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Course Director

Dónal Leech Room C205 (in Physical

Chemistry) E-mail:

donal.leech@nuigalway.ie Phone: 493563 (from outside),

ext 3563 (internal phones)

Web-site: http://www.nuigalway.ie/chemistry/staff/donal_leech/teaching.html

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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

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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

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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

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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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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

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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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To be presented in Lecture

Come to the lecture to see what is on this slide!

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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

Each curve

is called

an isother

m

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Charles’s Law

Each line is called

an isobar

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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 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

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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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Problem solved

Come to the lecture to see what is on this slide!

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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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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)

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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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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

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Come to the lecture to see what is on this slide!

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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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Derivation

Come to the lecture to see what is on this slide!

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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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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)

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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.