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1
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/chemistry/staff/donal_leech/teaching.html
2
Second Year Chemistry• 1st semester: Organic• 1st semester: Physical (2008-
2009)• December exams
• 2nd: Analytical & Environmental• 2nd: Inorganic
• Summer exams• Physical: 4 lecturers 8 topics• Dónal Leech: two topics
• Thermodynamics•Gases, Laws
3
Course Outline
• 8 topics, 2 per Lecturer• 3 Lectures per topic• Exam: 2 hour, answer 4 questions
• 1 Q per topic, 2 Q per section (Lecturer)
• Must attempt one Q per section
• See past papers• http://www.nuigalway.ie/chemistry/exam_papers.html
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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
5
Lecture Resources6 lectures leading to two exam questions
• Main Text: “Elements of Physical Chemistry”
Atkins & de Paula, 4th Edition (Desk reserve)http://www.oup.com/uk/orc/bin/9780199271832/
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/chemistry/courses.html
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
7
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.
8
Units of some properties• Mass, m: quantity of matter in kg (Pt-Ir sample near
Paris)=1000g
• Volume, V: space occupied in m3= 1000L
• Force, F: mass × acceleration in newtons (N=kg m s-2)
• Work, w: F × distance (N m = joule, J), form of ENERGY
(capacity to do work)
• Pressure, p: F/area (N m-2 = pascal, Pa)
• Temperature, T: determines in which direction energy will
flow (higher to lower), reported in K (= θ °C + 273.15)
• Amount, n: mole (number of atoms in exactly 12g carbon-12)
• Avogadro’s number, NA = 6.022 × 1023 mol-1
• Nb of atoms = n × NA
• Molar mass, M: mass per mole of substance (g/mol), M = m /
n
9
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).
12
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)
15
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 bar)
22.414 L/mol
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Applications
Surface of possible states
Barometric formula:
Variation of pressure with altitude, derived from kinetic theory (4th year)
Living Graph Barometric Formula
17
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
21
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
22
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
23
Real Gases• Perfect gas: only contribution to energy is KE of molecules• Real gases: Molecules interact if they are close enough, have a
potential energy contribution. • At large separations, attractions predominate (condensation!)• At contact molecules repel each other (condensed states have
volume!)
Ideal Real (CO2)
24
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
25
Critical Temperatures Critical temperature/°C
Noble gases
Helium, He 268 (5.2 K)
Neon, Ne 229
Argon, Ar 123
Krypton, Kr 64
Xenon, Xe 17
Halogens
Chlorine, Cl2 144
Bromine, Br2 311
Small inorganic molecules
Ammonia, NH3 132
Carbon dioxide, CO2 31
Hydrogen, H2 240
Nitrogen, N2 147
Oxygen, O2 118
Water, H2O 374
Organic compounds
Benzene, C6H6 289
Methane, CH4 83
Tetrachloromethane, CCl4 283
Gas cannot be condensed to a liquid above Tc
Vapour: gaseous phase below Tc
Gas: gaseous phase above Tc
27
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
31
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.
32
Critical constantspc
atm
Vc
cm3/mol
Tc
K
Zc TB
K
Ar 48.0 75.3 150.7 0.292 411.5
CO2 72.9 94.0 304.2 0.274 714.8
He 2.26 57.8 5.2 0.305 22.64
O2 50.14 78.0 154.8 0.308 405.9
Test vderW for reasonableness
Zc =pcVc/RTc = 3/8 (=0.375)
(see: principle of corresponding states)
33
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.
34
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.