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Second Year Chemistry. 1 st semester: Organic 1 st semester: Physical (2005-2006) December exams 2 nd : Analytical & Environmental 2 nd : Inorganic Summer exams Physical: 3 lecturers Þ ~ 8 topics Dónal Leech: four topics Thermodynamics Gases , Laws, Phases, Equilibrium. - PowerPoint PPT Presentation
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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
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 Thermodynamics000
0 ln
STHG
KRTG
rrr
r
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Lecture Resources12 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 athttp://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
Revision of gases Energy, heat and expansion work 1st Law of thermodynamics Thermochemistry and phase diagrams Entropy 2nd Law of thermodynamics Chemical equilibria
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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
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Pressure (revision)
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).
252
5
22
/1011
101/
/000,100/8.9000,10
.
mNm
NAFP
skgmsmkgF
amF
This unit is a Newton (N)
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 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 = nRTR = 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)
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Blank-to be presented in Lecture
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Gas mixtures
TiTT
ii
T
i
T
i
T
i
PxPn
nP
n
n
VRTn
VRTn
P
P
/
/
• 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
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 Based on 3 assumptions
Molecules are in ceaseless random motion
Size of molecules is negligibleMolecules do not interact
Can derive: (see further information 1.1 in textbook)
2
2
3
13
nMcpV
V
nMcp
Where c is the root-mean-squared (rms) speed
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Kinetic Molecular Theory Compare KMT to Ideal Gas Law
2/1
2
3
3
1
M
RTc
nRTnMc
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Maxwell Distribution of Speeds
Not all molecules travel at the same speed Distribution of speeds derived by James Clerk Maxwell
sesRT
Mf RTMs
.
24 2/2
2/32
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Diffusion and EffusionThomas Graham proposed a Law (1883) to summarize experimental observations on effusion
Rate of Effusion 1/√M
1
2
2
1
M
M
r
r
Relative rates of effusion
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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
RT
pV
pRT
V
V
VZ mm
om
m /
Z=1 for perfect gas.
Deviations from this measure how far gases depart from ideal behaviour.
• Small difference between real and perfect behaviour at high T, low p (see CO2 isotherms)
• Model using virial equation of state
• pVm = RT(1 + B’p + C’p2 + …)
• More convenient expression
• pVm = RT(1 + B/Vm + C/Vm2
+ …)• In each case Z = expression in
parentheses• B factor is most important, and is
positive for H2, negative for others in the figure
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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 gasesJohannes van der Waals (Dutch physicist) proposed in 1873 an alternate approximate equation of state
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Van der Waals equation of state2
V
na
nbV
nRTP
• Actual volume reduced in proportion to number of molecules present (repulsions)
• Attractive forces reduce frequency of collisions and their strength
• 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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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 ConstructionBelow 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 high-pressure gas, which cools still further as it expands. Eventually liquefied gas drips from the throttle.
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Summary
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.