Transcript 1 Second Year Chemistry

Second Year Chemistry
• 1st semester: Organic
• 1st semester: Physical (2005-2006)
• December exams
• 2nd: Analytical & Environmental
• 2nd: Inorganic
• Summer exams
• Physical: 3 lecturers 8 topics
• Dónal Leech: four topics
• Thermodynamics
• Gases, Laws, Phases, Equilibrium
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Course Director
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Dónal Leech
Room C205 (in Physical
Chemistry)
E-mail:
[email protected]
Phone: 493563 (from outside),
ext 3563 (internal phones)
Web-site: http://www.nuigalway.ie/chem/Donal/home.htm
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Introduction
Energetics and Equilibria
What makes reactions “go”!
This area of science is called THERMODYNAMICS
Thermodynamics is expressed in a mathematical language
BUT
Don’t, initially anyway, get bogged down in the detail of the equations: try to
picture the physical principle expressed in the equations
We will develop ideas leading to one important Law, and explore practical
applications along the way
The Second Law of Thermodynamics
 rG   RT ln K
0
 rG   r H  T r S
0
3
0
0
Lecture Resources
12 lectures leading to four exam questions
(section A, you must answer two from this section)
• Main Text:
“Elements of Physical Chemistry”
Atkins & de Paula, 4th Edition (Desk reserve)
http://www.oup.com/uk/booksites/content/0199271836/
OTHERS.
“Physical Chemistry” Atkins & de Paula, 7th Edition or any other
PChem textbook
These notes available on NUI Galway web pages at
http://www.nuigalway.ie/chem/degrees.htm
See also excellent lecture notes from James Keeler,
Cambridge, although topics are treated in a different running
order than here.
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Course Structure
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5
Revision of gases
Energy, heat and expansion work
1st Law of thermodynamics
Thermochemistry and phase diagrams
Entropy
2nd Law of thermodynamics
Chemical equilibria
Revision
States of Matter (bulk)
Gas: fluid form that fills container
Liquid: fluid form with well-defined surface, fills bottom of
container (in gravitational field)
Solid: retains its own inherent shape
Difference between these states related to freedom of particles
(molecules) to move past each other.
We describe the macroscopic physical state of matter under
conditions of volume, pressure, temperature and amount
present.
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Blank-to be presented in Lecture
7
Pressure (revision)
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Pressure is the force that acts on a given area (P=F/A).
Gravity on earth exerts a pressure on the atmosphere:
atmospheric pressure.
We can evaluate this by calculating the force due to
acceleration (by gravity) of a 1m2 column of air
extending through the atmosphere (this has a mass of
~10,000kg).
F  m.a
F  10,000kg  9.8m / s 2  100,000kgm / s 2
This unit is a Newton (N)
1  105 N
5
2
P  F/A

1

10
N
/
m
1m 2
This unit is a Pascal (Pa)
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Units of Pressure
S.I. unit of pressure is the N/m2, given the name Pascal (Pa).
A related unit is the bar (1x105 Pa) used because atmospheric
pressure is ~ 1x105 Pa (100 kPa, or 1bar).
Torricelli (a student of Galileo) was the first to recognise that the
atmosphere had weight, and measured pressure using a barometer
Standard atmospheric pressure was thus defined
as the pressure sufficient to support a mercury
column of 760mm (units of mmHg, or torr).
Another popular unit was thus introduced to
simplify things, the atmosphere (atm =
760mmHg).
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Pressure
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Atmospheric pressure and relationship between units
1 atm = 760 mmHg = 760 torr = 101.325kPa = 1.01325 bar)
Measuring Pressure: the manometer
Exercise:
On a certain day a barometer gives
the atmospheric pressure as 764.7
torr. If a metre stick is used to
measure a height of 136.4mm in the
open arm, and 103.8mm in the gas
arm of a manometer, what is the
pressure of the gas sample? (give in
torr, atm, kPa and bar).
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Ideal Gas Law
• Can specify state of sample by giving V, P, T and n.
•
These are however interdependent
Equation of state of low-pressure gas is known (from
combination of Boyle’s, Charles’s Laws and
Avogadro’s principle)
PV = nRT
R = 8.314 J K-1 mol-1 (= NAk)
(or L kPa K-1 mol-1 or m3 Pa K-1 mol-1)
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Boyle’s Law
Living Graph of Boyle's Law
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Charles’s Law
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Avogadro principle
• At a given T and p, equal volumes of gases contain the same number of
molecules, Vm = V/n
• Table below presents the molar volumes of selected gases at standard ambient
temperature (298.15 K) and pressure (1 atm)
Gas
Vm/(dm mol )
Perfect gas
24.7896*
Ammonia
24.8
Argon
24.4
Carbon dioxide
24.6
Nitrogen
24.8
Oxygen
24.8
Hydrogen
24.8
Helium
24.8
* At STP (0°C, 1 atm), Vm  24.4140 dm3 mol1.
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Blank-to be presented in Lecture
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Gas mixtures
• Dalton’s Law of partial pressures
The total pressure of a mixture of gases equals the sum of the
pressures that each would exert if it were present alone
(partial pressure)
PT=P1+P2+P3+….Pn
Mole fractions: xi = ni/n
Pi ni RT / V
n

 i
PT nT RT / V nT
 ni
Pi  
 nT

 PT  xi PT

Q: If dry air is composed of N2, O2, Ar at sea level in mass
percent of 75.5: 23.2: 1.3. What is partial pressure for each
when total pressure is 1.0 bar (100 kPa)?
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Kinetic model of gases
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Based on 3 assumptions
 Molecules are in ceaseless random
motion
 Size of molecules is negligible
 Molecules do not interact
Can derive: (see further information 1.1 in textbook)
nMc 2
p
3V
1
pV  nMc 2
3
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Where c is the root-mean-squared (rms) speed
Kinetic Molecular Theory
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Compare KMT to Ideal Gas Law
1
2
nMc  nRT
3
1/ 2
 3RT 
c

 M 
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Maxwell Distribution of Speeds
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Not all molecules travel at the same speed
Distribution of speeds derived by James Clerk Maxwell
 M 
f  4 

 2RT 
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3/ 2
2  Ms 2 / 2 RT
se
.s
Diffusion and Effusion
Thomas Graham proposed a Law (1883)
to summarize experimental observations
on effusion
Rate of Effusion  1/√M
Relative rates of effusion
r1

r2
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M2
M1
Blank-to be presented in Lecture
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Critical Point
•point at which surface separating two phases
no longer appears: interface between vapour
and liquid phases disappears, their densities
become equal-supercritical fluid
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Compression factor
Vm
Vm
pVm
Z o 

Vm RT / p RT
• Small difference between real and
perfect behaviour at high T, low p
(see CO2 isotherms)
• Model using virial equation of
state
Z=1 for
• pVm = RT(1 + B’p + C’p2 + …)
perfect gas.
• More convenient expression
Deviations
• pVm = RT(1 + B/Vm + C/Vm2 + …)
from this
• In each case Z = expression in
parentheses
measure how
• B factor is most important, and is
far gases
positive for H2, negative for others
depart from
in the figure
ideal
behaviour.
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Virial Coefficients and Boyle
Temperature
• Virial coefficients depend upon T
• T at which Z  0 is called the Boyle
Temperature (most like perfect gas)
• pVm = RTB
Although the virial equation of state is
the most reliable, it does not provide
much insight into the behaviour of
gases
Johannes van der Waals (Dutch
physicist) proposed in 1873 an
alternate approximate equation of state
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Van der Waals equation of state
• Actual volume reduced in
proportion to number of
P
molecules present (repulsions)
• Attractive forces reduce
Substance
frequency of collisions and their Air
Ammonia, NH
strength
nRT
n

 a 
V  nb
V 
a/(atm dm mol )
b/(10 dm mol )
1.4
0.039
4.169
3.71
Argon, Ar
1.338
3.20
Carbon dioxide, CO2
3.610
4.29
Ethane, C2H6
5.507
6.51
Ethene, C2H4
4.552
5.82
Helium, He
0.0341
2.38
Hydrogen, H2
0.2420
2.65
Nitrogen, N2
1.352
3.87
Oxygen, O2
1.364
3.19
Xenon, Xe
4.137
5.16
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• Parameters depend on the gas,
but are taken to be independent
of T.
• a is large when attractions are
large, b scales in proportion to
molecular size (note units)
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2
6
2
2
3
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Features of vdW equation
• Reduces to perfect gas equation at
high T and V
• Liquids and gases coexist when
attractions ≈ repulsions
• Critical constants are related to
coefficients. Flat inflexion of curve
when T=Tc.
• Can derive (by setting 1st and 2nd
derivatives of equation to zero)
expression for critical constants
• Vc = 3b, pc = a/27b2, Tc =8a/27Rb
• Can derive expression for the Boyle
Temperature
• TB = a/Rb
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Maxwell Construction
Below Tc calculated vderW isotherms have oscillations that are unphysical.
In the Maxwell construction these are replaced with horizontal lines, with
equal areas above and below, to generate the isotherms.
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Blank-to be presented in Lecture
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Liquefaction-Irish Links!
• Refrigeration developed by Carl von Linde in 19th
Century, in response to a request from Guinness in
Dublin for a new cooling technique.
• Based upon the fact that gases cool as they expand:
Joule-Thomson effect (William Thomson, later Lord
Kelvin, born in Belfast),
The Linde refrigerator combines the JT process with a
counter-flow heat exchanger.
The gas is re-circulated and it cools on expansion
through the throttle. The cooled gas cools the highpressure gas, which cools still further as it expands.
Eventually liquefied gas drips from the throttle.
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Summary
l
Simplest state of matter is that of a gas
• We can assemble an equation of state for an idealised gas
from experimental results (Boyle, Charles, Avogadro)
• Kinetic Molecular Theory can help explain the molecular
basis for these Laws
• Real gases differ from ideal gases because of inter-
molecular interactions.
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