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Enhanced solubility of quadrupolar molecules in benzene
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apd F!wnt ‘,
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-
mclecuies.
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mbjod~ction
The structures of molecular crystatii are governed by.the multipolar interactions between mdecla+ .‘, (IQ+& [I}). The cjstaf structure of carbon &oxide, for example; is represented by assembling about twenty pieces of mokcul~ models made of barium-ferrite magnets which simulate magnetically the electric qua’ drupole of the teat molecule (fig. 1); the crystal s&fcture of bkrrzeneis represented by assembbng qua&polar molecu&r models similai to the molecule of benzene (fig.’Z), ‘@es@quadrupole-quaclrupoJe interactions do not : play ti essential role in a gaseous state: Ehiira’s~core, potential of intermokcukir forces, which takes in ac.
.
._ ._,’ :
::
_
.:
_,I. .
.,,
count the size and shape of molecules, is a good ap prdx.&atiop [Z]. This core potential of intermolecular forces has b&n applied to sofubitity of gasesin liquids, The solubilities of Ne, Ar, Kr, Xe, N2, CO,, C3H6, and cyclopropane in cyclohexane are we,llrepresented by use of the core potential &rose parameters art$determined from fhe second,viriaf coefficients of gases j3j. The pirpose of the present papei is to show that the’ quadrupole-quadrupole ir~teractionspiay an important part if botfi the solute and solvent mblecties have appreciable ele&ric qluadrupoles, as in the case of carbon dioxide @Ibenzene.
~0Iume
CJiEMICAL PHYSICS
?J; number 1
Benzene-cyctohexane volubility
ratio
,c/cO in benzene c/co in cyclohexane
Temperature
Ne Ar
0.70
20 to w4O”C
0.70
20 to $WzR
[z;
Fe
0.70
20 to =4cFc 20 to c*40Y!
141
0.77 0.80
25°C
;:f
25°C
1.58
171
1.52
20°C 3PC
PI
1.75 1.25 1.05
4°C 20VC 40°C
Solute
cl.68
CHq Na co2
HC!=C!H BF3
15 September 1971
LIYITERS
Ref.
Fig. 3. Foosib!e coafiitior~
oECQ2 molwukk in liquid
benzene. Tabie 2 Quadrupole moments of motauics
191
llOi co2
G-b
N2
HC=Xli
-4.2
-3.6
-1S
+3.0
Table 1 gives, for a number of solutes, the observed ratio of the solubihty in benzene at a certain temperature to tire solubiiity in cyclohexane at the sarn~ temperature. The ratio is close to 0.70 for inert gases but somewhat larger for nitrogen and considerably larger
_.
for carbor! dioxide and acetylene. Lacking observed values of c/co of boron trifluoride
i 3.9A
L
in cyclohexane, we have used the values kLc/co = -0.611
at 20°C and -0.482 at 40% ,
Fig. 4. A possible conf$uration of an acetylene mokcuie in benzene.
on the basis of the core potential deter-
caIcuIated
mined from the second virial coefficient. (The core is a triangle joining fluorine atoms, V= 0, S = 4.86 A2, M= 1 I.17 -4, a = 2.23 A, e/k = 320% in the notation of ief. 131.)
pole-qua&pole
3. Explanation
For acetylene, A+# in eq. (I) is -250°K at 4°C; which is close to -260°K cakuIated for the configura-
interac.tian
energies -190’K
and shown in fig. 3. Here use has been made of f.k values of quadrupkle moments given ;~r tabk 2.
-380%
calcillated for the two configurations
tion shown in fig. 4. These enhanced soiubilities of quadrupolar molecules in benzene can be explained serni~quantitatively in terms of the energy Aq4(< 0) of quadrupole-quadrupoIe interaction between the soiute and solvent molecules:
c/co in benzene c/co in sy clohexane
= 0.70 exp(-AJkT)
,
(11
where kT is Boltzmann’s constant times the absolute .temperature. For.carbon dioxide, A,,lk in eq. (I) is -240°K
for 20 to -34°C. This value is between the quadru:
The authors wish to thank Dr. MS. Jhon of Korea Institute of Science and Technology for helpful infor‘r-nation abaut experimental data of solubility.
References (1) T.Kihara, Acta Crys~ 16 (1963) 1119; Zt (1966) 877; A26 (197Oj315. 63
.
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,.,‘-
:
.’
i&.-F&& ihys. 25 (1933j.i3& Adv&.‘&&i,~~ ; _I (71 J&.Gjaidb& Ad !&Hilde+ar$, 3. Am.,Cb&~~oc. .,._ ’...’.ii)T%hara, .’ 71 @49)(3147;‘.. ,’ J. 7.. ‘,:’ : ., Thy&Q (195Q 147;..’ _,.:,.. f8j J.CIir.Gjahlbaek; Acta Ch& SC&. 7 (1953) 5’37. T.Kihaza,‘K.Yimqaki, M$.Jhan arid +U&n, Cheni : ._ ‘_’ ; .. [9] M#%pley a& C&,Hpl$y Jr., J. && Chem.~Suc. 61. ~‘.’ : ,. :’ 1. Ph);s..tetters 9.f1971)62; T.para’and M.S.Jhon,~Chw@hys; Letten 7 !1970) :, f3j (i939) 1599; I .‘. ,., “. .’ ., ,.‘-,a$p3* ,. ._ :- .., .., ., jr01 C.~.Wheeler Jr. and H,P.Keating, 3. Pbys; C&m. 58’ fir) H.L.Ciciw, B.&&tino, J.HSay!osandP;M.Gross,,J. :._. (1954) 117,l.: .. fll] A.D.Buckfng?tam; AcWa&Chem.‘i%ys. 12 (1967)I&.; -“WLs Chdm. 61(1957) 1078. El21 D.E.Sirogryn and AD.Stxogryn, Mol. Phys. 11.(1966) .. 2.’ [S] @Xl&er;J. phys. C&-n. 62 (1?58) 375. ;3?1. 1‘ ; [6] A.Laiu&g a@ J.Cbr.Gjzldbaek, ActaCh&m, S,cand. 14 ‘. (1960) 1124, ‘. :, ‘. .: ::I .
,: :: :”
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;
”
.,
‘.’
.‘,.
apd F!wnt ‘,
:,
-
mclecuies.
:’
_.
_.’ ”
: ,_
mbjod~ction
The structures of molecular crystatii are governed by.the multipolar interactions between mdecla+ .‘, (IQ+& [I}). The cjstaf structure of carbon &oxide, for example; is represented by assembling about twenty pieces of mokcul~ models made of barium-ferrite magnets which simulate magnetically the electric qua’ drupole of the teat molecule (fig. 1); the crystal s&fcture of bkrrzeneis represented by assembbng qua&polar molecu&r models similai to the molecule of benzene (fig.’Z), ‘@es@quadrupole-quaclrupoJe interactions do not : play ti essential role in a gaseous state: Ehiira’s~core, potential of intermokcukir forces, which takes in ac.
.
._ ._,’ :
::
_
.:
_,I. .
.,,
count the size and shape of molecules, is a good ap prdx.&atiop [Z]. This core potential of intermolecular forces has b&n applied to sofubitity of gasesin liquids, The solubilities of Ne, Ar, Kr, Xe, N2, CO,, C3H6, and cyclopropane in cyclohexane are we,llrepresented by use of the core potential &rose parameters art$determined from fhe second,viriaf coefficients of gases j3j. The pirpose of the present papei is to show that the’ quadrupole-quadrupole ir~teractionspiay an important part if botfi the solute and solvent mblecties have appreciable ele&ric qluadrupoles, as in the case of carbon dioxide @Ibenzene.
~0Iume
CJiEMICAL PHYSICS
?J; number 1
Benzene-cyctohexane volubility
ratio
,c/cO in benzene c/co in cyclohexane
Temperature
Ne Ar
0.70
20 to w4O”C
0.70
20 to $WzR
[z;
Fe
0.70
20 to =4cFc 20 to c*40Y!
141
0.77 0.80
25°C
;:f
25°C
1.58
171
1.52
20°C 3PC
PI
1.75 1.25 1.05
4°C 20VC 40°C
Solute
cl.68
CHq Na co2
HC!=C!H BF3
15 September 1971
LIYITERS
Ref.
Fig. 3. Foosib!e coafiitior~
oECQ2 molwukk in liquid
benzene. Tabie 2 Quadrupole moments of motauics
191
llOi co2
G-b
N2
HC=Xli
-4.2
-3.6
-1S
+3.0
Table 1 gives, for a number of solutes, the observed ratio of the solubihty in benzene at a certain temperature to tire solubiiity in cyclohexane at the sarn~ temperature. The ratio is close to 0.70 for inert gases but somewhat larger for nitrogen and considerably larger
_.
for carbor! dioxide and acetylene. Lacking observed values of c/co of boron trifluoride
i 3.9A
L
in cyclohexane, we have used the values kLc/co = -0.611
at 20°C and -0.482 at 40% ,
Fig. 4. A possible conf$uration of an acetylene mokcuie in benzene.
on the basis of the core potential deter-
caIcuIated
mined from the second virial coefficient. (The core is a triangle joining fluorine atoms, V= 0, S = 4.86 A2, M= 1 I.17 -4, a = 2.23 A, e/k = 320% in the notation of ief. 131.)
pole-qua&pole
3. Explanation
For acetylene, A+# in eq. (I) is -250°K at 4°C; which is close to -260°K cakuIated for the configura-
interac.tian
energies -190’K
and shown in fig. 3. Here use has been made of f.k values of quadrupkle moments given ;~r tabk 2.
-380%
calcillated for the two configurations
tion shown in fig. 4. These enhanced soiubilities of quadrupolar molecules in benzene can be explained serni~quantitatively in terms of the energy Aq4(< 0) of quadrupole-quadrupoIe interaction between the soiute and solvent molecules:
c/co in benzene c/co in sy clohexane
= 0.70 exp(-AJkT)
,
(11
where kT is Boltzmann’s constant times the absolute .temperature. For.carbon dioxide, A,,lk in eq. (I) is -240°K
for 20 to -34°C. This value is between the quadru:
The authors wish to thank Dr. MS. Jhon of Korea Institute of Science and Technology for helpful infor‘r-nation abaut experimental data of solubility.
References (1) T.Kihara, Acta Crys~ 16 (1963) 1119; Zt (1966) 877; A26 (197Oj315. 63
.
...‘.
-‘y
,.,‘-
:
.’
i&.-F&& ihys. 25 (1933j.i3& Adv&.‘&&i,~~ ; _I (71 J&.Gjaidb& Ad !&Hilde+ar$, 3. Am.,Cb&~~oc. .,._ ’...’.ii)T%hara, .’ 71 @49)(3147;‘.. ,’ J. 7.. ‘,:’ : ., Thy&Q (195Q 147;..’ _,.:,.. f8j J.CIir.Gjahlbaek; Acta Ch& SC&. 7 (1953) 5’37. T.Kihaza,‘K.Yimqaki, M$.Jhan arid +U&n, Cheni : ._ ‘_’ ; .. [9] M#%pley a& C&,Hpl$y Jr., J. && Chem.~Suc. 61. ~‘.’ : ,. :’ 1. Ph);s..tetters 9.f1971)62; T.para’and M.S.Jhon,~Chw@hys; Letten 7 !1970) :, f3j (i939) 1599; I .‘. ,., “. .’ ., ,.‘-,a$p3* ,. ._ :- .., .., ., jr01 C.~.Wheeler Jr. and H,P.Keating, 3. Pbys; C&m. 58’ fir) H.L.Ciciw, B.&&tino, J.HSay!osandP;M.Gross,,J. :._. (1954) 117,l.: .. fll] A.D.Buckfng?tam; AcWa&Chem.‘i%ys. 12 (1967)I&.; -“WLs Chdm. 61(1957) 1078. El21 D.E.Sirogryn and AD.Stxogryn, Mol. Phys. 11.(1966) .. 2.’ [S] @Xl&er;J. phys. C&-n. 62 (1?58) 375. ;3?1. 1‘ ; [6] A.Laiu&g a@ J.Cbr.Gjzldbaek, ActaCh&m, S,cand. 14 ‘. (1960) 1124, ‘. :, ‘. .: ::I .
,: :: :”
.., ‘.
.. 1
. “--
-.
. .
_.
:
.’
:
/,
..:
‘.
(., ,.
.
-
,.
..,~...
.,
.-
‘.
: ,/‘.,
.’ :
,.(.
.
:
_’
.
.)
,’ ‘.
.
‘.
‘,.
.~
.’
,.
.
:
,..
;
”
.,
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