The effect of applied pressure on vapor pressure

rises. pressure vapour its phase,

condensed a toapplied is pressureWhen

ln (l)

(l)

(v) (l)

equili. preserves that changeany For

)()(

m,equilibriuAt

1

2

p

pRTPV

dpp

RTdPV

dd

gl

m

m

There is a relation between dp and dT that ensures that the system remains in equilibrium as either variable is changed.

The location of phase boundaries

Pressure and temperature at which two phases can coexist.

Relation between dp and dT

equation) (Clapeyron

),(),(

equal. still are

but changes potentials chemical theb,At

),(),(

,,,,

,,,,

V

S

dT

dp

dpSSdTVV

dpVdTSdpVdTS

dd

TpTp

TpTp

trs

trs

mmmm

mmmm

bb

aa

The solid –liquid boundary

curve Steep

large ve,

smallbut ve

ve

VT

H

dT

dp

fus

fus

Liquid –Vapour boundary

small ve,

large ve,

ve

VT

H

dT

dp

vap

vap

Equation)Clapeyron (Clausius

ln

(g)

2RT

H

dT

pd

p

RTT

H

dT

dp

VV

vap

vap

mvap

Solid-Vapour Boundary

vap-liquidan Steeper th

ve

large ve,

ve

VT

H

VT

H

dT

dp

vap

vap

sub

sub

1 bar

PF

PCF

3

system,component oneFor

2

Phase Rule

F=C-P+2

C = number of component

Total number of intensive variable = pc +2

Mole fraction of components in each phase must be one

Number of relation =number of phases= p

For chemical equilibrium,

Chemical potential of individual component will be same in each of the phases.

In each of the component

(p-1) relation for each of the component

Total number of relation for chemical equilibrium = c(p-1)

Degree of Freedom = pc + 2 – p - c(p-1)

= c – p + 2

.......1111

What happens to boiling point or freezing point of a liquid in the presence of a solute?

What happens to chemical potential of a liquid in the presence of solute?

solute. volatile-non ofaddition on

decreases liquid a of potential Chemical

) law s(Raoult' ln

ln

ln

(g) (l)

solute a of presenceIn

ln

(g) (l)

solvent pureFor

*

AAAA

AAA

AAA

AA

AAA

AA

xppxRT

p

pRT

pRT

pRT

There is elevation of boiling point upon addition of a solute.

There is depression of freezing point upon addition of a solute.

The elevation of boiling point

solvent.

theofconstant picebulliosco called is

)( 1

Where

2*

2*

b

Bb

ABvap

f

bAB

BA

BB

vap

Bf

K

mK

MmH

RTT

molalitymMmm

M

mx

H

RTK

KxT

1

(l) -(g) ln

ln (l) (g)

(l) (g)

T

TH

T

HTH

STHG

RT

G

RTx

xRT

vap

vapvap

vapvapvap

vapAAA

AAA

AA

Bvap

vapvapB

vapB

vapB

vapB

xH

RTT

T

T

R

H

TT

TT

R

Hx

TTR

Hx

TTR

Hx

TTR

Hx

2

2

11

11

111ln

The depression of Freezing point

constant. cryoscopic called is f

Bf

B

K

mKT

xKT

Solubility

TTR

Hx fusB

11ln

*

Solutes with high melting points and large enthalpies of melting have low solubilities at normal temperature.

Two component liquid Systems

ABAB

BAAA

BBAABA

BBB

AAA

xppp

pxpxp

pxpxppp

pxp

pxp

*

*

*

*

)1(

F=C-P+2 F=4-P

Maximum degree of freedom = 3

Temperature, pressure and composition.

ABAA

BA

ABAA

BAA

AABAAABA

ABAB

AAA

AA

yppp

ppp

yppp

pyx

yxpppxpy

xppp

pxy

p

py

Q. One mole of benzene is mixed with two moles of toluene. At 60 C , the vapor pressure of benzene and toluene are 51.3 and 18.5 kPa, respectively. (a) As the pressure is reduced, at what pressure will boiling begin? (b) What will be the composition of the first bubble of vapor?

581.0

4.29

p

py

kPaxpxpp

AA

BBAA