second year chemistry

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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:

donal.leech@nuigalway.ie 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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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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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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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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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.