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Gaseous and Liquid state

Thus matter is classified mainly into three categories depending upon its physical state namely solid,

liquid and gaseous states.

Distinction between three states of matter:

S.No Property Solid Liquid Gas

1 Shape Definite shape Indefinite shape Indefinite shape

2 Volume Definite Volume Definite Volume Indefinite Volume

3 Inter particular

Forces

Strong Inter

particular Forces

Comparatiely !ea"er Inter

particular Forces

Inte rparticular force

negligi#le

$ Inter particular

Space

%egligi#le inter

particular space

Comparatiely large inter

particular space

Very large Inter part

space

& 'articular (otion 'article motion is

restricted to i#ratory

motion.

'article motion is ery slo! 'article motion is e

and also random.

) 'ac"ing of

'articles

'articles are ery

Closely pac"ed

'articles are loosely pac"ed 'articles are ery lo

pac"ed

* Compressi#ility Incompressi#le Compressi#le +ighly Compressi#le

Density Very +igh Density -o! Density Very lo! density

Parameters of GasesThe characteristics of gases are described in terms of following four

parameters

(ass

Volume

'ressure

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Temperature

1. Mass (m):

The mass of the gas is related to the number of moles as

n = w/M

Where n = number of moles

w = mass of gas in grams

M = molecular mass of the gas

2. Volume (V):

Since gases occupy the entire space available to them, therefore the gas

volume means the volume of the container in which the gas is enclosed.

Units of Volume: Volume is generally epressed in litre (L), cm !!m

1m" 1#litre " 1#!m" 1#$cm.

. Pressure:

"ressure of the gas is due to its collisions with walls of

its container i.e. the force eerted by the gas per unit area on the walls

of the container is e#ual to its pressure.

"ressure is eerted by a gas due to $inetic energy of its molecules.

%s temperature increases, the $inetic energy of molecules increases, which

results in increase in pressure of the gas. So, pressure of any gas is

directly proportional to its temperature.

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Units of Pressure:

The pressure of a gas is epressed inatm, Pa, %m&2, bar andlb'n2 (si).

&'( mm = ) atm = )()*+. -"a= )()*+ "a= )()*+ m+

&'( mm of 0g = ).()*+ bar = )()*.+ milli bar = )1.& lb/+n+2psi3

. *emerature (*):

Temperature is defined as the degree of hotness. The S4 unit of

temperature is -elvin. o5 and o6 are the two other units used for

measuring temperature. 7n the 5elsius scale water free8es at (95 and boils

at )((95 where as in the -elvin scale water free8es at +&* - and boils at

*&* -.

+ " o - 2./

0 " ('/) o - 2

Gas Laws:1. o3le4s Law:5

At constant temperature, the pressure of a fixed amount

(i.e., number of moles n) of gas varies inversely with its

volume.

Grahical 6eresentation of o3le4s

Law :

plot of P ersus /0V at constant temperature for a fi1ed mass of gas !ould #e a straight

line passing through the origin.

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plot of Persus Vat constant temperature for a fi1ed mass of a gas !ould #e a rectangular

hyper#ola.

plot of P (or V ersus PVat constant temperature for a fi1ed mass of a gas is a straight

line parallel to the PV axis.

2. Charles Law:-

At constant pressure, the volume of a given mass of a gas

is directly proportional to its absolute temperature

or

Grahical 6eresentation of harles4s

Law :

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). 6or a definite mass of the gas a plot of Vvs T2o-3 at constant

pressure is a straight line passing through the origin.

+. % plot of V vs t2o53 at constant pressure is a straight line cutting

the temperature ais at :+&* o5

3. Combined Gas Law:-

This la! states that at constant volume, the pressure of a given mass of a gas is directly

proportional to its absolute temperature.

the com#ination of 4oyle5s -a! and Charles5 -a!6

. Gay Lussa!s Law:

Where,

P" Pressure of Gas

T" 7bsolute *emerature

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4f the pressure and temperature of a gas changes from P)! T1to P2! T2 ,

volume remaining constant , we have

where,

"t= "ressure of gas at t o5

"o = "ressure of gas at ( o5

t = Temperature in o5.

Grahical 6eresentation of Ga35Lussac4s Law

". #$o%adro Law:

Samples of different gases which contain the same number of molecules

(any complexity si!e shape" occupy the same #olume at the same

temperature and pressure$.

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4t follows from %vogadro;s hypothesis that 2when T and " are

constant3.

Mathematicall3

&. 'deal Gas (quation:

Ideal gas o#ey all the three la!s i.e. 4oyle5s, Charles5s, and ogadro7s la! strictly.

p 8 n9T

:here,

where < is the constant of proportionality or universal gas constant

The value of < was found out to be

< = .*)1 > mol)-)

< = (.(+) litre atm -)mol)

< = + cal -)mol)

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Ideal gas equation is also "no!n as equation ofstate.

). *altons law o+ partial pressures:

The total pressure of mi1ture of non;reactie gases at constant temperature and pressure is equal to

the sum of the indiidual partial pressures of the gases.

ptotal 8 p/

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The aerage "inetic energy of the particles of a gas is directly proportional to the a#solute

temperature.

'ressure of the gas is due to the collision #et!een gas molecules and !alls of the container.

*he +inetic 8uation

Velocities of 9as molecules

#$era%e ,elo!ity

%verage velocity =

oot ean Square ,elo!ity:-

Mawell proposed the term Drmsas the s#uare root of means of s#uare of all

such velocities.

also

ost probable $elo!ity:-

4t is the velocity which is possessed by maimum no. of molecules.

6urthermore

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+inetic 8ner93 of Gas

%s per $inetic e#uation

6or ) mole m E n = Molecular Mass 2M3

%lso

Where $ is the Folt8mann constant 2$ = < / 3

Graham4s Law of Diffusion'8ffusion:

/. *i++usion:a#ility of a gas to spread and occupy the !hole aaila#le olume irrespectie of other gases

present in the container

2. (++usion:process #y !hich a gas escapes from one cham#er of a essel through a small opening or

an orifice

r ) / Gd

where r is the rate of diffusion and d is the density of the gas.

ow, if there are two gases % and F having r )and r+as their rates of diffusion

and d)and d+their densities respectively. Then

r) )

and

r+

or

,

The rate of diffusion @r of a gas at constant temperature is directly preoperational to its pressure

De;iation from i!eal 9as beha;ior:

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0or ideal %as1

Compressi#ility factor i.e. A 8 'V0n9T 8/

For non;Ideal gas, A B/

Thus for non;ideal gas,A can #e / or /

hen 4 /, it is a negatie deiation. It sho!s that the gas is more compressi#le than e1pected

from ideal #ehaiour.

hen 5 /, it is a positie deiation. It sho!s that the gas is less compressi#le than e1pected from

ideal #ehaiour.

/. Causes o+ de$iation +rom ideal beha$iour:

The olume occupied #y gas molecules is negligi#ly small as compared to the olume occupied #y

the gas.

The forces of attraction #et!een gas molecules are negligi#le.

2. ,an der waals (quation:

:here,

a and # are an der !aals

constants.

t lo! pressures6

'V 8 9T > a0V

or

'V 9TThis accounts for the dip in 'V s '

isotherm at lo! pressure

#t +airly hi%h pressures

a0V2 may #e neglected in comparison !ith '. The Vander :aals equation #ecomes

'V 8 9T < '#

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or

'V 9T

This accounts for the rising parts of the 'V s ' isotherm at high pressures

6oyles 7emperature 87b9 :-temperature at !hich real gas o#eys the gas la!s oer a !ide range of

pressure.

T#8 a 0 9# 8 /02 T/

Liuefaction of 9ases:

Criti!al temperature 87!9:- temperature at !hich a gas liquefies. Tc8 a 0 2*9#

Criti!al ,olume: 8,!9 :-olume of one mole of a gas at critical temperature.Vc8 3#

Criti!al pressure 8p!9:-pressure of gas at its critical temperature. 'c8 a02*#2

olar heat !apa!ity o+ ideal %ases:-the amount of heat required to raise the temperature of /

mole of a gas trough /EC.

5":5V= < !

"oissonHs ratio 2I3 = 5"/5V

6or monatomic gas 5p= cal and 5v=* cal

I = /* = ).'&

6or diatomic gas 5p= & cal and 5v= cal

I =&/ = ).1

6or polyatomic gas 5p= cal and 5v= cal

I = /' = ).**

%lso 5p= 5pm,

Where, 5pand 5vare specific heat and m, is molecular weight.

Liui!

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Surface tension @ 8 :or" done 0 Change in area

Gnits6 CGS:dcm;/

S': %m;/

The surface of the liquid tends to contract to the smallest possi#le

area for a gien olume of the liquid i.e. spherical shape.Surface Tension of liquid decreases !ith increase of temperature

and #ecomes Hero at its critical temperature.

Sur+a!e 7ension in e$eryday li+e:

Cleansing action of soap and detergents.

fficacy of tooth pastes, mouth !ashes and nasal Jellies.

,is!osity:

It is the force of friction !hich one part of the liquid offers to another part of the liquid.

Coefficient of iscosity6 is the force per unit area required to maintain unit difference of elocity

#et!een t!o parallel layers in the liquid one unit apart.

Gnits6CGS:dscm;/

S.': %sm;/

Viscosity of liquid decreases !ith increase in temperature.