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Infinite dilution activity coefficients of ethanol-n-alkanes mixtures
103
Fluid Phase Equilibria, 27 (1986) 103-118 Elsevier Science Publishers B.V.. Amsterdam - Printed in The Netherlands
INFINITE
DILUTION
COEFFICIENTS
ACTIVITY
OF
ETHANOL-n-ALKfANES
MIXTURES L. .
CX3li1’and
Mont.edi
c Italv
pe
F:‘. DELUG!I’
Research
Centrc,
Via
San
F’iett-0
56,
Boll
ate,
Mi 1 an
).
Infinite ethanol
dilution
a.cti.vity
coefficients
o.f
the
system
formed
o .+ funct.j.on n--al kanec, have been measured as a and tempera.t.ure by a yas sir-ippj ng method. Li near dependence5 c!-f’ .the i n have been found ,for al 1 systems studied In y (D on temperature the 1 imj t a+ the e::pet-imental errors. Regular trends along thtn--*l.l.anes homologue series have been observed. Gibbs ex tees The paraxeters of the most popular models of en?rqy have been 0bt.a.i ned. They allowed the predi.ct.ion of vapo~w-3 ~.quid equil ibria of the systems studied. The comparison between cal.c~~lat~?d and experj.menta.1 data taken from the literature showed i..I/ ?i:t t.he four parameters Wilson model is at the moment tlie b e E-,1.. model for thc35x Eyst.ems, becac!E;e it is able to describe at %.l-lE:! z’iam~+ time the depende.nce of ym on temperature and composi 1:ion.
by
I
Nl’F?m.NJCT IC!N
5q’l t.e In thermodynamics A cnrrc?ct vnsal ved.
o+ of
descr
thi? qt-eat: number alcc!hols-.hydr-ocal-bons :I pti. on
cl+ sLlc:h
of
rzystwms
studi es solut.ions, must.
st i 11
devoted to probl.em the be
c3nai
.I:. h E’
o-f der t+c.i
i_t\*:> nature o-f alcohol. 5 severe1 y tries mol ecu1 ar i.nterractj on t he I j cp.1.i CA at.. their crapabi 1 i t.y tn .f or m mu 1 t i I:!1.~5 pal. +.ri ty and hydrugsn bonds make inadequate t.tle “physical ” thenries; t-he pur CI ar e a I.S!L) chwn1 cal thec.ir i ec t I7e i r more simple form j. n r e z1.1. :i ncuf.ficiw-+t.. INi.x ed thee-it5 sAuca.1 d better drzcri, be the behavi our , a~, they take into account both chemical. and phyelca.11. iI~i.:eracticws. tk!\ler-the1 ~!z-E not even t. her;c theorj e5 can cot-rec_t_l y r eprc~wnt, the who1.e set of experxmerltal obrervatj enc. ‘Thr ) j. 5 normal :t.y iL!dUEL.d qnodneac, of a theory ( or of a model When the par *met c’rci by 1 ts al;i lity tn fit t.he expel-j mental de1t.a. 1.2 -E d model da.t..a 1.15c?d t. c:> are dw-i vcd irnm t.he Sd”w! ~,tF”_‘l-irnerlt~aI what we real1.y test ic it.s dcrcti 1 i .ky mc.crc? tec,t the model itself, t h,ari zta agreement. t.o ttle physi.cu; of the phenomenon. A poly nutni $1. t he ~ec)l.rat i Clr, c3.f 5ui t.ahl e ab1.e tc1 fit degree ma \y be “H3l-e e 3 p e r i ,”C.! n t ill 1:t 15 i_.h E! dr1.a t I-Ian P f wdwment.al phyci cal model . a,-,i , c1se t. o “When consi.der inq the ~~a.1idit.y of ci t.e f:)l--au5r:l t.z : (4t_,&a? I_b,0.2 1 t II’ tIiE!ot-y o-f 501. ~4i.i onEi ii. ic; more impnrtclnt to incl!.!ire 5’c1 ;;,, + :I not based or, it cari be supported by evi dencec, I..1,&I;.,, L.!:’ pl~ysi cochemi c:.al. properties. ‘1he v b 1.I clj. t: y Cl:: iin j ;lQ-e<..‘l’,“, : I.. i.f it. can tcE> <.hc:,iw 1 o t!!:$ i r, 5 o 1 I..., t i on s iE: mluch enhanced (c;$2IA i. t i !:at:+ .!.i.~j. 1) nj 1-h obr;ervnd physi c:a:l. pr r:~pc=~ t..i r’~.: ~4..t ,t:!I 1.I 1;:tr) i..h ci5 +I’c. e::
The
i st i rly thew 5.t.at.c2; their
0378-3812/86/$03.50
chemj
j. es,
cal.
cm the
0 1986 Elsevier Science Publishers B.V.
104
105
106 TABLE
I
Experimental activity system ethanci-n-altane.
coefficients
at infinite
dilution
for
_--___---__--___--_~~--~~~-~~~~--~~~~~~~~~~~_~~~~_--~~_-~~__~~~__ ALKANE
T/C
y”
Tl C
Ym
ETUANOL ALWANE _---__--___-____-_______________________________________________
n-pentane
36.5 37.0 50.5 b5.5 $6.0
47.0 49.5 33.0 21.0 23.0
26.5 31.0 37.2 39.0 40.0 49.0 51.5 62.0 69.0 79.2 El.0 81.2
8.9 ?.1 8.7 0.6 8.5 8.3 8.3 8.2 7.8 7.0 b.? 7.4
n-hexaoe
24.0 24.2 24.5 43.4 45.5 io. 8 bO.8 78.3 78.4
62.6 58.2 59.4 37.6 35.4 22.4 21.9 14.7 1488
47.0 81.0
ID.0 8.7
n-heptane
41.4 41.3 59.0 76.4 lb.4 93.6
34.6 36.3 23.2 14.6 15.1 9.8
49.b 64.5 81.b
1280 11.2 lb.P
49.0 b4.0 RD.5
14.5 13.1 13.0
27.9 47.7 47.7 82.0
20.8 IV. 8 18.9 15.5
n-octane
n-mane
22.9 22.9 29.2 39.2 39.1 41.8 42.3 so. 5 50.5 AD.! 6O.U 82.3 82.3
50. ? 51.7 42.4 32.3 32.6 30.4 30.4 24.2 23.8 18.6 lB,B 11.5 11.4
n-decane
33.2 48.2 65.5 84.3
37.5 25.5 15.9 ID.9
the
107 6
ETHANOL
0
10
20
-
JO
TEMPERATURE
c
nPENTANE
40
50
‘C
60 10 80 90 100
( Scale:
l/T
140 K J
ETHANOL
-
“OCTANE
ETHANOL
-
.OECANE
t
120
TEMPERATURE
‘C
I Scale:
l/l
K 1
108 to operate at temperature even higher than the That al 1 ow5 the Moreover t. h (2 normal bailing point of solvent. evaporation rate of the solvent can be controlled. the more the gas stripping technique only the y m of 2) By Luckjly, in can be easi 1 y measured. volatile component minimum azreotropic systems, 1iL:e ethanol-n al kanes, the more volatile component is alwa_ys that at high dilution. In t.1-1at ccw be obtained by the same technique. case bot.h the y o 5) The accuracy afforded by out- apparatus was Uy = 0.5 in the experimental range. The accuracies of the measured variables were: up = 1 mmHg , (I D - 4.0 ml. ./h, (IT =0,5 “C. Tt,e reprodcrcibi 1 i ty of the measures wac at worst f5i: of the mCari val ur.
RESCJLTS The obtained resultc, r7re shown in table I. Rlong the series o.i n-al i::anes C5-Cl0 only the activity coefficients of ethanol in Doctane were not measured at ~711, whi 1 e mcas~tr ement of y m of n -decane in ethanol were unsuccessful 1y because of the tried limits of our g;?c,c~,rornatoRraphic detector. Figure 2 shows how In y o varies with 1iT; it allowLl t he thr?& compar i 501, wi t h the few data found in the literature OrI systems (hlessi and k::ikic, 1985 ). The compari sun I ookrj quite good when the hydrocarbon is; the z.ia1ut.e; when ethanol i 5 the c D 1 1.1 te the Ii terature values are lower then those measured in this WOI-I.:. Howeverthe data from the li.terat.ure are qc!ite spread and the) don ‘t af ,Ford a reyul car t.rcnd al.onq the homnl,oque Eeries. Owing to t.he I inear dependence o-f: lrl y m on 1.11. ra-f t.he d3t.a eactf s,,stem have been linearly inter-palat.ed. Table 11 ShoGJL- 1.h~’ i,i and F . par amct er-ci of t.he eq1.rat.i en
I
C1 i
In ri* r Ai+Bi/T
obtained for- every c,yst.em. The sjtraiqht lines chown in fis. have been cal c~1.1ated with the parameter 5 of that table. The 51 ape D i is di.rectly related to the heat. of dilc!ti,orl
ethanol 17y d r UC C!r b on
_ _._. -- . ....___.--...-..-
hydror,srbnn
..__ - ..._.- ..._.
_..... _......_.__. _._.._. ___-_....__
‘2 at
109 Ini-inite dilution mear,w-emcnts n+
Lf the
usually enthalpy
Xt is
.
excecs Li”
=lim
experimental. val ue!s The system UC ihc c: c:,mp c 5 i t..i ~7n 5 sseqvat I on 1 i I..:e the I Rc!qal 51: i. , I.977 1 eqc!a?: i nn
=
o-f
from the
calorimet.ric equation (. 7; , .
dXi
measured nf: hE a,- e i nterpol atcd Symmetrical ! sc!m ci f
mWLxlg2 :I
obtained means
SF_
If0
$
hy
5 + ( wL
at by
1
di+feren-t e,icI,t.abl e Functi ens>
, .a 1 -:a
VL’2
2 )
?
O.F.
=
NEXPl r i-1
GXP
-YPjl&
2
NEXPL 4.
2 i-1
"&XP
OD - ‘2iCAL
I2
i. :‘, )
113
In
I,==
cl2
In
yzBe
c21
(6)
results That dependence
in of
a
1 inear
parameters
Cl2
C1, vs temperature, in and agreement with the theory of equation I F’rausni t.z , t hc Ii i I.969 ). The ~ i and shown in table II qive directly t.he dependence of C:ii The on temperature. prediction of the dependence activity Of the coefficient5 nn composi. t i on is very good. Fnr t.he not system ethanol --n-heptane the Ei bbs energy of mixing ha2 calculated following been the rel ati ens:
FIG. 4. Ethanol-n-hcptane system at ‘T=40°C. Gibbs energy 0.f mixinq computed by Van Laar model.
(7)
,-Al3 RT
id
ciE obtained
which
doesn
cw-ve,
‘t
actual
k!.i.I.z!E _es..~!tAx!,
x, In '1 +
(9)
12x1 4 C2? “2
shown in 1 y ex i St.
fiq.
At. infinite In
"2 'nx?
Cl2 c21 Xl ‘2
RTCC The
L
4
4,
predict
djlution
81 -In Aii--Aii
it
is
a miscibility
( Wilson,
gap
1964
)
i : 1.2
j : 2.1
where
*xp(_$)
n&i “i
! 11)
1 /T impossible t.o deecribe the dependence It is of lnym vsi with this equation by I_eeping A i .i ‘5 independent of ten!perat.ure,. Neverthel err, 5 I. i near dependence on T t..h e a reproduces experimental data wj thin the experimental error, 5 shc!ws as f1.q. for the system ethanol-n-pental-le. Table IV q i vec5 i.tlc= kJi 1 son o_i I‘ constants der i ved from experimental data for all ttle systems studied. s);ct.amci ‘The VLE for ethanol s-n-l>exane, n-heptane and n-nnnane ha ;e been calculated at the same temperature where e:.:perl merlt.al cwd5 ) C3at.a Table IV rtlew5 the root rne~n 5quare are available.
tht? ac:t.i vity relation5
cnwff
icients
0
71
=
K+l
=
K+l K
(D
y2
derivat.i
\‘es
on
di 1ut.i on
temper-atc.lre bin 70D K 1 =I-bu / T ) K+l ilInyT W/T
1
1
Ah R Ah
=-K+l
R
are
ylvcn
bit
c.he
113
gE=LIE +gEthem phyr
1)
1:t 5~iOUlCl ,,,clr-f? accI..lr-at.e1> describe t.he dependence 04 ~2E over any t il E’ -F1.11 1 r a 1-1 gc 0.f composj t i an. It 5hfml dn : C prrdi ct. VL f.: d d t. ir ‘I m.i.5 c i t2i 1 i t..f it z.h cx! I.d i rnpr exe t. he! f i t. 04: g t\p j avoiding !systemat.ic: trnndr, 0.1 error5 with composit.ion.
114 c’)
L
predict the correct dependence 0i: I II y a nn rhoul d 1.t e qu i 1.i. h I_1.um throuqh that of t-he associat.ion temperatcrre of: temperature in place the ar-hitrar-,constar7t.s on param~l.ere on ‘17. I. inear dependence of physical. interaction has (3 paramet..wE3 ct:: “, ) A 11* < l-he model of: Nath and Drnder
1::: *“, , AhAm , AI.,:~ , duo,, pas-arnet:.et-s can be estimated
, Au;,,
, AL,;*
1: a ma:x~m.~mCT+: ;I
i 61 par wwters model , the binary assnci c&t-ion. Physi. cal y).
parameters par amciterc
‘i *i-e al I. physxcitl. r7re est.imat.ed .f’rarri
.From
the val ues and i r-om t.hk?1 I-. so , it 1s necessary tc3 f:j.:: 3 pr1.cwa dependence on t.emperature. d I-, 4 ‘S_r we,-p Ii; ‘=._ and t: h E! vi\1 c!es of at. l.east 4 paramet.et-s. arid IWI~W, 1’7t?l i, i I obtained .i:rom the proper-Ci,es of pure A i Nath F’r~r t.he other b par amrt er r, WE:have t I- i ed t tie f:ol I ow3 ng clloi cfzfc :.
nn crossed
TkBLE IV Yilson node1parametersfor ethanol Ill-n-alkane (21 aysters
n-dkane
Parametersfron this work i calicole
42
cal /sole
n-pentane n-hexane n-heptane
2757.2 2b99.2
n-nonane
A0 32 21 cal/nolei°C caliaale
Cwparisonnith data frost the literattire
i Gr cal/mole/°C
343.24 363.96
-0.8421 -G.X%
273b.b
-9.986 -9.512 -10.025
457.56
-0.3723
2681.8
-9.221
579.lb
-0.0256
Refwences
T/Y
RI6 on y RHC; on P lLPai
Janaszewskl1982 Janaszewsii1982 Rerro 1982 Berm 1982
40 40 70 76
O.OiiS4 0.0055 0,0109 o.co25
3.4E: c.23 z.01 7.39
115
> c c.2 <
-
ETHANOi
-
nHEPTANE
8 0
IO
20
30
40
50
TEMPERATURE
F1.G.
7.
Effect of temperature coeff icier-its for the between c::perj,mental model
nlodel
5. val
uez.:
(-)
C
60 70 80 90 100
( Scale:
on the infinite ethanol ---n--hcptane a~ld romputed model a;
by (-a-*-)
140
K 1
dilution system. Mal:h and modal
activity Cornpat-i E.O~ Ecender b; C....)
c.
0.m
X
FIG ” 8.
120
l/T
\‘LE predi.ction Nsth and b ; C----J
Render model.
.For ethanol models: C.
1
ETHANOL
--n-heptane !-_)
model
system a;
at
(----_)
4Cf’C
by
model.
116 CUICLUS
1 ONS
allow a. strict te~.t 05 the gE data shown in this paper No clf’,e systems ethanol --,r~-..,alkarres. ity to represent the a t: t hE’ 5<3”,E tj me used Cli-l predict normal 1 y I C The assnci .t.“~~~ and compocl ti on. of y ’ or3 temperatLu-e 1:h (L’ bctC aC tt1e moment iurt.her, model 5 s,cem to be wotrt,h worki.ng parameter:: model q wJ.t h .fit5 lrii 1 cion t!eat: are obtained by the The set_ o.(’ data obt.a.ined ic: dependent, on temperature. 1 inenrly anti it allows the eval uirtinn of the behax/iotr! cp1 te homogcncou~, I ti c OLII. d be t a 1..en P s> iz, ~3I.on !:I tli v home! 1 ng~lk3 se,. i e6 of n--it 1 kan ~3. !ztart.inq point For. <:ur-ther improvements on the exiE.t.1 nq tnodc?.Is. The new mndels abll o -f t: hnsc dependence
117 non arsscjci ati c:~~~c.~ssc-cl a5snci
. E
M i ci 0
ng
cumpanent
at i on
at infinite dilution e:.:c.c5s f:unction mi ): i nq j. d a a 1 Cemperature t.emperakwe
independent dependent
term term
118 ki., Leroj q J.C., Masson, J.C., Fabriee, J.F., Muacurcment 0.f Activity Coefficjents 1.977. fkcurate dilution by Inert Eae Strippinq and Gas Chramat.ography. lncl. Eny. Chem. Process Des. Dev., I&: 13Y--144.
Renon,
Rngal ski 1: 137.
Ynung,
,
C.L.,
W.
,
Ma1annwski
1868.
Chromatag.
,
5. ,
Rev.,
1977.
Flcti cl Phase
Sanni
er,
at.
Infini
I#.
,,
tt2
Equi 1.i. bri 3,
1f.l:129.
Wi 15on , G.M., 1964. Vapaur,-Li quid expt-esfion Tut- the exce55 .ft-ee energy of 80: 1L‘27- 1 :;o _ J . Am. Chem. Sot.
Eqctil ibrictm mir:incj.
XI.
F,
r,F O&J
Fluid Phase Equilibria, 27 (1986) 103-118 Elsevier Science Publishers B.V.. Amsterdam - Printed in The Netherlands
INFINITE
DILUTION
COEFFICIENTS
ACTIVITY
OF
ETHANOL-n-ALKfANES
MIXTURES L. .
CX3li1’and
Mont.edi
c Italv
pe
F:‘. DELUG!I’
Research
Centrc,
Via
San
F’iett-0
56,
Boll
ate,
Mi 1 an
).
Infinite ethanol
dilution
a.cti.vity
coefficients
o.f
the
system
formed
o .+ funct.j.on n--al kanec, have been measured as a and tempera.t.ure by a yas sir-ippj ng method. Li near dependence5 c!-f’ .the i n have been found ,for al 1 systems studied In y (D on temperature the 1 imj t a+ the e::pet-imental errors. Regular trends along thtn--*l.l.anes homologue series have been observed. Gibbs ex tees The paraxeters of the most popular models of en?rqy have been 0bt.a.i ned. They allowed the predi.ct.ion of vapo~w-3 ~.quid equil ibria of the systems studied. The comparison between cal.c~~lat~?d and experj.menta.1 data taken from the literature showed i..I/ ?i:t t.he four parameters Wilson model is at the moment tlie b e E-,1.. model for thc35x Eyst.ems, becac!E;e it is able to describe at %.l-lE:! z’iam~+ time the depende.nce of ym on temperature and composi 1:ion.
by
I
Nl’F?m.NJCT IC!N
5q’l t.e In thermodynamics A cnrrc?ct vnsal ved.
o+ of
descr
thi? qt-eat: number alcc!hols-.hydr-ocal-bons :I pti. on
cl+ sLlc:h
of
rzystwms
studi es solut.ions, must.
st i 11
devoted to probl.em the be
c3nai
.I:. h E’
o-f der t+c.i
i_t\*:> nature o-f alcohol. 5 severe1 y tries mol ecu1 ar i.nterractj on t he I j cp.1.i CA at.. their crapabi 1 i t.y tn .f or m mu 1 t i I:!1.~5 pal. +.ri ty and hydrugsn bonds make inadequate t.tle “physical ” thenries; t-he pur CI ar e a I.S!L) chwn1 cal thec.ir i ec t I7e i r more simple form j. n r e z1.1. :i ncuf.ficiw-+t.. INi.x ed thee-it5 sAuca.1 d better drzcri, be the behavi our , a~, they take into account both chemical. and phyelca.11. iI~i.:eracticws. tk!\ler-the1 ~!z-E not even t. her;c theorj e5 can cot-rec_t_l y r eprc~wnt, the who1.e set of experxmerltal obrervatj enc. ‘Thr ) j. 5 normal :t.y iL!dUEL.d qnodneac, of a theory ( or of a model When the par *met c’rci by 1 ts al;i lity tn fit t.he expel-j mental de1t.a. 1.2 -E d model da.t..a 1.15c?d t. c:> are dw-i vcd irnm t.he Sd”w! ~,tF”_‘l-irnerlt~aI what we real1.y test ic it.s dcrcti 1 i .ky mc.crc? tec,t the model itself, t h,ari zta agreement. t.o ttle physi.cu; of the phenomenon. A poly nutni $1. t he ~ec)l.rat i Clr, c3.f 5ui t.ahl e ab1.e tc1 fit degree ma \y be “H3l-e e 3 p e r i ,”C.! n t ill 1:t 15 i_.h E! dr1.a t I-Ian P f wdwment.al phyci cal model . a,-,i , c1se t. o “When consi.der inq the ~~a.1idit.y of ci t.e f:)l--au5r:l t.z : (4t_,&a? I_b,0.2 1 t II’ tIiE!ot-y o-f 501. ~4i.i onEi ii. ic; more impnrtclnt to incl!.!ire 5’c1 ;;,, + :I not based or, it cari be supported by evi dencec, I..1,&I;.,, L.!:’ pl~ysi cochemi c:.al. properties. ‘1he v b 1.I clj. t: y Cl:: iin j ;lQ-e<..‘l’,“, : I.. i.f it. can tcE> <.hc:,iw 1 o t!!:$ i r, 5 o 1 I..., t i on s iE: mluch enhanced (c;$2IA i. t i !:at:+ .!.i.~j. 1) nj 1-h obr;ervnd physi c:a:l. pr r:~pc=~ t..i r’~.: ~4..t ,t:!I 1.I 1;:tr) i..h ci5 +I’c. e::
The
i st i rly thew 5.t.at.c2; their
0378-3812/86/$03.50
chemj
j. es,
cal.
cm the
0 1986 Elsevier Science Publishers B.V.
104
105
106 TABLE
I
Experimental activity system ethanci-n-altane.
coefficients
at infinite
dilution
for
_--___---__--___--_~~--~~~-~~~~--~~~~~~~~~~~_~~~~_--~~_-~~__~~~__ ALKANE
T/C
y”
Tl C
Ym
ETUANOL ALWANE _---__--___-____-_______________________________________________
n-pentane
36.5 37.0 50.5 b5.5 $6.0
47.0 49.5 33.0 21.0 23.0
26.5 31.0 37.2 39.0 40.0 49.0 51.5 62.0 69.0 79.2 El.0 81.2
8.9 ?.1 8.7 0.6 8.5 8.3 8.3 8.2 7.8 7.0 b.? 7.4
n-hexaoe
24.0 24.2 24.5 43.4 45.5 io. 8 bO.8 78.3 78.4
62.6 58.2 59.4 37.6 35.4 22.4 21.9 14.7 1488
47.0 81.0
ID.0 8.7
n-heptane
41.4 41.3 59.0 76.4 lb.4 93.6
34.6 36.3 23.2 14.6 15.1 9.8
49.b 64.5 81.b
1280 11.2 lb.P
49.0 b4.0 RD.5
14.5 13.1 13.0
27.9 47.7 47.7 82.0
20.8 IV. 8 18.9 15.5
n-octane
n-mane
22.9 22.9 29.2 39.2 39.1 41.8 42.3 so. 5 50.5 AD.! 6O.U 82.3 82.3
50. ? 51.7 42.4 32.3 32.6 30.4 30.4 24.2 23.8 18.6 lB,B 11.5 11.4
n-decane
33.2 48.2 65.5 84.3
37.5 25.5 15.9 ID.9
the
107 6
ETHANOL
0
10
20
-
JO
TEMPERATURE
c
nPENTANE
40
50
‘C
60 10 80 90 100
( Scale:
l/T
140 K J
ETHANOL
-
“OCTANE
ETHANOL
-
.OECANE
t
120
TEMPERATURE
‘C
I Scale:
l/l
K 1
108 to operate at temperature even higher than the That al 1 ow5 the Moreover t. h (2 normal bailing point of solvent. evaporation rate of the solvent can be controlled. the more the gas stripping technique only the y m of 2) By Luckjly, in can be easi 1 y measured. volatile component minimum azreotropic systems, 1iL:e ethanol-n al kanes, the more volatile component is alwa_ys that at high dilution. In t.1-1at ccw be obtained by the same technique. case bot.h the y o 5) The accuracy afforded by out- apparatus was Uy = 0.5 in the experimental range. The accuracies of the measured variables were: up = 1 mmHg , (I D - 4.0 ml. ./h, (IT =0,5 “C. Tt,e reprodcrcibi 1 i ty of the measures wac at worst f5i: of the mCari val ur.
RESCJLTS The obtained resultc, r7re shown in table I. Rlong the series o.i n-al i::anes C5-Cl0 only the activity coefficients of ethanol in Doctane were not measured at ~711, whi 1 e mcas~tr ement of y m of n -decane in ethanol were unsuccessful 1y because of the tried limits of our g;?c,c~,rornatoRraphic detector. Figure 2 shows how In y o varies with 1iT; it allowLl t he thr?& compar i 501, wi t h the few data found in the literature OrI systems (hlessi and k::ikic, 1985 ). The compari sun I ookrj quite good when the hydrocarbon is; the z.ia1ut.e; when ethanol i 5 the c D 1 1.1 te the Ii terature values are lower then those measured in this WOI-I.:. Howeverthe data from the li.terat.ure are qc!ite spread and the) don ‘t af ,Ford a reyul car t.rcnd al.onq the homnl,oque Eeries. Owing to t.he I inear dependence o-f: lrl y m on 1.11. ra-f t.he d3t.a eactf s,,stem have been linearly inter-palat.ed. Table 11 ShoGJL- 1.h~’ i,i and F . par amct er-ci of t.he eq1.rat.i en
I
C1 i
In ri* r Ai+Bi/T
obtained for- every c,yst.em. The sjtraiqht lines chown in fis. have been cal c~1.1ated with the parameter 5 of that table. The 51 ape D i is di.rectly related to the heat. of dilc!ti,orl
ethanol 17y d r UC C!r b on
_ _._. -- . ....___.--...-..-
hydror,srbnn
..__ - ..._.- ..._.
_..... _......_.__. _._.._. ___-_....__
‘2 at
109 Ini-inite dilution mear,w-emcnts n+
Lf the
usually enthalpy
Xt is
.
excecs Li”
=lim
experimental. val ue!s The system UC ihc c: c:,mp c 5 i t..i ~7n 5 sseqvat I on 1 i I..:e the I Rc!qal 51: i. , I.977 1 eqc!a?: i nn
=
o-f
from the
calorimet.ric equation (. 7; , .
dXi
measured nf: hE a,- e i nterpol atcd Symmetrical ! sc!m ci f
mWLxlg2 :I
obtained means
SF_
If0
$
hy
5 + ( wL
at by
1
di+feren-t e,icI,t.abl e Functi ens>
, .a 1 -:a
VL’2
2 )
?
O.F.
=
NEXPl r i-1
GXP
-YPjl&
2
NEXPL 4.
2 i-1
"&XP
OD - ‘2iCAL
I2
i. :‘, )
113
In
I,==
cl2
In
yzBe
c21
(6)
results That dependence
in of
a
1 inear
parameters
Cl2
C1, vs temperature, in and agreement with the theory of equation I F’rausni t.z , t hc Ii i I.969 ). The ~ i and shown in table II qive directly t.he dependence of C:ii The on temperature. prediction of the dependence activity Of the coefficient5 nn composi. t i on is very good. Fnr t.he not system ethanol --n-heptane the Ei bbs energy of mixing ha2 calculated following been the rel ati ens:
FIG. 4. Ethanol-n-hcptane system at ‘T=40°C. Gibbs energy 0.f mixinq computed by Van Laar model.
(7)
,-Al3 RT
id
ciE obtained
which
doesn
cw-ve,
‘t
actual
k!.i.I.z!E _es..~!tAx!,
x, In '1 +
(9)
12x1 4 C2? “2
shown in 1 y ex i St.
fiq.
At. infinite In
"2 'nx?
Cl2 c21 Xl ‘2
RTCC The
L
4
4,
predict
djlution
81 -In Aii--Aii
it
is
a miscibility
( Wilson,
gap
1964
)
i : 1.2
j : 2.1
where
*xp(_$)
n&i “i
! 11)
1 /T impossible t.o deecribe the dependence It is of lnym vsi with this equation by I_eeping A i .i ‘5 independent of ten!perat.ure,. Neverthel err, 5 I. i near dependence on T t..h e a reproduces experimental data wj thin the experimental error, 5 shc!ws as f1.q. for the system ethanol-n-pental-le. Table IV q i vec5 i.tlc= kJi 1 son o_i I‘ constants der i ved from experimental data for all ttle systems studied. s);ct.amci ‘The VLE for ethanol s-n-l>exane, n-heptane and n-nnnane ha ;e been calculated at the same temperature where e:.:perl merlt.al cwd5 ) C3at.a Table IV rtlew5 the root rne~n 5quare are available.
tht? ac:t.i vity relation5
cnwff
icients
0
71
=
K+l
=
K+l K
(D
y2
derivat.i
\‘es
on
di 1ut.i on
temper-atc.lre bin 70D K 1 =I-bu / T ) K+l ilInyT W/T
1
1
Ah R Ah
=-K+l
R
are
ylvcn
bit
c.he
113
gE=LIE +gEthem phyr
1)
1:t 5~iOUlCl ,,,clr-f? accI..lr-at.e1> describe t.he dependence 04 ~2E over any t il E’ -F1.11 1 r a 1-1 gc 0.f composj t i an. It 5hfml dn : C prrdi ct. VL f.: d d t. ir ‘I m.i.5 c i t2i 1 i t..f it z.h cx! I.d i rnpr exe t. he! f i t. 04: g t\p j avoiding !systemat.ic: trnndr, 0.1 error5 with composit.ion.
114 c’)
L
predict the correct dependence 0i: I II y a nn rhoul d 1.t e qu i 1.i. h I_1.um throuqh that of t-he associat.ion temperatcrre of: temperature in place the ar-hitrar-,constar7t.s on param~l.ere on ‘17. I. inear dependence of physical. interaction has (3 paramet..wE3 ct:: “, ) A 11* < l-he model of: Nath and Drnder
1::: *“, , AhAm , AI.,:~ , duo,, pas-arnet:.et-s can be estimated
, Au;,,
, AL,;*
1: a ma:x~m.~mCT+: ;I
i 61 par wwters model , the binary assnci c&t-ion. Physi. cal y).
parameters par amciterc
‘i *i-e al I. physxcitl. r7re est.imat.ed .f’rarri
.From
the val ues and i r-om t.hk?1 I-. so , it 1s necessary tc3 f:j.:: 3 pr1.cwa dependence on t.emperature. d I-, 4 ‘S_r we,-p Ii; ‘=._ and t: h E! vi\1 c!es of at. l.east 4 paramet.et-s. arid IWI~W, 1’7t?l i, i I obtained .i:rom the proper-Ci,es of pure A i Nath F’r~r t.he other b par amrt er r, WE:have t I- i ed t tie f:ol I ow3 ng clloi cfzfc :.
nn crossed
TkBLE IV Yilson node1parametersfor ethanol Ill-n-alkane (21 aysters
n-dkane
Parametersfron this work i calicole
42
cal /sole
n-pentane n-hexane n-heptane
2757.2 2b99.2
n-nonane
A0 32 21 cal/nolei°C caliaale
Cwparisonnith data frost the literattire
i Gr cal/mole/°C
343.24 363.96
-0.8421 -G.X%
273b.b
-9.986 -9.512 -10.025
457.56
-0.3723
2681.8
-9.221
579.lb
-0.0256
Refwences
T/Y
RI6 on y RHC; on P lLPai
Janaszewskl1982 Janaszewsii1982 Rerro 1982 Berm 1982
40 40 70 76
O.OiiS4 0.0055 0,0109 o.co25
3.4E: c.23 z.01 7.39
115
> c c.2 <
-
ETHANOi
-
nHEPTANE
8 0
IO
20
30
40
50
TEMPERATURE
F1.G.
7.
Effect of temperature coeff icier-its for the between c::perj,mental model
nlodel
5. val
uez.:
(-)
C
60 70 80 90 100
( Scale:
on the infinite ethanol ---n--hcptane a~ld romputed model a;
by (-a-*-)
140
K 1
dilution system. Mal:h and modal
activity Cornpat-i E.O~ Ecender b; C....)
c.
0.m
X
FIG ” 8.
120
l/T
\‘LE predi.ction Nsth and b ; C----J
Render model.
.For ethanol models: C.
1
ETHANOL
--n-heptane !-_)
model
system a;
at
(----_)
4Cf’C
by
model.
116 CUICLUS
1 ONS
allow a. strict te~.t 05 the gE data shown in this paper No clf’,e systems ethanol --,r~-..,alkarres. ity to represent the a t: t hE’ 5<3”,E tj me used Cli-l predict normal 1 y I C The assnci .t.“~~~ and compocl ti on. of y ’ or3 temperatLu-e 1:h (L’ bctC aC tt1e moment iurt.her, model 5 s,cem to be wotrt,h worki.ng parameter:: model q wJ.t h .fit5 lrii 1 cion t!eat: are obtained by the The set_ o.(’ data obt.a.ined ic: dependent, on temperature. 1 inenrly anti it allows the eval uirtinn of the behax/iotr! cp1 te homogcncou~, I ti c OLII. d be t a 1..en P s> iz, ~3I.on !:I tli v home! 1 ng~lk3 se,. i e6 of n--it 1 kan ~3. !ztart.inq point For. <:ur-ther improvements on the exiE.t.1 nq tnodc?.Is. The new mndels abll o -f t: hnsc dependence
117 non arsscjci ati c:~~~c.~ssc-cl a5snci
. E
M i ci 0
ng
cumpanent
at i on
at infinite dilution e:.:c.c5s f:unction mi ): i nq j. d a a 1 Cemperature t.emperakwe
independent dependent
term term
118 ki., Leroj q J.C., Masson, J.C., Fabriee, J.F., Muacurcment 0.f Activity Coefficjents 1.977. fkcurate dilution by Inert Eae Strippinq and Gas Chramat.ography. lncl. Eny. Chem. Process Des. Dev., I&: 13Y--144.
Renon,
Rngal ski 1: 137.
Ynung,
,
C.L.,
W.
,
Ma1annwski
1868.
Chromatag.
,
5. ,
Rev.,
1977.
Flcti cl Phase
Sanni
er,
at.
Infini
I#.
,,
tt2
Equi 1.i. bri 3,
1f.l:129.
Wi 15on , G.M., 1964. Vapaur,-Li quid expt-esfion Tut- the exce55 .ft-ee energy of 80: 1L‘27- 1 :;o _ J . Am. Chem. Sot.
Eqctil ibrictm mir:incj.
XI.
F,
r,F O&J