Thermo & Stat Mech - Spring 2006 Class 141 GASEOUS STATE PHYSICAL CHEMISTRY B.Sc. FIRST YEAR FIRST SEMESTER.

Thermo & Stat Mech - Spring 2006 Thermo & Stat Mech - Spring 2006 Class 14 Class 14 11

GASEOUS STATE

PHYSICAL CHEMISTRY B.Sc. FIRST YEAR FIRST SEMESTER


Maxwell Velocity Maxwell Velocity DistributionDistribution

Maxwell’s in 1886 suggested that :Maxwell’s in 1886 suggested that : “ “At a particular temperature ,the At a particular temperature ,the

fraction of molecules possessing fraction of molecules possessing particular velocities remain almost particular velocities remain almost constant.”constant.”


On the basis of laws of probability, On the basis of laws of probability, fraction of molecules having velocities fraction of molecules having velocities

between c and c+dcbetween c and c+dcWhere dnc is the no of molecules having Where dnc is the no of molecules having velocities between c and c+dc,out of a total of n velocities between c and c+dc,out of a total of n molecules of the gas and T are the molecular molecules of the gas and T are the molecular mass and absolute temperature of the gas.mass and absolute temperature of the gas.

kT

mc

kT

mc

eckT

mdcdnn

dceckT

mndn

22

23

22

23

2

2

24/)/1(

24/

The above equation may be rewritten as


C

p

=1/n

.d

nc /

dc

α

FIGURE:-1 MAXWELL’S DISTRIBUTION OF VELOCITIES


MAXWELL’S DISTRIBUTION OF VELOCITIESMAXWELL’S DISTRIBUTION OF VELOCITIES The Fraction of the molecules having very low The Fraction of the molecules having very low

velocities or very High velocities are very small.velocities or very High velocities are very small.

The fraction of molecules possessing higher The fraction of molecules possessing higher speeds keeps on increasing till it reaches a peak speeds keeps on increasing till it reaches a peak and thereafter it starts decreasing.and thereafter it starts decreasing.

The maximum fraction of molecules possess a The maximum fraction of molecules possess a velocity corresponding to the peak in the velocity corresponding to the peak in the curve .This velocity is referred as curve .This velocity is referred as Most probable Most probable velocityvelocity..


EFFECT OF TEMPERATURE ON MAXWELL’S DISTRIBUTION OF VELOCITIES

With increase of temperature, the curve shifts as shown in fig. Two changes may be noticed:

i)The peak of the curve shifts forward.

i)The peak of the curve shifts downward and is flattened.

FIGURE:-2 DISTRIBUTION OF VELOCITIES AT TWO DIFFERENT TEMPERATURE

T1

T2


Collision diameterCollision diameterThe closest distance of approach The closest distance of approach

between the centres of the between the centres of the molecules taking part in a collision is molecules taking part in a collision is called collision diameter. it is usually called collision diameter. it is usually represented by represented by σσ..

σ

FIGURE:3 MOLECULAR DIAMETER


Collision NumberCollision Number The no of collision which a single molecules The no of collision which a single molecules

makes with other molecules in one second is makes with other molecules in one second is called collision number.called collision number.

On the basis of kinetic theory of gases, it can On the basis of kinetic theory of gases, it can be shown that:be shown that:

NNCC ==√2√2ππννσσ22nn

Where v=average velocity of the gas molecules in cmWhere v=average velocity of the gas molecules in cm

per secper sec

σσ=molecular diameter in cm n=no of molecules/cm=molecular diameter in cm n=no of molecules/cm


Derivation of collision no & collision frequencyConsider a particular molecule A moving in a particular direction .

Average speed of the molecule = v cm/sec Distance travel in one second = v cm Radius(equal to molecular diameter) = σ

FIGURE:-4 MOVEMENT OF MOLECULE A ASSUMING OTHER MOLECULES TO BE STATIONARY

2σ

σ

v cm

A


TYPES OF MOLECULAR TYPES OF MOLECULAR COLLISIONCOLLISION

(a) (b) (c )(a) (b) (c ) Relative velocity=0 Relative velocity=2v Relative Relative velocity=0 Relative velocity=2v Relative

velocity=velocity=√2√2νν

FIGURE:-5 TYPES OF MOLECULAR COLLISION


COLLISION FREQUENCYThe number of collision which takes place in one second among the molecules present in one centimeter cube of the gas is called collision frequency.(Z) Z=1/√2πνσ2n2

Thus Z is directly proportional to 1)average velocity of the gas molecules(v)2)Square of the molecular diameter (σ2)3)Square of the molecules per cm cube (n2)


THE FREE PATH OF A THE FREE PATH OF A MOLECULEMOLECULE

The distance travelled by a molecule before The distance travelled by a molecule before colliding with another molecule is called the free colliding with another molecule is called the free path.path.

FIGURE:-6 DIFFERENT FREE PATHS OF A MOLECULE


THE MEAN FREE PATHTHE MEAN FREE PATH The mean distance travelled by a The mean distance travelled by a

molecule between any two molecule between any two successive collision is called the successive collision is called the mean free path. mean free path.

ll==v /Nv /Ncc

but Nc=but Nc=√√22ππνσνσ22nn

therefore l=v/therefore l=v/ √√22ππνσνσ22nn

l=1/l=1/ √ √22ππσσ22nn


IDEAL AND REAL GASESIDEAL AND REAL GASES

IDEAL GAS:-A gas which obeys the gas equation (PV=nRT) under all condition of temperature and pressure is called an ideal gas.for example: hydrogen, oxygen, nitrogen REAL GAS:-A gas which obeys the gas laws fairly well under low pressure or high temperature.for example: carbon dioxide,sulpur dioxide , ammonia


DEVIATION FROM THE GAS LAWS DEVIATION FROM THE GAS LAWS AND EXPLAINATION IN TERM OF AND EXPLAINATION IN TERM OF COMPRESSIBILITY FACTOR AND COMPRESSIBILITY FACTOR AND

BOYLE TEMPERATUREBOYLE TEMPERATURE

The Effect of temperature and pressure The Effect of temperature and pressure on the behaviours of a gas may be on the behaviours of a gas may be studied in terms of a quantity ‘z’ called studied in terms of a quantity ‘z’ called compressibility factor which is defined as compressibility factor which is defined as

z=PV/nRTz=PV/nRT


EFFECT OF EFFECT OF PRESSURE:COMPRESSIBILITY FACTORPRESSURE:COMPRESSIBILITY FACTOR

Compressibility factor ,z is mathematically expressed as

z=PV/nRTIn case of ideal gas,PV=nRT z=1In case of real gas,PV≠nRT

z≠1Thus in case of real gases ,the value of z can be <1 or > 1.(i)When z<1, it indicates negative deviation.(ii)When z>1 ,it indicates positive deviation .it means gas is less compressible .


PLOT OF COMPRESSIBILITY FACTOR (z ) VS PRESSURE FOR SOME GASES

FIGURE:-7 PLOT OF Z vs P


EFFECT OF TEMPERATURE:BOYLE EFFECT OF TEMPERATURE:BOYLE TEMPERATURETEMPERATURE

The deviation from ideal behaviour The deviation from ideal behaviour become less and less with increase become less and less with increase in temperature. The temperature at in temperature. The temperature at which a real gas behave like an ideal which a real gas behave like an ideal gas is called boyle’s temperature.gas is called boyle’s temperature.

The boyle temperature is different The boyle temperature is different for different gases.for different gases.


z

P (Atmosphere)

IDEAL GAS

50⁰C

100⁰C

-50⁰C

0⁰C

PLOT OF COMPRESSIBILITY FACTOR z vs pressure FOR N2 AT DIFFERENT TEMPERATURE.

50°C-50°C

0°C

FIGURE:- 8 PLOT OF z vs P FOR N2 AT DIFF. TEMP


CRITICAL CONSTANTSCRITICAL CONSTANTSThe critical temperature, critical pressure and critical The critical temperature, critical pressure and critical

volume of a gas are collectively called as the critical volume of a gas are collectively called as the critical constants .These constants are represented by Tconstants .These constants are represented by TC ,C ,PCC VC.C.

Critical Temperature of a gas may be defined as that temperature Critical Temperature of a gas may be defined as that temperature

above which the gas can’t be liquefied.above which the gas can’t be liquefied.

Critical pressure of a gas may be defined as the minimum Critical pressure of a gas may be defined as the minimum

pressure required to liquefy the gas at critical temperature.pressure required to liquefy the gas at critical temperature.

Critical volume of a gas may be defined as the volume occupied Critical volume of a gas may be defined as the volume occupied

by one mole of the gas at the critical temperature and by one mole of the gas at the critical temperature and

pressure.pressure.


MEASUREMENT OF CRITICAL MEASUREMENT OF CRITICAL CONSTANTSCONSTANTS

The measurement of critical temperature is The measurement of critical temperature is based upon the observation that whenbased upon the observation that when a a liquid is heated in a closed space , the liquid is heated in a closed space , the surface of separation between liquid and surface of separation between liquid and the vapour disappears at a definite the vapour disappears at a definite temperature and on cooling ,the surface temperature and on cooling ,the surface of separation reappears at the same of separation reappears at the same temperature.The temperature at which temperature.The temperature at which this occur is called critical temperature.this occur is called critical temperature.


MEASUREMENT OF CRITICAL TEMPERTURE AND CRITICAL PRESSURE

AIRMANOMETER

HEATING JACKET

VAPOUR

LIQUID OR LIQUIFIED GAS

FIGURE:-9


MEASUREMENT OF VMEASUREMENT OF VCC

The measurement of critical volume is based upon a rule given by Cailletet and Mathias in 1886 which states that “the mean of the densities of any substance in the state of liquid and saturated vapour at the same temperature is the linear function of the temperature”.


DETERMINATION OF CRITICAL DENSITYDETERMINATION OF CRITICAL DENSITY

B

D

A

MEAN DENSITIES

DENSITIES OF LIQUID

C

DENSITIES OF VAPOUR

(dl +dv)/2

DE

NS

ITY

TEMPERATURE

FIGURE:-10


ISOTHERMS OF CARBON ISOTHERMS OF CARBON DIOXIDEDIOXIDE

Andrews ,in 1861, was the first to study Andrews ,in 1861, was the first to study the effect of temperature and pressure the effect of temperature and pressure on the volume of carbon dioxide. Each on the volume of carbon dioxide. Each time, keeping the temperature constant time, keeping the temperature constant at a particular value, he measured the at a particular value, he measured the volume of carbon dioxide at different volume of carbon dioxide at different pressure. He then plotted the volumes pressure. He then plotted the volumes against pressure,at constant against pressure,at constant temperature. Such a plot of P vs V at temperature. Such a plot of P vs V at constant T is called as isotherm or constant T is called as isotherm or isothermal.isothermal.


ISOTHERMS OF CARBON DIOXIDEISOTHERMS OF CARBON DIOXIDE

PRESSURE

VOLUME

C B

LIQUID

GASEOUS

A

E

a

b

48.1°C

35.5°C

32.5°C

31.1°C

21.5°C

13.1°C

FIGURE :-11


LIQUEFACTION OF GASESLIQUEFACTION OF GASES

A gas can be liquefied by cooling A gas can be liquefied by cooling or by application of pressure or or by application of pressure or by the combined effect of both.by the combined effect of both.

No of attempts were made No of attempts were made earlier,that of Faraday is well earlier,that of Faraday is well known in 1823.known in 1823.


Reactants

Liquefied gas

Freezing mixture

FARADAY’S METHOD

FIGURE:-12


PERMANENT GASESPERMANENT GASES

Gases like Gases like hydrogen,helium,oxygen,nitrogen etc hydrogen,helium,oxygen,nitrogen etc however , could not be liquefied by the however , could not be liquefied by the application of pressure alone, however high application of pressure alone, however high it may be. Such gases , therefore, called it may be. Such gases , therefore, called “permanent gases”.“permanent gases”.

Even these gases could be liquefied Even these gases could be liquefied provided these were first cooled to or below provided these were first cooled to or below their respective critical temperatures.their respective critical temperatures.


EARLIER METHODSEARLIER METHODS

By the rapid evaporation of By the rapid evaporation of volatile volatile

liquids.liquids.

By the use of freezing mixturesBy the use of freezing mixtures


MODERN METHODSMODERN METHODS

1)BY THE ADIABATIC EXPANSION OF 1)BY THE ADIABATIC EXPANSION OF COMPRESSED GAS-LINDE’S COMPRESSED GAS-LINDE’S PROCESSPROCESS:-:-

This process is based upon Joule-This process is based upon Joule-Thomson Effect which states :-Thomson Effect which states :-

When a gas under high pressure is When a gas under high pressure is allowed to expand adiabatically allowed to expand adiabatically through a fine hole into a region of low through a fine hole into a region of low pressure it is accompanied by cooling.pressure it is accompanied by cooling.


A C

H2OD

FE

G

LINDE’S PROCESS FOR LIQUEFACTION OF AIR

B

FIGURE:-13


2)BY THE ADIABATIC EXPANSION OF A COMPRESSED GAS INVOLVING MECHANICAL WORK-CLAUDE’S PROCESS:-

This is based upon principle that when a gas expands adiabatically against a piston in an engine, it does some external work; hence its internal energy falls and consequently the temperature of the gas falls.


CLAUDE’S PROCESSCLAUDE’S PROCESS

AIR

COMPRESSOR

X

Y

J

D

G

LIQUID AIR

FIGURE:-14


3)BY ADIABATIC DEMAGNETISATION:-

This process was given independently by Debye and Giauque.This process is based upon the principle that when a magnetised body is demagnetised adiabatically the temperature of the body must fall.


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Thermo & Stat Mech - Spring 2006 Class 141 GASEOUS STATE PHYSICAL CHEMISTRY B.Sc. FIRST YEAR FIRST SEMESTER.

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