Vapour pressures and enthalpy of vaporization of L-alkanols in terms of associated mixtures models.

53

Fluid Phase Equilibria, 27 (1986) 53-60

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

VAPDllR PRESSURES AND ENTHALPY OF VAPORIZATION OF I-ALKANOLS

IN TERMS OF

ASSOCIATED MIXTIJRES MODELS.

M.Rogalski(l)

and

(1) Laboratoire 132PR (2)

A.Treszczanowicz(2)

de Chimie

Faculte

Physique,

des

Sciences

de

Luminy,

9 (France)

Marseille

Institute

of

Physical

Chemistry,

Warsaw

presents

a correlation

(Poland)

ABSTRACT This the

article

term

of

the

tion

describing

a chemical

Clapeyron

were

equation.

determined

Prediction

of

of

vapour

contribution The

enthalpy

independently

vapour

pressures

the

First

International

the

method

is

of

and

pressures

included

the

into

entropy

from

l-alkanol-n-alkane

I-alkanols

using

of

of

I-alksnols

when

the

integrated

form

hydrogen

bond

mixtures

a concept

of

forma-

properties.

the

homomorph

is

discussed.

INTRJ-JDUCTION During presented alkanols heat

and

with

the

use

obtained

extrapolation series

IUPAC Workshop

correlation

Results

homologous as

n-alkanes

capacity).

pressure

of

and (Rogalski,

for

in

of

subatmospheric

of

thermal

proved

the

(enthalpy

usefulness

of

of vapour

The

basic

last

vapour

data

representation

19R4,19PS).

Zaborow,

year

of

this

of

of

l-

vaporization,

method

pressures

equation

we have

pressures

for in

this

low

a given

method

are

follows: T

h(p/q,)

=

lw/RT2dT

(1)

r, w

q

wo+(dw/dT)o(T-To)

= (dw/dT),

where

w = AH,,/AZ, o and

(3)

dw/dT

q

b denote

and AC, ere

respectively

the

vapour

liquid

heat

calculated

for

(dw/dTJo

were

0378-3812/86/$03.50

AC,/AZ

-

wdln(AZ)/dT,

respectively

AH,

and

(2)

+ f(T)

dw/dT

subscripts

+jf(T)dT k

the

Tz298.15

enthelpy

capocities each

compound

of at

AZ = (Vg-V’)p/RT K and

boiling

vaporization the

from

saturation experimental

0 1986 Elsevier Science Publishers B.V.

and

point

and

the

where

conditions. difference

conditions.

AH, and (A$),

of w.

and data

54 (A$

is

the

difference

Tsonopoulos

method

gas

nonideality.

are

presented

values f(T)

of

in

5 Xl (Tb)

X2

=

which

of are

and using

and AZ due to

the

not

chain

the

length

stable

liquid

and at To

by extrapolation.

(4)

x?(Tb)

(6) xi

ssure

all

of

alkanes boiling slkanols

determined

by the

Parameters

Xi result

considered

members

eq.(l)

calculates

temperature).

This

is

gives

data

standard deviation data

degree

function observed

the

incompatibility

data

for

hiqher

-

to

systematic

errors

-

to

the

introduced data

as long

accuracy

verified.

temperature be no more hol-s. would

for

valid.

for

be also

that

in

n-alkanes similar

pressures

used

this

to

this

of in

two

times

sets

more

lthan

of vapour

experimental

pre-

dispersion

respectively

calculations

data

of

linear

(in

this

problem to

not

in

we have

in Tb

fact

thermal

reliable these

alcohols

and the

f(T)

in

not

(4)

may

in the eq.(l)

eq.(2) of

data

influence

vaporization

correlation

is

relation

introduced of

results

dsta

and thermal

liquid

enthalpy

function

resulting

of

confirmed

vaporization the

for

were

sccurscy

occuring

of

obtained

of

for

1-slkanols;

is

phenomena

the

the

can be due

of

enthalpy

case

of

accuracy

eq.(4-6).

correctness

and that

deviation

function correlation

is

and thermal

The analysis

contribution

standard

separate

the

preto n-

by extrapolation);

1-alksnols

the

than

a given

Applied

experimental

which

of

I-alkanols

model,

To elucidate chemical

of

the

kPa, fit

pressures

by the

model of

to

xl and x2 are

obtsined

vapour

(1970).

as the

more

with

of

of vapour

series.

The analogous

the

case

vapour

Association

We expect found

of

dependence

describing

this

l/Tb).

were

and Sprake

possible

in of

I-alkanols

pressure

Ambrose

this

in the case

to

errors

times

(in

data fit

and quadratic

close

from

and three

and third

very

s(p)=n.n34

pressure

A disagreement

pressures

deviation

to eq.(l)

homologous

linear

resulting

data

pressure

simultaneous

in calculations.

used

vapour

term

vapour

result

vapour

a given

respectively

pressure

of from

and x2 are

standard

Vapour

of

fit

kPa (xl

vapour

ssure

are

(n=5-16)

s(p)=fl.Oln

of

obtained

and liquid)

(AC,),

as functions

I. For compounds

were

gas to

(5)

to eq.(l).

-

ideal

+ x2(T2-T2)0

compound

the

of

a cont.ribution

correlated

the Appendix

Parameters

the

capacities

compute

were

w. and (dw/dT),

xl

heat to

Results

= xl.(T-To)

the

of (1973)

of

would vapour

a

alco-

approach pressures

n-alkanes.

PROPOSE@METHOD Gibbs the

Gibbs

chemical

free free

energy energy

equilibrium:

of

pure of

the

associated monomer

compound and of

the

may be considered contribution

as

the

resulting

sum of

from

55

G=G

If

monomer

one

approximates G* eq.(7)

rbon G

G*

I

from

vapour

in

this the

as

Gibbs

free

energy

of

a homomorphous

hydroca-

follows:

calculated of

way

the

associating

hydroxyl

homomorph

group. by the

be preferable

as

defi.nition

applied

the

es

in

same

structure.

This

is

why Weimer the

can

should

Wsals

n* carbon

(1965)

molar

volume

defined

as group

utilize

the

the

simple

a hydrocareplacing properties would

definition

volumes.

who as

using

methyl

and Prausnitz

der

Van

be

the

1983; deteBrandsni

Prausnitz

Huyskens

with

homomorph

the

(Huyskens,

compound.

having

the

I-elksnols

parameters

and

alkanol

of

eq.(8)

a homomorphous

the

having

of

of

Association

of

terms

a hydrocarbon

base

homomorph

an

association

by Weimer

s similar

that

structure

association.

when

homomorph

ss

considered

The

of

proposed

a hydrocarbon

well

the

1984).

definition as

as

as

a similar

unaffected

on the

of

on the

Buchowski,

concept

arguments

having

psrameters

compounds

and

depend

species,

structural

pure

Ksiazczak

homomorph

defined

the

written

authors

19R3;

adopted

rbon

be

pressure

Erendani,

have

by the

Gmonomer

can

several

rmined

(7)

Gas,

+

Recently

n

GfIss

+

If

we consider

atoms

* = “alksnol

the

Huyskens

(in

terms

into

the

Van der

expression

eq.(2),the ntly.

interpretation

of

the

This

concepts

calculated

using

Kehiaian

mixing

and

and

Treszczanowicz

-Ahh;;(l

q

-

K = exp(l

-

As0

= Asi

- Rln(rJ

and

Ah;

given

(Ah;

= -2Q400

by the

ratio

Simple

thermodynamic

12 the

expressions

look

for

of

homomorph.The

the

athermal

association

and k

of

(1985). of

the “the

Weimer .44.

q

determined

best”

values

of

the

of

vapour

parameters of

to

contribution

was

presented

from

with

expression

verify

term type

determined

I-alkanols

resulting

pressure independe-

k and

Mecke-Kempter

with

concept

we introduce

of

mixtures

The

Prausnitz study

parameters

chemical

vaporization

and

In our

dependence

model

(1970)

capacity

enthalpy

ln(l

with

to

Rogalski

the

term

allows

heat

and to

gives

temperature

Treszczsnowicz

excess

contribution

Hass where

the

k = 1

volumes)

contribution

approach

in

results

Waals

describing

chemical

different

by

(9)

+ k

heat

of

n-alkanes

for

the

by

chemical

is:

(IO)

+ K)/K)

- T&‘)/RT)

(11)

(12)

J mol-’

of

i AsH’ -

Ven der

Waals

considerations giving

chemicsl

-50.7

J K-l

volume alow

of to

contributions

mol-1;

r

the

alkanol

formulate to

is

the and

on the the

heat

number

of

segments

of

methane.

basis

of

capacity

of

eqs

and

lo-

Gibbs

56 free

use of

W

o

of slksnols

energy

1985).

(as was

The proposed

method

wo,

and f(T).

of

(dw/dt),

two contributions,

shown

by Treszczsnowicz

eq.(l-3),for All

calculation

these

homomorphic

end

end

of

quantities

Treszczsnowicz,

vapour

pressures

can be represented

makes

by the

sum

chemical.

* ass w. + w.

q

(dw/dT),

f(T)

(dw/dT);

q

= f*(T)

where

(13)

wssa

+

(14)

(dw/dT)E=

+ fess(T) q

(15)

-H,s,/AZ

TARLE I Different using I

cases

of

correlation

end (dw/dT),

calculated

and prediction

of

vapour

from

f(T)

pressures

w.

found

pressure

eq.(A?)-(Al2) II

f(T) ss

in

I

as in

III

I

f*(T)

o

(dw/dT), w. as

found

from

of

as

+

calculated

from

n-alksnes,

w calculated

table

I sre

of to

from

vapour eq.(l)

f(T) for

eq.(A7)-(A8)

n-slkanes

as III

from eq.(17)

shown

In

of of

the this The

(dw/dT)E" (dw/dT),

eq.(A4)-(A6)

variant

correlation.

1-alkapols.

fit

as III

= (dw/dT);

fit

the

in I

(dw/dT),

objective

vapour

to eq.(l)

I-slksnols

calculated

in IV

The first the

from w. for

(dw/dT+

for

In

of

and (A7)

eq.(AS)

VI

fit

=w;+

w.SSS * w. calculated

W

the

f*(T)+fass(T)

q

f*(T)

from

n-alkanes,

V

1-alksnols

of 1-alkanols

pressure

IV

of

eq.Cl)

using

different

second

vapour

function

to

one

the

f*(T)

is

pressure

of

previously

pressures

calculation

vapour

possibilities

corresponds the

the

of should

function

1-alkanols improve

carrying

published

homomorphic

to

of

the

to

out

homomorph

the

computations.

(Rogslski, f*(T)

es.(l)

vapour

be in principle

the

is with

pressure close

to

1984,1985) determined eq.(l5). correlation the

one

by The of

found

57

58 previously rent

for

n-slkenes

predictions

vspour

case

III

concept.

In the

the

as utilized

same

in

V vapour

,eq.(A3)

of

pressure

rmstions

concerning

a rouqh

test

of

only

of

the

Appendix

of

I-alkanols

function

I end

in

of

pressures II.

I-alkanols

alcohols.

validity

f(T)

In the

The cases on the

is

III-V

base

predicted,

case

of

without

obtained

in

diffe-

homomorph

are

are

predicted

and

any experimental. III-V

points

the homomorph concept

give the

w. and (dw/dT),

IV w. and f(T)

are predicted

Results

of

I.

in the

can

info-

constitute

homologous

series

of

3 -alkanols. RESULTS The main numbers Table

results

in each

I.

Two first

taneous

fit

eq.(l).

of

from

clear

for

for value the

of

s(p). for

value

lower

present

approach

ssure

no

of

the

capacity

that

the

ctions

are

lower

of

quite

added

(case f(T)

It

the

wss

of for

volume results

observed

f*(T)

for

the

k-0.34.

the

with

In the

homomorph. the

higher

It

(5)-

parameters for

of

eqs

Thus

the

representation

difference

predi-

between It

was

vaporization

predi-

value

of

The value

obtained

using

the

(case

1-alkanols of are

k gives Waals

previously f*(T),

independent prediction

Van der

the

clearly

k

volume calculsgives

results

chain

for of

III),

the

the

found

cent.

For higher

pre-

of

this

of

true

of vapour Results

of

to

into

is

7 per

value

when a correction I-slkanols,the

(AsJo

due term

f*(T),eqs

reported.

As was stated

predicted

probably

results

the

to

pressure

chemical

model

also

devia-

about

of

to the value

up to l-pentanol. that

of

standard

n-alkanes.

and enthalpies

case

deviation

close of

pressures

are

average

of vapour

concept.

and of

(A$),

the

n-alkanes.

show

s(p)

corresponds

function

the

homomorph

(AHJ~

as

are

of

of

that

the

for

III-V

forms

may be observed

I-alkanols

partially

and liquid

vapour

way is

pressure

only

vaporization gas

the

series

obtained

two

in

simul-

very

fits of

and higher ones

The cases using

a systematic

in this

to

of

ideal

obtained

vapour

improve

I-slkanols

results

acceptable

worse. is

of

calculate

tion

to

the

the

deviation

the

ethanol

of

homolgous

to

kPa which

the separate with

l-octsnol to

l-alkanols.

enthalpy

I-alkenols

determined to

of

best

For

0.017

The

is

disregarded,

parameters

the

from

as large

The introduction

of

for

similar of

from

It

twice

is

II.

described

The improvement

ethanol.

are

l-alkanols

Table

standard

series.

than

Difficulties

values

allows

the

more

resulting

found

more

pressure

heat

ones

resulting

considered

excepting

is

properties.

in

ones

prediction

ction

series

in cases

in eq.(l),the

all

and I-dodecanol

l-alkanols.

are

vapour

the

s(p)

1-alkanols

included

s(p)

s(p)

thermal

the

(5)-(h) of

of

result

to

for

is

all

presented

to different

deviations

kPa for

alcohols.

in

should

only

of

remaining

particular

(h),close

of

term

When ethanol

uncertainties eq.(l)

pressures

are

correspond

show standard

members

the

performed

Table

and I-dodecanol

s(p) of

raws chemical

lower

average

data

this

Cl.034 kPa to n.024

ethanol

tion

calculations

vapour

When the

falls

of

row of

are

lenght, improved

III-I) = fass(T)

+ f*(T)

+ 0.115m(T-To)

n
m=fl

n>8

m=l.

(16)

59 This

correction

only

a compensation

enthalpy

of

ethanol

significant of

for

It

higher

homomorph of

is

not

a good

vaporizatiop

of

enthelpies

of

IV).

stated

from

tion

of

from

experimental

vapour

(A$),

and of

vapour

errors

mol -3

is

enough

all

and model

to

II,(VI),are

W

= RT2dln(P*)/dT

Results ding

directly

obtained we can

caution.

+

value

much

improved. the

case.

pressure vapour

other

pressure

of

is

of

order

this

(V-4)

is

(A$)o of

error

end of

when

the

subtracted (&$)o

of

the

At the

prediction

pressures

depredic-

function,experime-

hand

prediction.

the vspour

this

error

On the

and

experimental

of

The prediction

A systematic

this

the with

in the poor

prediction of

that

pressure

with

also

complexity

vaporiza-

systematically

5 J K-’ mol-1

the

from

the

5 J K-l is

the

large table

function

f(T)

homomorph

Hass/AZ

in this

say

good

of

from

that

(17) especially

way, the

When vapour

predicted

due to

vapour

results

not the

calculated

agreement (Ac;)~

considered,

point in

fair

which

s constant

is

results

shown

calculated

If

in

vapour

pressures

predicted

V-3)

imperfections.

deteriorate

is

(case

Vapour

of

suggested

of

is of

deviations

enthalpies

may be

prediction

it

l-slkenols

important

the it

that

prediction for

more

case

the

are

(V-2)

acceptable

this

for

of

satisfactory

discuss

1-alkanols.

I-alkanols

delicate

rather

model

(V-l).

the

pressures

a very

in

previously

values

Results

very to

vaporization

pressures

for

certainly ntal

As was

IV and V proving

Nevertheless

higher

data viate

are

beacause

predicted (case

IV-l)

III,

errors.

difficult

by extrapolation.

concept

enthalpy

is

slcohols

obtained

cases

systematic

(case

I-octanol.

were

in the

some

vaporization

to

observed tion

is

pressures

results

for

homomorph

lower

l-alkanols,

concept

is

useful1

or parameters

of

association

can be expected

for

lower

are

when

it

poor. is

models

Conclu-

used are

with to

be

l-alksnols.

REFERENCES D. and Sprake,

Ambrose,

1970,

C.,

Brandsni,

V.,

1983,

Fluid

Huyskens,

P.,

1983,

J.Moleculer

Kehiaian,H.snd

Phase

Equilib.,

12,

Struct.,

2,

631.

87.

100,

403.

Treszczanowicz,A.,197O,Bull.Acad.Polon.Sci.,Ser.Sci.Chim.,l8,693.

Ksiazczek,

A. end Buchowski,

Rogslski,

M.,

Vapour-Liqud Rogelski,

J.Chem.Thermodyn.,

lRA4,

paper

Equilibria

M.,

1985,

Treszczanowicz,A.

H.,

1984,

Fluid

presented

at

Phsse

the

in I-Alkanol-n-Alkane

Thermochim.

Acta,

and Rogalski,M.,

90, 19R5,

Equilib.,

First

16,

353.

International

Mixtures,

Zaborow,

Workshop

on

1984.

125. Bull.Acad.Polon.Sci.,Ser.Sci.Chim.,

in

press. Treszczanowicz, for

A. and Treszczanowicz,

T.,

3985,

Fluid

Phase

Equilib.,

publication.

Tsonopoulos Weimer,

, C.,

1074,

R. and Prsusnitz,

Am.Inst.Chem.Eng. J.,

1965,

J.,

Hydrocarbon

20,

263.

Proc.,

44 (9)

237.

submitted

60

APPENDIX In

I

this

appendix

calculate

the

of

(dw/dT),

where

(Ac,/AZ

q

dh and

dc

parameters and

are

are f(T)

for

reported

which

n-alkanes

and

are

necessary

to

I-alkanols.

- dh

(Al)

- w dln(AZ)/dT)o

= (A$),

contributions

- dc

resulting

from

(A21

real

gas

properties.

n-alkanes

(Al(,),

= 1.892

+ 4.953n

(AC;),

= -18.8

- 4.76n

dh = -4486.

-6n.h

Xl

=

-0.9114

+ n.34341

X2

=

0.25A57

ln-*

for

n > IIl

for

I-alkanols = 33.16Il

(AC;),

= -2A.n

dh = -774.2

lo-3Tb

lo_4

for

q

dc

(A41

J mol-l J mol-1

(A51

K-l

+ 0.24239

(~6)

(A7)

10-5T;

(A8)

KJ mol-’

J mol-’

-

(A91

K-l

17.2381~~

(AlO)

3 mol-1

(All)

J 11101-l K-1

101

x2 = 0.755565

K-l

= 0

+ b.6771n

+ 0.985n

J mol-’

1-l.41244 10-5Tb

+ 233.77n

dh

0.137n2

n.5A93n2

-9.4Rn

= -0.5on376

n > R

-

dh = dc

(Atlv)o

dc = -7.4

-

(A31

mol-’

51.5n2

-

q

+ ll.Rn

kJ

-

+ 957.39n

dc

xl

and w,,(dw/dT)o

(AH,/AZ),= (AH,),

w. =

for

functions

values

+n.fl5707

(Al*)

+ &RR16 lOlT,l

q

0

(A13)

10-3Tb

-

0.462673

104T,*

+

O.R51375

106Ti3

(A141