/dp can be determined using
  virial equation
• Substitute for Vm (Vm Z Vm) and VmRT/p
• Slope B 2pC .
• As p 0, dZ/dP B, not necessarily 0.
  Although eqn of state approaches ideal behavior
  as p 0, not all properties of gases do
• Since Z is also function of T there is a
  temperature at which Z 1 with zero slope -
  Boyle Temperature, TB
• At TB , B 0 and, since remaining terms in
  virial eqn are small, p Vm RT for real gas

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Critical Constants

• Consider what happens when you compress a real
  gas at constant T (move to left from point A)
• Near A, P increases by Boyles Law
• From B to C deviate from Boyles Law, but p still
  increases
• At C, pressure stops increasing
• Liquid appears and two phases present (line CE)
• Gas present at any point is the vapor pressure
  of the liquid
• At E all gas has condensed and now you have
  liquid
• As you increase temperature for a real gas, the
  region where condensation occurs gets smaller and
  smaller
• At some temperature, Tc, only one phase exists
  across the entire range of compression
• This point corresponds to a certain temperature,
  Tc, pressure, Pc , and molar volume, Vc , for the
  system
• Tc, Pc , Vc are critical constants unique to
  gas
• Above critical point one phase exists (super
  critical fluid), much denser than typical gases

2 phases
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Real Gases - Other Equations of State

• Virial equation is phenomenolgical, i.e.,
  constants depend on the particular gas and must
  be determined experimentally
• Other equations of state based on models for real
  gases as well as cumulative data on gases
• Berthelot (1898)
• Better than van der Waals at pressures not much
  above 1 atm
• a is a constant
• van der Waals (1873)
• Dieterici (1899)

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van der Waals Equation

• Justification for van der Waals Equation
• Repulsion between molecules accounted for by
  assuming their impenetrable spheres
• Effective volume of container reduced by a number
  proportional to the number of molecules times a
  volume factor larger than the volume of one
  molecule
• Thus V becomes (V-nb)
• b depends on the particular gas
• He small, Xe large, bXe gtbAr
• Attractive forces act to reduce the pressure
• Depends on both frequency and force of
  collisions and proportional to the square of the
  molar volume (n/V)2
• Thus p becomes p a (n/V)2
• a depends on the particular gas
• He inert, CO2 less so, aCO2 gtgtaAr

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van der Waals Equation - Reliability

• Above Tc, fit is good
• Below Tc, deviations

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van der Waals Loops (cont.)

• CO2 Critical Temperature 304.2 K (31.05C)
• Below Tc, oscillations occur
• van der Waals loops
• Unrealistic suggest that increase in p can
  increase V
• Replaced with straight lines of equal areas
  (Maxwell construction)

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van der Waals Equation - Reliability
van der Waals _at_T/Tc
20
van der Waals Equation

• Effect of T and Vm
• Ideal gas isotherms obtained
• 2nd term becomes negligible at high enough T
• 1st term reduces to ideal gas law at high enough
  Vm
• At or below Tc
• Liquids and gases co-exist
• Two terms come into balance in magnitude and
  oscillations occur
• 1st is repulsive term, 2nd attractive
• At Tc, we should have an flat inflexion point,
  i.e., both 1st and 2nd derivatives of equation
  w.r.t Vm 0

• Solving these equations for p,Vm and T gives
  pc,Vc and Tc in terms of a and b
• Hint you must use original eqn to do this
• pc a/27b3, Vc pc 3b and Tc 8a/27Rb
• Critical compression factor, Zc, can be
  calculated using definition for Z
• pVm RTZ
• This should be a constant for all gases and is
  (Table 1.4 )

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Comparing Different Gases

• Different gases have different values of p, V and
  T at their critical point
• You can compare them at any value by creating a
  reduced variable by dividing by the corresponding
  critical value
• preduced pr p / pc Vreduced Vr Vm / Vc
  Treduced Tr T/ Tc
• This places all gases on the same scale and they
  behave in a regular fashion gases at the same
  reduced volume and temperature exert the same
  reduced pressure.
• Law of Corresponding States
• Independent of equations of state having two
  variables

p (atm)
pr