ajc03

7/17/2019 Ajc03

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ANDERSON

UNIOR

OLLEGE

CHEMISTRY

C1

LECTURE

.The

understandirp

f the

behavior ases

s

an important

spect

n

chemist'.

t

ne ongtn

ot wnat

afe

Rnown

oday

as

tha

gas

taws,

staded

n

1M3 with

the nvenfi5n

oJ_ ",_ "ro.y.d?1.by

lmOelisto

Toniceili.

ter,

Ronen

Boyte

u'tisnea

iye:s'ia:;.

t n,s

Ew

srated

hat

at

constant

emperature

he

wluine

of a

gas

s

invers

ly

proport:nnat

to

the

pressuro.

he

obse'ations

by Robeft

Boyle

nd

otheiscientisfs

uch

"ir"q"";

charles

andJohn

Dalton

ed

to the

development

t the

gas

aws.

n

the

tate

ninetiiin

century,

he

kinetic-molecular

heory

was

hen

developed

y

screnfr.sts.

ni"

iiiorv'ii

based

on

3 fundamentat

ssumpfions

hat

are

used

o explain

he

prop.ii"i

iiii"J

gases'

Antdea,gas s an maginaryas hatperfecttybeysheseassumption"

""

,"/

as the

Boyle's

aw

andChartes'

aw.

Assessment

Obiectives

o

state

he basic

assumption

f the

kinetic

heory.as

ppried

o

an idealgas

.

Explain

ualitatively

n

terms

of intermolecular

orces

and

molecular

izi:

o The

condition

ecessary

or

a

gas

o approach

deal

behaviour

o

The

imitation

f ideality

t very

high

pressure

nd

very

ow

temperatures

o ptatggnouserhegenerar asequation V=nRT n carcurationincruding

.

thedeteimination

f Mr

.

Describe,

sing

a

kinetic

rnolecularmodel,

he

iquid

state;

melting;

vaporization

ndvapour

pressure.

Lecture

Outline

.

Introduction

.

Summary

f

the kinetic

oncept

f

the

state

of matter

o

The

Gas Laws

o

ldeal

gases

and

he

kinetic-molecular

heory

of

gases

.

Maxwell-Boltzmann

istribution

f

molecular

pecies

Chemisrry 004

Mr

Matthew

Soh

7/17/2019 Ajc03


Introduction

States

of

Matter

a

a

'

These

b,ulk

roperties

an

be exprained

y

the

kinetic

concept

f the

three

states

of

matter

as

briefly

ummarized

eiow. The

kinetic

heory

oiS""""

will

be studied

n

detail

ater

n the

ecture)

Many

pure

substances

an

exist

n

a[

of the

three

states

of

matten

sorid,

liquld

and

gas,

depending

n

condition

f temperatuie

and

pressure,

Each

state

can

be

classified

by

its

particutar

properlies

Some

of the

bulk

properties

are

Vltt/)

Solid

Liquid

Gas

Volume

Fixed

olume

Fixed

volume

Nof

h;a{

)oeurrrc

Shape

Fixed

hape

Not

ixed;

assurne

shape

of

container

Not

ile<i;

assumJ

shape

of

annlainar

Compressibility

Virtually

incompressible

Virtually

incompressible

Compressible

Chemistrv 004

Mr

Matthew

Soh

7/17/2019 Ajc03


Solid

Liquid

Gas

Arrangement

of

particles

Strong

orces

between

he

partides

Particles

re

packed losely

in a regular

arTangement

.

Strong

orces

between

he

particles

.

Particles re

not as

close-packed

s in

the solidstateand

not n an orderly

arrangement

.

Negligible

orces

between

he

particles.

.

Particles

are far

apart, and in

r:rndom

arangement.

Degree

of

movement

f

particles

.

Particles

an

only

vibrate

and

otate

abouta

fixed

position.

.

Particles

cannot

move

throughout

solid,

.e.,

no

translational

movement.

Particles ave

more

energyhan

in the

solidstate

Partides

an vibrate,

rotateand slideover

each

other(have

translational

movement)

r

Particles

have

more

energy

than n the

sotid

or

liquid

tates

.

Particles

have

unrestricted

movement;

an

vibrate, otate

and move

anywherewithin

the container

Process or

changeof

state

.

Merung

Particles

ain

energy

o melt.

Energy equired

o

overcome

trong

forcesholding

he

partides

n fixed

positions

.

Boiling

Occurswhen he

saturated

apour

pressure

f the iquid

s

equal

o the

external(atmospheric)

pressure.

Energyequiredo

overcome

he orces

between

he

particles

n

the

iquid

and

c increase

the

distance etween

them

so

hat more

molecules aveenergy

to escape

nto he

vapour

ohase-

The

average inetic

energy

of the molecules

remainingn

the iquid

doesnot ncrease,hus

the emDerature

emains

constant

hen he iquid

boi ls .

7/17/2019 Ajc03


7/17/2019 Ajc03


Charles'law

's

Law

Quick

A sampleof gasoccupies volumeof 7.50dm3at 0.988atm and2B.OC

(a)

Calculate

he

pressure

f

the

gas

f

its volume

s decreased

o

4.89

dm3

while

the emperature

s heldconstant

(

'l

atrn

=

101

KPa)

Pd.f

P,

V, : 91

V1

-1 ' lx

0,4t?

- -

?L/ '

)+,201

r tr .

t ,

5t 7a

77

.

At constiant

pressure,

he volume

of a fixed

mass

of

gas

is

direcfly

proportional

o its absolute

emperature

temperalure

xpressed

n

Kelvln)

i.e

V

cc

T at constant

P

V=constantXT

r/k)

Law

Quick

What s theeffecton lhe volumeof one moleof a gaswheneachof thefollowing

happens

(i)

The

emperature

hanges

rom600K

o 300 K at

constant

ressure

(ii)

The emperature

hanges

rom300

K to 600 K at

constant

ressure

t',t

d

vol.lt'r bcrtmt

^a

t'

lit"'l

(;r)

0

nlqpf

"tl

ir^ctat

h0 +.4 *s'/-tj'

Chemistry 004 Mr MatthewSoh

7/17/2019 Ajc03


Avoqadro's

Law

' Under he sameconditionof temperatureand pressure,equar

vorumes

of

all

gases

contain

he

equal

number

of

moleculei.

'

Th.e

volume

occupied

by one

more

of

gas

is

rhe

same

or a[

qases.

rt is

cafled

the

gas

molar

volumes.

t

measuies

at22.4

dm3at

s.t.p

dJt;.o

;;:

at

r.t.p.

'

Therefore

he

morar

mass

of a

gas

can

be

determined

when

the

volume

occupied

y

the

gas

s

known.

ie

Vot

,rloU.t

"f3os

atconstantrandP

'

Gases

which

obey

Boyres's

aw

and

charres'

aw

under

a[

conditions

re

called

deal

gases

.

By

Combining

oyles's

aw(pV

=

constant)

nd

Charles'

aw(V/T

=

constant),

ne

obtain

he relationship

PV=Constant

P,Vt

.

I Prr

T

:

:

(6416f

:

rLv:

t, 1;

This

s

often

written

as

PrVr

=

PrV"

Tr

Tz

The

ldeal

Gas

Equation

Chemistry 004

. Theequation f state oran idealgascan be expressed:

P

X

V

=

conslant

or

a

given

mass

of

gas

T

'

lt-follows

rom

Avogadro's

aw

that

he

constant

s

the

same

or

one

mole

of all

gases.

t

is

called

he

universal

as

constant,

with

symbol

R.

fhe

equation

ecomes

PV=RT

This

is

called

the

idear

gas

equation.

For

n mores

of

gas

the

equation

becomes

Mr

Matthew

Soh

7/17/2019 Ajc03


PV

=n

Gas

Constant

R

o

Note hat

he value

of R depends

n

the unitsof P,V

T

and n

Value

of R

Units

8.314 qrl-'K'

S.l

unit)

0.08206

L atm mol-1

K-1

1.987

Calmol-1

-1

WHY

R

=

8.314?

o

The value

of R in

S.l units s

calculated sing

molar olume

of a

gas

at

s.t.p ondition

(

s.t.p

onditions

eans

tandard

emperatures

0

oC

and1 atmospheric

ressure)

MolarVolume

Volume

f 1 mde of

gas)

at stp

=

22.4dm'3

2.24X'lO-2

3

Pressure

1

atm

=

101325

aor Nm-z

Temperature

ooo

=

273.15K

Using

PV

=

nRT,

thus R

=

PV/nT

=

1

o1

325-Pzz_2

24_X

2_st'

lmol

X 273.'15

=

8.314 Jmol-l

K

a

a

PV= m RT

E-

PXMI=

wherem = mass fgasand l = Molarmass fgas

RT=

p

R T

where

=

densityof

as

Chemistry 004

Mr Matthew Soh

7/17/2019 Ajc03


|

." --

tog

6q

lr-1

--

19

s

.^ j

I

drn

t

r

luor j

cl ,3

I

qro

drn

?

--

lrnr

ldeal Gas Quick Check

t ,6t

x t03

Solving

aJinear

equation

would

tell

you

that

there

can

only

be

one

unknown

n

this

linear

equation.

f

you

had

h"o

;il;"

in

this

equation,

either

you

are

wrong

or lhe

question.

Remember

P

V,

T and

n

must

be

in

their

correct"

nits.

^.

P'

_

Fl

I 9r

xrot

<

' l

P6

x,o- l

8-r

19

x

jrb

-"

o,

o

rPf,

"o {

A volume

85cm3 f a gasm-easuredt40 c ofvapourmeasuredt 1.01 105Nm-'has

a

mass

of

1.715 .

Calculate

ne

motai

mals

ot

gas

(

ans

=

4 omot

1)

' -

"

q. i "* '

{ , .

**

Dalton's

Law

of

partial

pressure

Chemistry 004

=

at I

ft".|-' l

ln

a

mixture

f

gases

A,

B,

C and

D),

each

gas

behaves

s

if it

were

he

only

gas

present

This

s

based

on

the

assumption

hat

here

are

no

chemicar

nteractions

between

he

gases.

Thecontribution hicheachgasmakeso thetotarpressurescatedthe

partial

pressure.

ln

a

mixture,

ach

gas

exerts

ts

own

pressure;

ndependent

f

the

other

93:."

t

assuming

achgas

behaves

deally).

.lt

is

equal

o

the

pressure

hich

he

gas

would

exert

f

it alone

occupied

the

container

The

partial

pressure

f

each

gas

depends

n

the

totar

pressure

and

on

the

mole

raction

of

the

gas

9.2

X

't0

'm

Mr

Matthew

Soh

7/17/2019 Ajc03


lllustration

Gas

A alono

at

tempt.

T

and

\rol

V

gas

A

molecule

gas

B

molecule

Pressure fA, pA

=

nARf

Totalpressurep=Pl+Pg

Chemistry2004'

o

o

.

T.h"

t99l

pressu.e,

"r.f$

by

a

mixture

of

gases

whicfi

do

not

react

chemicalry,

s

the

sum

of

the

partiar

pd"uL'"r"rt"o

by

the

constituent

gases

i.e

for

a miliure

of

gases

A

and

B

in

a

volume

V,

nA

no.

of

mol

ofA

Partial

Pressure

ofA

,

pA

=

nART

when

PAo

portd

pms$rr

otA

PB

r:

perthl

pnrrurc

of A

B

at

Temot

T

and

wl

V

o

o

o

oo

Ot

Mr

Matthew

Soh

7/17/2019 Ajc03


This

aw

assumes

ach

gas

n

the

mixture

beys

he

deal

gas

equation,

Ptor.t

=

naRT

+nERT =

lltoufif

VVV

Mole

Fraction

o

Mole

raction

s

a dimensionress

umber

hat

expresses

he

ratio

of

the

number

of

moles

of one

component

as

lo the totalnumberof moles nthemixture.

In a

mixture

f

gas

A and

gas

B,

Mole

raction

f

A

=

Da__

ol

+

Fle

Mole

fraction

of B

=

Ilg

ne

*

Ile

r

Sum

of

mol fraction

=

1

.

Since nA

is

proportional

o VA ( Avogadro's aw), mol fractioncan also be

expressed

as a ratio

of volume.

Mole

raction

of

A

=

Vq_

Va+Ve

Relationship

between

mole

frac-tion

and

partial

pressure

Partial

Pressure

1

3.00dm3

nitrogen

t

a

pressure

f

101

Kpa and

7.00

dm3

of hydrogen

at a

pressure

f 101KPa

re

ed into

a

10.0

dm3conlainer.

Wnit

islne

partial

ressure

f

each

gas?

Chemistry2004

l0

Mr

Matthew

Soh

7/17/2019 Ajc03


Ptno

=

?r"H,

x

g, .ogrtot

"

t '

Lo

x lss

P.7,

/0,5

1

'd5

xpr

t

'

,

#,

x

lnr

4r.tt

.

( l

x lgr

P11,

:

t . , to

x

tot

Pa//

2.

A cylinder

eceives

2.50

dm3

of

methane,

7.S0

dm3

of

ethane

and

0.500dm"

of

propane,

ll

at the

same

emperature

nd

pressure.

he

pressure

nside he cylinder s 5.0S X 105pa. What is the partialpressure

f each

gas?

The ideal

gas

equalion

describes

wo

gases

behave,

but

it

does

not

explain

why

hey

behave

s

they

do,

eg. Why

does

a

gas

expand

when

heated

nder

constant

ressure?

An ideal

gas

s

a hypotheticalas

hat obeys

Boyles's

aw

and Charles'

law

at all

temperature

nd

pressure

onditions.

The kinetic-rnolecularheorywas developedo explain he properties

and

behaviour

f

ideal

gases

described

y the

gas

aws.

The

kinetic

heory

of

gases

was

put

forward

by

RJ

Clausius

and

JC

Maxwell

n 1857

and

1859

respectively.

The

theory

tackles

these

questions

y making

hree

undamental

ssumptions

.

Gases

cpnsist

of molecules

hat

are

in a

constant

state of

random

motion;

moving

n

a straight

ine.

The

molecules

move

n straight

ine

until they collidewith each other or with the walls of the container.

These

collisions

are

perfec

y

elastic;

this

means

hat

molecules

bounces

part

with

no net

oss

of

energy.

.

The volume

of all

molecules

of the

gas

s negligible

ompared

o

the

total

volume

in

which

the

gas

occupies.

The

molecules

re

far

apart

.

The

molecules

ave

a range

of speeds.

The speed

of a

molecule

depends

n its

kinetic

energy.

As

the

temperature

ncreases

he

kinetic

energy

ncreases

s,

as a

result,

he

average

speed

ncreases.

The

averag€ kinetic energy is proportional to the absolute

temperature;

herefore

certain

emperature

ll

gases

have

he

same

average

inetic

nergy.

Srrrr

h.,rc

neglrfttc

&r.r

*

.*zc{rbrt.

l l

hemistry 004

Mr

Matthew

Soh

7/17/2019 Ajc03


behaviourof gases

lS""T".

-

Wtren

moving

object

collides

with

a

surface

t

exert

a force.

I

ne

colrslon

of

gas

molecules

ith

he

walls

of

the

ontainer

exert

a force

which-results

n

a

pressure.

The

greater

he

number

f

mole"ur""

ano

n"

more

requent

nd

he

pressure

hly

coltide

with

he

watts

t

e

gr""t

r ih"

pressure

s.

Boyle's

Law (V

o

'rtp)

A

decrease

n

the

volume

of

gases

wiil

cause

he

distance

between

he

moleculees

and

the

*"if"

if

the

container

o

decrease.

oflisions

are

more

requent

and

the

pressure

exerted

by thegas hereforencreases.

charles'

Law (V

o T)

-

As

the

temperature

ncreases,

oth

the

kinetic

energy

and

the

average

molecular

peed

ncreases.

Molecule

hits

the

wall.more

reguenfly

nd

with

more

orce,

ncreasing

he

pressure

xerted

by the

gas.

As

a result

he

wall

moves

outwards:"the

olume

ncreases

until

a

constant

ressure

s restored.

ldealgases

do

not

exist

n

practice

Accurate

measurement

how

hat

all

real

gases

do

not

obey

the

ideal

gas

equation

or

Boyles'

Law

and

charles'

Law)

under

certain

onditions

of

temperature

r

pressure

The

extent

o

which

a real

gas

departs

rom

deal

behaviour

an

be

seen

from

the

PVIRT

plots

beljw

(

Fi

1

and

Zl .

fnese

pfots

are

obtained

from

resullsof

Boyles'Law

xperiment

foi.t

mol

of each

gas.

a

a

Chemistry 004

l2

Mr

Matthew

Soh

7/17/2019 Ajc03


)J/cn,

, '

{----yrtur-

i l

1000K

800

1000

P

(atm)

rrgure

J-

pv/

RT versusn..t<<,.. r^. 1 -^, .

a

Figure

z'

PVlRTwc;

:i::*,::*:,i;ift,Ttrff:.,,j:rtr#:i:i:i'r:ffif"l.;tr'[[r

(

So....c

.-

Tvr

c_

Ce.^I'-,l(

scn

o.^4)

Note:

PV

=

nRT

ideal

gas

equation

pV

=n

RT

For one mole of ideal oas

u""run.iio'.ioi'di"i1'#i:,"{*Hl,:,r1 Ti":lll,i;,l,l1lir

'

lmportant

features

rom

pV/RT

plot

Fig

1-

Pressure

condition

'

ffiJr':lt

f,ffiiln;"*"

deviation

rom

deal

ehaviour

s

rarse

nd

s

o At

lower

pressure

usually

elow

10

atm),

he

deviation

s

small

Deviation

or

gases

uch

"s.co,

"no

r.rH:;;;

;.n".

Deviation

or

H2

gas

s

relativellisrn"li."

.

"'"

''

Fig

2

-

Temperature

ondition

.

'

At

a

higher

emperatllg,

fle.leyia-tion

s

smater

Behaviour

f

a rear

qas

pproaches

more

closely

o

ttrat

oi

an'io:e"l.gl"""t

nignu,

emperature

Chemistry

004

| 1

Mr

Matrhew

oh

7/17/2019 Ajc03


Hence,

deviation

rom

ideality

s

greatest

at

these

conditions:

'

In

generar'

he

deviations.from

dear

behaviour

ncrease

s

temperature

decrease.

he

deviation.lecomgs

ig;in;ni'neir

tne

temperature

t

which

he

gas

s converted

nto

a

liouid

]wo..b3si9

assumptions

f

the

kinetic

_

molecular

heory

or

ideal gases

are

nvalid

at

these

conditions

the

iaear

gas

;oi;ri""

"r"

assumed

o

have

negligible

olumes,

nd

have

no

or

negligible

ntermolecutar

ttractions.

Real

gases

molecules

do

have

finite

volume,

ancl

they

have

significant

intermolecular

ttraction.

'

Average

distance

between

morecures

s

smal (

morecures

re

very

crose

together)

o

Intermolecular

ttraction

evelop,

nd

.

Volume

.of

gas

molecule

become

significant

ompared

o the

volume

occupied

y

the

gas

lmpact

on

PV/RT

(refer

o Fig

.t)

'

At hrgh

pnessure,

he

attractive

orces

educe

he

force

with

which gas

molecules it thecontainer

This

mplies

hat

pressure

f

real

gas

s

less

han

hat

of

an

ideal

gas

Therefore

PV/RT

<

1

Chemistry004

l4

Mr

Matthew

Soh

7/17/2019 Ajc03


.

Al

v€ry

high

pressure,

lhe

volume

of

gas

molectles

become

more

significant

nd

tends

o-be

greater

han

that

predicted

y

the idear

as

equation.

he

volume

effects

ominate

t very

high

pressures.

This

mplies

hat

volume

of

gas

molecrles

become

ignificant

nd ends

o

be

greater

han

hat

predicted

y

the deal

gas

equalion

The volume

effects

dominate

at very

high

pressures

Therefore

PV/RT

>

1

The

molecules

ave ow

average

kinetic

energy.

This reduces he energyneeded o overcome ntermolecularttractive

orces.

Thus,

intermolecuLi

attraction

re

signifi

ant.

lmpact

on

PV/RT refer

o

Fig 2)

.

significant

ntermolecular

ttraction

t

low temperature

educes

he

force

with

which

gas

molecules

it the

container

PV/RT

<1

(negative

eviation)

o

Finite

volume

of

gas

morecures

auses

he

positive

deviation pv/RT >1)

at low

emperature

r high

emperature

ith

high

pressure

ondition.

(Notice

hat

as

temperature

ncreases,

he negative

deviation PV/RT <

1)

decreases.

his

s

due o

less ntermolecular

ttraction

t higher

emperature.

NH3

Cq

and

other

polar'

molecules

have

significant

ntermolecular

attractions

These

molecules

are

also relatively

arge,

thus

lhe

volume

of

the

gas

molecules

s not

negligible.

(*

This term

will

be

studied

under chemical

boding

ecture)

Chemistrv

004

t5

Mr

Matthew

Soh

7/17/2019 Ajc03


deviation?

Hz,Arand

Ne

are non

polar-

moleorles,

hus

hey

have

elati\rety

eak

intermolectrlar

orces,

almost

ike

deal

gas€s.

These

re

also

elatvely

small

molecules.

NOTE

Many

gases

apprcximate

o ideal

behaviour

at loriv

pressurc

usually

<10

atm)

and

at

high

emperatures

temperature

elt

auove

ire

ooilinspolil

6f

the;;si

Mosr

gases

at

np

or stp

behave

ike

ideal

gases

or

prac{icafpurposes

PV=nRTcanbeused.

Chemistry2004

l6

Mr

Matthew

Soh

7/17/2019 Ajc03


Based

on the kinetic

heory, he

absolute

emperature

f a

gas

s a

measure

of the

average

inetic

nergy

f it molecules

For example,ncreasinghe temperaturef a gas by 10 C will doubte he

.

aveEge

kinetic

energy

of its molecules.

hus,

molecular

peed ncreases

with ncreasing

emperature.

At

conslant

emperature,

he

molectles

n a sample

of

gas

have avemge

kineticenergy,

hus

an average

peed;

ut he ndividual

moleculesmove

at a

varying

peeds.

t any

nstant,

omeare

moving apidly,

thersmoreslowly

This

distribution

f molecular

peed

or energy

s summarized

raphica

in

the

Maxwell Boltzmann

istribution

urve

fraction

of

molecules

with

speed

x

sample

Chemistry

004

A typicat

M-B

curye

at a

particular

temperature

molecular peed,

x

The

curve shows

he fraction

of moteculesmovingat

each speed.

At any instant,a small numberof moleculeswitl be almoststationary

and a

small number

will be

movingat very high

speeds. However,

he

majority

will

have speeds

between hese wo extremes.

The

largest

number

has a speed

conesponding o the

maximum

of the

curve,

hat is

,

more

molecules

ossess

his

speed han

any other.

This

is the

most

probable

peed.

The

area under

he curve

reflects he

total

number

of molecules

n

the

Mr

Matthew

Soh

7

7/17/2019 Ajc03


ra

As

the

temperature

f

the

g:"^1"_

:,_r."d,

he

average

kinetic

energy

hus

he

average

peed

of

the

gas

molecule

ncreasJJproportionaily.

At

high

temperarure,

he

curve

s

shifted

";il;dh:,

speed

as

the

;i#3::g#ijr:j::

with

ow

"p;;

;;;;;;;#'

ll

"

num

er

wnh

fraction

of

molecules

with

speed

x

M-B

curvcs

ofa

gas

at

two

different

Iemperatures:

-

at

lower

empcrature,

l

-

at

highcr

tempcrahuc,

T2

molecular

speed

x

a

fraction

of

molecules

ith

speed

X1

or

greater,

at

Tl

fraction

f molecules ithspeedX1or greater,at T2

Note

hat

he

fraction

r

number

f

molecutes

ith

speed

X1

or

greater

is

considerably

arger

at

higher

emperature

2

Chemistry

004

l8

Mr

Matthew

Soh

7/17/2019 Ajc03


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