Physical Chemistry

1
Physical Chemistry
Physical Chemistry

• Cheng Xuan

February 2004, Spring Semester
2
Physical Chemistry
Physical Chemistry
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3
Summary
Physical Chemistry
Ideal Gases/Perfect Gases
Key Notes
Gases a fluid which has no intrinsic shape, and
which expands indefinitely to fill any container
in which it is held.
The ideal gas equations the relations among the
amount of gas substance, temperature, pressure
and volume.
PV nRT
PVm RT
Vm molar gas volume
4
Summary
Physical Chemistry
Ideal Gases/Perfect Gases
Key Notes
Partial pressure the pressure exerted by each
component in a gaseous mixture.
Px nxRT/V
nx mole
Pi xiPtotal
xi mole fraction
Daltons law the total pressure exerted by a
mixture of ideal gases in a volume is equal to
the arithmetric sum of the partial pressures.
Ptotal ntotalRT/V
5
Physical Chemistry
Chapter 2
CHAPTER 2 The First Law of Thermodynamics
Basic Concepts
Isothermal A system which is held at constant
temperature
Adiabatic A system in which energy may be
transferred as work, but not as heat.
Diathermic A system which allows energy to
escape as heat through its boundary if there is a
difference in temperature between the system and
its surroundings.
6
Physical Chemistry
Chapter 2
Internal Energy
Internal energy Total amount of energy in a
system. The sum total of all kinetic and
potential energy within the system.
Internal energy changes The sign of ?U Negative
values a system loses energy to the
surroundings Positive values a system gains
energy from the surroundings
7
Physical Chemistry
Chapter 2
Thermodynamic Properties of system
Extensive property The value of the property
changes according to the amount of material which
is present (e.g., mass, volume, internal
energy) Intensive propertyindependent of the
amount of material which is present (e.g.,
temperature, density)
State functions the value of a particular
property for a system depends solely on the state
of the system at time (e.g., pressure, volume,
internal energy, entropy)
Path functions A property depends upon the path
by which a system in one state is changed into
another state (e.g., work, heat)
8
Physical Chemistry
Chapter 2
Work
Work the transfer of energy as orderly motion
due to energy being expanded against an opposing
force (in mechanical terms)
Reversible P-V Work
9
Physical Chemistry
Chapter 2
Reversible P-V Work
(a) Expansion (dV gt 0)
(b) Compression (dV lt 0)
10
Physical Chemistry
Chapter 2
Heat the transfer of energy as disorderly motion
as the result of a temperature difference between
the system and its surroundings.
exothermic a process that releases energy as
heat (all combustion reactions)
endothermic processes that adsorb energy as
heat (the vaporization of water)
an adiabatic system
(a) an endothermic process
(b) an exothermic process
11
Physical Chemistry
Chapter 2
Heat the transfer of energy as disorderly motion
as the result of a temperature difference between
the system and its surroundings.
endothermic energy enters as heat from the
surroundings, the system remains at the same T (c)
exothermic energy leaves as heat from the
system, the system remains at the same T (d)
a diathermic container
An isothermal process
12
Physical Chemistry
Chapter 2
Heat
Two bodies at unequal temperatures are placed in
contact
m2, c2, T2 (T2gtT1)
m1, c1, T1
Tf
T1ltTfltT2
13
Physical Chemistry
Chapter 2
Heat
14
Physical Chemistry
Chapter 2
The First Law of Thermodynamics
The total energy of an isolated thermodynamic
system is constant
the conservation of energy
Energy cannot be created or destroyed
Closed system at rest in the absence of external
fields
q is the heat supplied to the system w is the
work done on the system ?U is the internal energy
of the system
15
Physical Chemistry
Chapter 2
Heat and Work
Both are measures of energy transfer, and both
have the same units as energy.
The unit of heat can be defined in terms of joule.
The calorie defined by (2.44) is called
thermodynamical calorie, calth
16
Physical Chemistry
Chapter 2
Enthalpy
Since U, P, V are state functions, H is a state
function.
Let qP be the heat adsorbed in a
constant-pressure process in a closed system,
from the first law
P1P2P
17
Physical Chemistry
Chapter 2
Enthalpy
For any change of state, the enthalpy change ?H
(2.47)
U and V are extensive, H is extensive.
The molar enthalpy of a pure substance
18
Physical Chemistry
Chapter 2
Enthalpy
Let qV be the heat adsorbed in a constant-volume
process in a closed system, if it can do only P-V
work, then
dw - PdV 0
Since dV 0
Then dw 0
So w 0
From the first law
(closed syst., P-V work only, V const.)
(2.49)
19
Physical Chemistry
Chapter 2
Enthalpy
For a reaction involving a perfect gas
Example
(1 mole of gaseous CO2 is created)
at 298 K
20
Exothermic and Endothermic
Physical Chemistry
Chapter 2
The sign of enthalpy change indicates the
direction of heat flow
21
Physical Chemistry
Chapter 2
Heat Capacities
heat capacity at constant pressure CP (isobaric
heat capacity)
heat capacity at constant volume CV (isochoric
heat capacity)
22
Physical Chemistry
Chapter 2
Heat Capacities
(2.53)
CP and CV give the rates of change of H and U
with temperature T.
23
Physical Chemistry
Chapter 2
Heat Capacities
The slope of the curve at any temperature
constant volume heat capacity (isochoric heat
capacity) CV
24
Physical Chemistry
Chapter 2
Heat Capacities
The slope of the H-T curve at any temperature
constant pressure heat capacity (isobaric heat
capacity) Cp
25
Physical Chemistry
Chapter 2
The relation between CP and CV
26
Physical Chemistry
Chapter 2
At constant P
Substitution of (2.59) into (2.57)
27
Physical Chemistry
Chapter 2
Why?
(first law)
28
Physical Chemistry
Chapter 2
(1) In a constant pressure process, part of the
added heat goes into the work of expansion
intermolecular potential energy
internal pressure
29
Homework (2.1-2.6)
Physical Chemistry
Chapter 2
2.6
2.12
2.26
2.29
Due next Monday before the class
30
Physical Chemistry
Chapter 2
Joule experiment
Chamber A filled with a gas
Chamber B is evacuated
Valve is closed
Valve is opened
Chamber A releases a gas
Chamber B filled with a gas
After equilibrium is reached
The temperature change in the system is measured
by the thermometer.
31
Physical Chemistry
Chapter 2
Joule experiment
q 0 (the system is surrounded by adiabatic
walls)
w 0 (gas expansion into a vacuum)
?U q w 0 0 0 (a constant-energy process)
The experiment measures ?T with ?V at constant
internal energy,
Joule coefficient
32
Physical Chemistry
Chapter 2
Joule experiment
total differential of z(x,y)
total differential of z(r,s,t)
When y is kept constant
When x is kept constant
33
Physical Chemistry
Chapter 2
Joule experiment
Division by dzy gives
From the definition of the partial derivative
When z stays constant
34
Physical Chemistry
Chapter 2
Joule experiment
Division by dyz gives
Using (1.32) with x and y interchanged and
multiplied by
35
Physical Chemistry
Chapter 2
Joule experiment
Replaced x, y, z with T, U, and V, gives
When (1.32), (2.53) and (2.62) were used
36
Physical Chemistry
Chapter 2
Joule-Thomson experiment
Adiabatic Wall
Porous Plug
B
P1
P2
P1
P2
P1, V1, T1
P1
P2
(b)
(a)
P1
P2
P2, V2, T2
P2 lt P1
(c)
Fig. 2.7 The Joule-Thomson experiment.
37
The slow throttling of a gas through a rigid,
porous plug. The system is enclosed in adiabatic
walls. The left piston is held at a fixed
pressure P1, the right piston is held at a fixed
pressure P2 (ltP1).
Chapter 2
The partition B is porous but not greatly so.
This allows the gas to be slowly forced from one
chamber to the other. Because the throttling
process is slow, pressure equilibrium is
maintained in each chamber. Essentially all the
pressure drop from P1 to P2 occurs in the porous
plug.
B
P1
P2
P1
P2
P1, V1, T1
P1
P2
(b)
(a)
P1
P2
P2, V2, T2
(c)
P2 lt P1
Physical Chemistry
38
Physical Chemistry
Chapter 2
Joule-Thomson experiment
The work done on the gas in throttling it through
the plug
w P1V1 - P2 V2 q 0 (adiabatic process)
U2 - U1 q w w P1V1- P2 V2
U2P2 V2U1P1V1
H2H1 or ?H 0
Joule-Thomson coefficient
39
Physical Chemistry
Chapter 2
Example
Calculate the work done when 50 g of iron reacts
with hydrochloric acid in (a) a closed vessel of
fixed volume (b) an open beaker at 25 oC.
In (a) the volume cannot change, so no work is
done
In (b) the gas gives back the atmosphere and
therefore
The amount of H2 produced
40
Physical Chemistry
Chapter 2
Example
Calculate the work done when 50 g of iron reacts
with hydrochloric acid in (a) a closed vessel of
fixed volume (b) an open beaker at 25 oC.
The reaction is
1 mole H2 is generated when 1 mole Fe is consumed
The system does 2.2 kJ of work driving back the
atmosphere
Molar mass of Fe
41
Physical Chemistry
Chapter 2
A perfect gas
Reversible isothermal process in a perfect gas
Reversible adiabatic process in a perfect gas
42
Physical Chemistry
Chapter 2
A perfect gas
If CV,m is constant (independent of T over a wide
temperature range)
Reversible adiabatic process, CV is constant
43
Physical Chemistry
Chapter 2
A perfect gas
An alternative equation can be obtained by using
44
Physical Chemistry
Chapter 2
A perfect gas
Heat capacity ratio
45
Physical Chemistry
Chapter 2
Thermodynamic Processes
Key Notes

• Cyclic process the systems final state is the
  same as the initial state.

• Reversible process the system is always
  infinitesimally close to equilibrium, and an
  infinitesimal change in conditions can restore
  both system and surroundings to their initial
  state.

• Isothermal process temperature is held constant
  throughout the process.

• Adiabatic process dq0 and q0

• Isochoric (isobaric) process volume (pressure)
  is held constant throughout the process.

46
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas
• Adiabatic expansion of a perfect gas into vacuum.

• Reversible phase change at constant T and P

47
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P

48
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas
• Adiabatic expansion of a perfect gas into vacuum.

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change

49
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change

50
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas
• Adiabatic expansion of a perfect gas into vacuum.

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change

51
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change

52
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas
• Adiabatic expansion of a perfect gas into vacuum.

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state

53
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state

54
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas
• Adiabatic expansion of a perfect gas into vacuum.

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas

55
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas

56
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas
• Adiabatic expansion of a perfect gas into vacuum.

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas

57
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas

58
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas
• Adiabatic expansion of a perfect gas into vacuum.

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas
• Adiabatic expansion of a perfect gas into vacuum.

59
Physical Chemistry
Chapter 2
Calculation of First-Law Quantities

• Reversible phase change at constant T and P
• Constant-pressure heating with no phase change
• Constant-volume heating with no phase change
• Perfect-gas change of state
• Reversible isothermal process in a perfect gas
• Reversible adiabatic process in a perfect gas
• Adiabatic expansion of a perfect gas into vacuum.

60
Physical Chemistry
Chapter 2
Molecular interpretation of heat and work
Heat is the transfer of energy that makes use of
chaotic molecular motion
(thermal motion)
Heat is identified as energy transfer making use
of thermal motion in the surroundings
Work is the transfer of energy that makes use of
organized motion
Work is identified as energy transfer making use
of the organized motion of atoms in the
surroundings
61
Physical Chemistry
Chapter 2
Molecular interpretation of heat and work

• Work
• In a uniform manner

(b) Heat In a chaotic manner
62
Physical Chemistry
Chapter 2
The molecular nature of internal energy
The internal energy is energy at the molecular
level.
gas CO2
moves the same distance in the same direction
A translation
The spatial orientation changes, but the
distances remain fixed
A rotation
the atoms oscillate about their equilibrium
positions
A vibration
Fig. 2.14
63
The internal energy
Physical Chemistry
Chapter 2

• Transnational energy, Utr
• Rotational energy, Urot
• Vibrational energy, Uvib
• Electronic energy, Uel
• Energy due to intermolecular forces, Uintemol
• Rest-mass energy of the electrons nuclei, Urest

64
Physical Chemistry
Chapter 2
The internal energy
For a gas or liquid, the molar internal energy
constant
constant
No chemical reactions T is not extremely high
For a perfect gas
constant
0
65
Homework (2.7-2.11)
Physical Chemistry
Chapter 2
2.31
2.37
Due on Monday, March 1 before the class
2.41
2.44
2.51
General
2.61
2.62
2.69
66
Announcement
Physical Chemistry
No classes will be offered on Monday, March 23
and Wednesday, March 25.
One class will be rearranged to this Wednesday,
February 18 from 10-1140.
Another class will be rescheduled.