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Apparent molar volumes, isobaric expansion coefficients, and isentropic compressibilities for some non-aqueous carbohydrate solutions
o-147 .I. (‘hmt. Thermodvnamics 1986, 18. 969-978
Apparent molar volumes, isobaric expansion coefficients, and isentropic compressibilities for some non-aqueous carbohydrate solutions a PEDRO
J. BERNAL*
and W. ALEXANDER
VAN HOOK
Chemistry Department, University of Tennessee. KnoxviIle Tennessee 37996-1600. U.S.A. /Received Ii June 1985; in revised,form
28 January 1986)
The molar volumes and isentropic compressibilities of a number of carbohydrates and some of their deuterated isomers have been determined in several non-aqueous solvents (dimethyl sulfoxide, dimethyl formamide, ethylene glycol, and methanol) at several temperatures. The results are compared with similar measurements in aqueous solvents. A correlation of the limiting apparent molar volumes with solvent compressibility is discussed.
1. Introduction Bernal and Van Hook’” have commented on recent efforts devoted to the study of aqueous carbohydrate solutions. Some of the interesting effects observed in aqueous sugar solutions, such as stereospecific solute-solvent interactions, have been attributed to structural features which are presumably unique to water.“’ To test this view we thought it appropriate to perform measurements in non-aqueous solutions because the comparison might highlight the effects peculiar to aqueous solutions. Also the measurements are of interest since non-aqueous solvents, especially dimethyl sulfoxide (DMSO), are being increasingly used in spectroscopic and chemical-reactivity studies involving carbohydrates.
2. Experimental D( + )-glucose, myo-inositol, IX- and P-methyl-D-glucosides were obtained from Sigma Chemical Co. High-purity glucose was supplied by Chemical Dynamics Corp., and galactose by Aldrich Chemical Co. About 0.3 kg of special-production high-purity sucrose was a gift of Professor Andrew Van Hook of Holy Cross College. All compounds were dried under vacuum at about 350 K for several days and used without further purification. ” Abstracted from part of a PhD. thesis of P. J. Bernal, University of Tennessee, 1984. * Present address: Chemistry Department, University of Oklahoma, Norman OK 73019, U.S.A. OOZl-9614/86/100969+
IO $OZ.OOjO
Ft 1986 Academic Press Inc. (London) Limited
P.J.BERNALANDW.A.VANHOOK
970
Gold label (greater than 99.9 moles per cent) dimethyl sulfoxide (DMSO) was obtained from Aldrich Chemical Co. Ethylene glycol, NJ-dimethyl formamide (DMF), and methanol (certified ACS grade), obtained from Fisher Chemical Co., were dried over molecular sieve and further purified by distillation under reduced pressure. Density and speed of sound measurements were made using a Mettler Paar DMA 601 HT vibrating densitometer ( f 0.002 kg. m- 3, and Nusonics Solution monitor SSM 6105 or CA 6080 respectively (LO.02 rn. s-r). The techniques have been described elsewhere and we have also quoted equations to obtain apparent molar volumes V,. @, or apparent molar isentropic compressibilities ks, 2,9 from the measurements.‘”
3. Results We have previously reviewed the influence of anomeric interconversion on the density of aqueous carbohydrate solutions.“) Other processes, like furanose-topyranose interconversion, might also affect densities even though the effect may be impossible to quantify because of the presence of competing equilibria. While the influence of these processes on the density of non-aqueous solutions is probably negligible, it is nonetheless important to specify which species are present. In water and in DMSO, glucose exists in two anomeric forms and at room temperature the equilibrium composition is about the same in the two solvents (0.36a-glucose + 0.64&glucose). The furanose and open-chain forms only make up about 0.003 mole per cent of the glucose present. (3) In DMF, however, the solution contains about 4.5 moles per cent of the furanose form at 343 K,(4) and in ethylene glycol the behaviour of glucose has been described as “abnormal”(5~ although we are not aware of any study about the equilibrium composition. The effect of temperature on the anomeric equilibrium is small.@ In water, galactose, unlike glucose, exists in more than two isomeric farms.(3) An aqueous solution of galactose at equilibrium is approximately (0.32a-D-galactopyranose + 0.63l3-D-galactopyranose and O.OScr- and (3-D-galactofuranose).(‘) In DMSO, furanose increases to about 0.15.@) In this case a temperature increase favors the formation of more furanose. Sucrose is a disaccharide and is not capable of the configurational changes common to monosaccharides. It can, however, form intramolecular hydrogen bonds and undergo rotation about the glycoside linkage.‘@ While the conformation of sucrose in aqueous solution is still a subject of controversy,“’ it is clear that disaccharide conformation does depend markedly on solvent.‘@ The relative densities (p -p:) were fitted with the equation: (P-d)
= ~(~,l~l~l)+~(~,l~l~l~2+C(~,l~,~l)3.
(1)
where n2 and n, are the amounts of substance of solute and solvent, respectively, M, is the molar mass of solvent, and p: and p are the densities of pure solvent and solution. The coefficients of equation (I), the variance 0’ of fit, and the number N of points per run are given in table 1.
6.o. (av,,,laT),. AND km OFNON-AQUEOUS
CARBOHYDRATES
971
TABLE 1. Coefficients of equation (1)
n21hMI) mol.kg-’
N
A
kg2.m-3.molF’
B
7 5 7 7 7 6 6 6 6 5 6
298.15 K 67.096 56.740 72.489 67.209 67.07 1 125.601 53.484 52.172 75.851 66.494 82.595
7 7 6 6 7 6 6
313.15 K 67.738 67.689 126.787 126.324 54.641 52.616 76.461
- 9.096 - 30.254 -27.348 -9.533 - 7.592 - 10.642
0.07 to 0.40 0.04 to 0.18
7 6 6
288.15 K 74.774 141.645 140.666
-9.872 -49.623 - 32.798
hX'OSe+DMF
0.07 to 0.40 0.04 to 0.18
r-Methyl glucoside + DMF Glucose +ethylene glycol r-Methyl glucoside+methanol
0.03 to 0.35 0.15 to 0.33 0.03 to 0.25
6 6 6 6 6 6 6
298.15 K 74.713 141.896 141.013 66.522 57.309 79.437 78.675
-9.397 -48.516 -33.348 -9.261 -6.300 - 18.783 - 10.146
6
313.15 K 79.345
- 11.879
G1ucose + UMso-d, Glucose-d, + DMSO Galactose + DMW
0.07 0.06 0.07 0.07
to to to to
0.65 0.29 0.49 0.65
Sucrose + UMSO a-Methyl glucoside + UMSO B-Methyl glucoside + UMSO Myo-inositol + DMSO Myo-inositol+ DMso-d, Myo-inositol-d, +DMSO
0.03 0.07 0.10 0.06 0.05 0.05
to to to to to to
0.49 0.60 0.64 0.30 0.30 0.18
Glucose + DMSO Galactose + DMW Sucrose + UMSO
0.07 to 0.65 0.07 to 0.65 0.03 to 0.49
z-Methyl glucoside + UMSO P-Methyl glucoside + uMS0 Myo-inositol+ DMSO
0.07 to 0.60 0.10 to 0.64 0.06 to 0.30
Glucose + UMF
GlucOSe
+ DMSO
SUCrOSC+l>MF
Glucose + DMF
a-Methyl glucoside + methanol 0.03 to 0.15
C
- 9.827 - 8.666 - 11.595 - 9.336
- 8.667 - 30.686 - 7.690 -9.291
10Jd -?1
kg3.m-3.mo]-’
kg2.m-h
1.189
0.24 2.76 0.2X 0.19 0.70 0.24 3.05 0.92 1.71 0.23 0.2X
3.163 0.724 4.538 1.995
- 9.920
- 9.668 - Il.841
1.65 2.74 I .02 4.22 0.28 3.00 0.05
- 8.838
4.089 1.931
2.74 0.9x 3.20
63.972
1.17 0.60 2.46 1.20 1.14 0.67 2.77
57.672
24.811
13.98
Values of V2.@were least-squares fitted with the equation:
vZ.9= 1/;1~+S,(n,/nIMI)+L,(n,lnIMl)2. Coefficients of equation (2) are reported in table 2. Comparison with results in the literature is possible only in three cases. Sears er ul.‘l”) have measured densities of glucose and sucrose solutions in DMSO at 298.15 K and the agreement with the present results is excellent. Dack”” has measured V2.,+ of sucrose solutions in DMF but with low precision (f 1 or 2 x 1O-6 rn3. mol-‘). The present results fall within his error band. While on the
972
P. J. BERNAL TABLE
2. Coefficients
of equation
AND (2):
W. A. VAN
V2,+ = l/,“Pm+Sv(n,/n,M,)+L,(n,/n,M,)*
106V” 2.4 m3,mol-’
HOOK
106S, kg.m3,mol-*
298.15 K GhlCOSC+DMK3
Glucose-d, Galactose
+ DMSO + DMso
SUCrOSCfDMSO
cc-Methyl glucoside + DMSO P-Methyl glucoside f DMSO Myo-inositol + DMSO Myo-inositol-d, + DMSO Myo-inositol+ DMso-d, GhCOSe+DMKJ-d,
108.56 108.74 108.42 207.67 132.61 133.92 101.11 101.12 101.01 108.55
1.4369 1.4512 1.3155 2.7114 0.5622 0.7386 2.0202 2.4179 2.2097 1.8516
0.29 1.79 0.39 3.53 2.09 0.70 0.14 1.66 0.46 2.80
1.5226 1.7757 2.5945 1.0685 0.8769 2.3418
I .30 0.60 0.78 2.03 0.34 0.16
313.15 K
a-Methyl glucoside + DMSO P-Methyl glucoside + DMSO Myo-inositol+ DMSO
108.56 108.59 208.07 132.96 134.45 101.21
GhCOSC+DMF SUCrOSCf DMF
106.24 202.9
Glucose + DMF Glucose + ethylene glycol a-D-Methyl glucoside + DMF a-D-Methyl glucoside + methanol
106.47 115.70 130.50 118.6 203.1
GhlCOSC+DM%l
Galactose
+DMso
&lCrOSC+DM%3
288.15 K 5.9793 29.894
-5.165 - 85.29
2.40 8.90
298.15 K
SUCl'OSC+DMF
6.0437 -0.6591 6.1491 17.493 28.916
- 5.848 -8.861 - 37.61 -78.21
1.70 3.90 1.30 3.30 9.40
313.15 K a-D-Methyl
glucoside
+ methanol
118.0
9.427
18.40
subject of error we emphasize that the limiting values VZy+reported in table 2 for DMF and methanol solvents are not as reliable as those in water and deuterated water,“) or DMSO, because the extrapolation to infinite dilution is complicated by a good deal of curvature in the non-aqueous solvents. More precise limiting values will require more density measurements on dilute solutions. To exemplify the quality of the results, plots of V,, + against nz/(nI M,) for glucose and galactose at 298.15 and 3 13.15 K in DMSO, and for glucose at 288.15 and 298.15 K in DMF, and at 298.15 K in ethylene glycol are shown in figure 1. Expressions relating isentropic compressibilities K~ to speeds of sound u and defining the apparent molar isentropic compressibility k,, 2, + have been presented earlier.‘” For non-electrolytes Hemmes et ~l.,“~’ Rao,‘13’ and Gucker and Haag”*’ have reported that the relative change in speed of sound in dilute solution is a linear
6s. (av,,,PT),, AND kz.+
OF NON-AQUEOUS
973
CARBOHYDRATES
FIGURE 1. Plots of V2,+ against (n,/n, M,) in different solvents at various temperatures: *, glucose in at 288.15 K; A, glucose in DMF at 298.15 K; 0. galactose in DMSO at 298.15 K; IJ, glucose in DMW at 298.15 K; n , glucose in DMSO at 313.15 K; 0. galactose in DMSO at 313.15 K: A. glucose in ethylene glycol at 298.15 K.
DMF
TABLE
3. Parameters
of equation
(3) for some solutions
Warn) m~s~‘~kg.rnol
’
7
102Q m.s-‘~kg.mol-’
K
Glucose + H,O’ Fructose + H,O Sucrose + H,O Myo-inositol+ H,O
68.51 kO.01 74.42 k 0.61 99.36kO.06 86.45 kO.01
4.61 5.08’ 6.78 5.90
288.15 288.15 288.15 288.15
Glucose+H,O Fructose + H,O Sucrose + H,O Myo-inositol + H,O Myo-inositol+ D,O
62.06 f 0.0 I 66.5120.47 91.42kO.07 79.15 k 0.08 92.34kO.3
4.15 4.44 c 6.11 5.29 6.59 4.91 5.21 7.92 3.58 3.73 3.43 3.73
298. I5 298.15 298.15 298.15 298.15
b
GhCOSC+DMW‘+
Sucrose + ~xw~ a-D-Methyl glucoside O-D-Methyl glucoside GhCOSe+DMFP
” For H,O du,(298.15 “~~(298.15
+ +
DMSO DMXI
72.83 +0.04 74.65 kO.05 113.56kO.05 53.13*0.01 55.34_io.o1 51.28_+0.01 54.27kO.01
solutions (see reference 1); b u&298.15 K) = 1400.59 rn. s- I; c Infinite K) = 1483.91 m.s-‘; ~~(313.15 K) = 1433.94m.s-*. K) = 1494.96m.s-‘; u,(313.15K) = 1455.56m.s-‘.
dilution
298.15 313.15 313.15 313.15 298.15 288.15 298.15 values,
974
P. J. BERNAL TABLE
4. Coefficients
of equation
AND
W. A. VAN
(4) for several
HOOK
compounds
10’5k” s. 2.4 m3.Pa-‘~mol-’
in non-aqueous
solutions 10-2 m6~Pa-*~mol-’
1015L m3.k$.mol’3.pam1 288.15 K
-22.12
GhlCOSCfDMF
9.642
- 5.992
2.75
-6.711
0.33 4.78 0.07 0.66
298.15 K -28.44 - 15.25 9.42 9.36
GhlCOSCfDMF
Glucose + DMSO a-D-Methyl glucoside P-D-Methyl glucoside
+ DMSO + DMKI
10.548 2.808 -0.017 0.033 313.15 K
-20.71 -21.28
GhlCOSC+DMKI
Sucrose + DMSO
3.742 1.745
5.62 0.56
function of molality: wu = Qh/n,M,)~ (31 and carbohydrates are no exception to this rule. In table 3 values of 6u/u and Q are reported for aqueous and non-aqueous solutions. These values are useful because Q has been regarded as a qualitative measure of solute-solvent interaction. Values of k,, 2, + were least-squares fitted with the equation: (41 plots of compressibility
ks.,,+ = k~,.,+S,(n,ln,M,)+L,(n,ln,M,)‘, and the coefficients are reported in table 4. Representative are shown in figure 2. 4. Discussion
The values for I& reported in this and the previous paper”’ vary widely with solvent. Some solvent properties which might influence I’,. ,+,are listed at 298.15 K in table 5. They include the cohesive energy density, AU,/V,. the internal pressure Pi, the molar volume V,, the isothermal compressibility tiT, and the dielectric constant -i5
I
-14-
E 72 -16-
I
+.+
+’
I
1
I
10
.-
-----+
I
9-@
z -,8‘+CI P-x -2 -2o-
I
I
I
0
”
rl /* 0
0.1
0.2
0.3
0.4 (nzln,
9I 0.5
8o
I
I
q u
I 0.1
u
u I 0.2
1 0.3
I 0.4
I 0.5
I 0.6
0.7
M,)l(mol.kg-‘)
FIGURE 2. Plots of kS.2.0 a g ainst (n,/n,M,) in different solvents: A. sucrose *, glucose in DMSO at 313.15 K: f. glucose in DMSO at 298.15 K: 0. P-D-methyl 298.15 K; 0. r-D-methyl glucoside in DMSO at 298.15 K.
in DMSO at 313.15 K; glucoside in DMSO at
b.r. (a%&T)p. AND ks.l.+OF TABLE
VMF Methanol
6. Apparent
molar
volume
at 298.15
536 548 172 518 477 297
as a function
of solvent 298.15 K
Solvent
55.93 39.89 18.07 71.33 77.44 40.74
892 1575 2302 705 582 874
compressibilities
for several
10”Vz~d(m3. glucose
3.7 4.1 4.6 5.3 6.5 12.6
Ethylene glycol Formamide Hz0 VMSO VMP
Methanol ’ Reference
K
J.rne3
3.7 4.1 4.6 5.3 6.5 12.6
VMSO
properties
CARBOHYDRATES
106p,
Pa-’
Ethylene Glycol Formamide HZ0
TABLE
5. Solvent
lo’%,
Solvent
NON-AQUEOUS
26; b reference
sucrose
compounds
at
mol-‘) myo-inositol
galactose
37.1 109.5 78.5 48.5 36.7 32.6
methylglucosides Z-D-
B-D-
133.2" 132.61 130.50 118.6
135.5 133.92
115.70 218.9h 211.45 207.67 203.1 187.0b
111.99 108.56 106.47 93.7' 11: ’ reference
110.7" 108.42
100.78 101.11
30.
E. The only clear correlation is that V2,+ decreases with or as shown in table 6 and plotted in figure 3 for all non-electrolytes in the table except sucrose. The table and figure show that V2,+ is not a simple linear function of K= in spite of the claim made by Dack (rl) for sucrose and urea. More precise results for urea”” clearly show curvature like that reported here for glucose and sucrose. I
136-
I
I yo +
12x7 5 E “’
120:
0
‘I
+
.s
‘- 112xci L. 5 104-
B n
0
** WII 2
I
4
I 6
,
/
8
I(1
,: 0 I2
IO”‘K ,/Pa? FIGURE 3. Results f, a-D-methyl glucoside; see tables 5 and 6.
for V’z.+ plotted against q.: 0, glucose; Cl, S-D-methyl glucoside. The compressibility
a. galactose; *, myo-inositol; is varied by changing solvents.
976
P.J.BERNALANDW.A.VANHOOK
The correlation between V,,, and i+ is better documented for electrolyte(‘6.‘7’ solutes than it is for non-electrolytes. However, in 1972 Hamilton and Stokes’15) noted the existence of the correlation for urea dissolved in six polar solvents and their approach was further explored by Dack. (rl) More recently French and Crisso8) refined ideas dating back to Eley”” and Uhlig(*” qualitatively to rationalize the correlation. Similarly Edward and Farrell’21.2’) using a model proposed by Stillinger (23’ have shown that a volume contraction of the solvent cavity results when a hydrophilic solute is dissolved in a polar solvent. The shrinkage is expected to be proportional to tiT because solvents with low compressibilities and high packing densities are not susceptible to further volume reduction due to hydrogenbond formation (solvation). If for hydrophilic solutes in polar solvents, the value of V2,$ reflects a process of cavity formation followed by volume contraction due to solventtsolute interaction, then one would expect V2,+ to depend on the magnitude of K~ in each of these two processes. Both cavity formation and volume shrinkage are expected to be easier in solvents of high compressibility. (18) The inverse correlation which is observed between V2,s and K~ indicates control by volume contraction instead of cavity formation. However, such arguments are applicable only to hydrophilic solutes dissolved in polar solvents, because otherwise there is no mechanism to produce marked volume contraction. For non-polar solutes exactly the opposite behaviour has been observed. Thus V,, + for benzene is higher in methanol than in water.‘24-26’ Such behaviour is expected of solutes where V2,+ is governed by cavity formation. Myo-inositol, for which there are only two points (in H,O and DMSO), appears to be an exception to the rule. This seems reasonable in view of the very large negative value of V2,4 for myo-inositol in water. (l) This indicates an unusually large increase in packing density around the solute. The volume reduction is apparently enough to compensate for the slightly higher compressibility of DMSO. If the correlation between V,. + and K~ is more than coincidental then one expects the temperature dependencies of V2.+ and K~ also to be related. (The results show the expansivities of carbohydrates in non-aqueous solution to be very low. The expansivity of cl-D-methyl glucoside in methanol is negative.) In pure DMSO, DMF, and methanol an increase in temperature leads to an increase in xr. which, according to the arguments above, should result in a reduction of V2,+ in the carbohydrate solutions. Of course this decrease will be countered by the effect of thermal expansion of solute and solvent. The two effects tend to cancel, the result being low values for (av2ya7-),, as observed. According to this argument, negative (aV,q?,/aT), in methanol results because K~ increases with temperature fast enough to more than compensate for the thermal expansion of solvent and solute. The discussion can be extended to aqueous solutions. For H,O below 322 K, KT decreases with temperature, and according to the model this should cause less cavity shrinkage and hence an increase in V2,+. That increase will be complemented by thermal expansion of solute and solvent and will result in large values for (a vi:+iaT),, as observed. It is also in agreement with the observation that the addition of OH groups to the solute renders (aV2T,/aT), larger.‘26, 27) Such simple arguments have, we think, even more explanatory power. Consider for example, the increase in slope observed at low temperatures in a plot of V2,* against T in aqueous
K,,, (W.,/aT),. AND ks.2.~OF
NON-AQUEOUS
CARBOHYDRATES
917
solutions. This is predicted by the present model, the temperature coefficient of compressibility of H,O increases rapidly as temperature falls. It also rationalizes the inverse H,O/D,O isotope effect on (av&@T), as a consequence of the inverse isotope effect on the temperature coefficient of K~ of these two solvents. Arguments of the type set forth in the preceding few paragraphs are an oversimplification. Other factors are at work including the very important and better documented structural effects unique to aqueous solutions. Still, it is comforting to see a simple model based on a well characterized solvent property produce a high degree of qualitative agreement in both aqueous and non-aqueous solvents. Finally in this section dealing with volumes it is appropriate to comment on changes in I’*,+ p reduced by stereochemical differences. Table 1 shows that 1/2.4 of c1-and @D-methyl glucosides are not identical in DMSO. The assumption is that such differences are a consequence of structural effects. Certainly they cannot be rationalized in terms of models like the kind above which are designed to rationalize differences for the same solute in different solvents, not for different solutes in the same solvent. It is interesting that the difference between the methyl glucosides is much smaller in DMSO than it is in water.““’ Values of k,, 2. + for glucose in DMSO and DMF, and for sucrose in DMSO, are large and negative indicating a high degree of solute-solvent interaction. Values of k&b for c1- and B-D-methyl glucosides are positive and nearly identical. Methyl . substltutlon thus renders k; 2, + more positive in DMSO than it does in water. The similarity of the values indicates that DMSO is not as sensitive as H,O in distinguishing between closely related molecular conformations. The temperature dependence of kz 2, + in the non-aqueous solvents is smaller than in H,O. This behavior is similar to that of (av2;,/aT),. Furthermore (i?k,, 2,a/i3T), is negative, as is the temperature coefficient of the compressibility of the pure solvents. Recently Criss and co-workers (l’) have reported that for electrolytes k,, 2.+ becomes more negative as the isothermal compressibility of the solvent increases. This observation is implied in the equation commonly used to calculate hydration numbers nh from compressibility measurements;(z8’ (5) ks . 2.+ = nh Vl*xT. Equation (5) is derived assuming an incompressible solvation shell and is therefore not expected to be quantitatively correct for non-electrolytes. However it is qualitatively useful in showing that the temperature dependence of k,,,,+ should reflect that for K~. Thus in non-aqueous solvents an increase in temperature increases K~ and results in a more negative k,,,+ In water exactly the opposite effect is observed. An increase in temperature lowers tiT rendering V, + more positive, as observed. The situation is complicated by the large difference in V,, of the solvents being compared. We have not presented enough results to establish a correlation, but for the two organic solvents of similar molar volume the expected trend is observed. The dependence of k; 2,+,on I+. can also be rationalized from the inverse relation between k’;, + and K= commented on previously; kg 2.,+is the negative of the pressure coefficient of V2y+: ki’t 2. $I = -(a h:ml+)T. (29) Therefore a negative kc 2,4 implies that
978
P. J. BERNAL
AND
W. A. VAN
HOOK
I/& must increase with pressure which can only occur if rcT decreases as the pressure is raised. This is the normal situation for most liquids including H,O, DMSO, and DMF. For most liquids l/~~ varies linearly with p provided that p is not too high. At 298.15 K in DMSO the glucose/glucose-d, isotope effect, (AV,Jm = {VT&H)-VT+(D)} = -0.18 x low6 m3.mol-‘, as compared with the effect in H,O/D,O which varies from 0.41 to -0.18 x 10e6 m3.mol-’ between 288.15 and 328.15 K.(r) This is just the effect one would expect were solvent structure making a significant contribution in the aqueous but not in the non-aqueous case. (The structural contribution in water is expected to fall markedly as temperature increases.) For myo-inositol both solute and solvent isotope effects on limiting apparent volumes at 298.15 K were determined in DMSO. The solute effect is negligible, the solvent effect positive, but small, (AV,,,)m = 0.1 x lO-‘j rne3. mol-‘, as compared with (AV’,,,)m in H,O/D,O where effects of 0.88 (288.15 K) and 0.56 x 10m6 (298.15 K) are observed. Again the isotope effect is much larger in aqueous solvent, generally regarded as more structured. This research was supported by the National CHE 81-12965 and CHE 84-13566.
Science Foundation
under grants
REFERENCES 1. Bernal, P. J.; Van Hook, W. A. J. Chem. Thermo&namics 1986, 18. 955. 2. Suggett. A. Water-A Comprehensive Treatise, Vol. 4. Franks, F.: edition. Plenum Press: New York. 1973. 3. Wolfram. M. L.; Tipson, R. S.: editors. Advances in Carbohydrate Chemistry, Vol. 24. Academic Press: New York. 1%9. 4. Reine. A.; Hevding. J. A.; Kjolberg. 0.; Westbye. 0. Acfa Chem. Stand. 1974, 28, 690. 5. Dzhundubaev, K. D.; Kozhakhmetova. R. I.; Sarybaeva, R. I. Izv. Akad. Nuuk. Kirg. SSR 1966,69. 6. Franks, F. Phil. Trans. Roy. Sot. London B 1977, 278, 581. I. Shallenberger, R. S.; Birch, G. G. Sugar Chemistr.v AVI Publishing: Westport. CT, 1975. 8. Mackie. W.: Perlin. A. S. Can. J. Chem. 1966, 44, 2039. 9. Mathlouthi, M.; Vinhh Luu. D. Carbohydrate Res. 1981, 91. 113. IO. Sears, P. G.; Siegfried, W. D.; Sands, D. E. J. Chem. Eng. Dafa 1964, 9. 261. I I. Dack. M. R. Aust. J. Chen7. 1976, 29, 779. 12. Hemmes, P.; Mayevsky. A. A.; Buckin, V. A.: Sarvayan. A. P. J. Phw. Chm7. 1980, 84, 699 13. Rao, M. R. Current Sri. 1940, 9. 534. 14. Gucker. F. T.: Haag, R. M. J. Acoust. Sri. Am. 1953, 25. 470. 15. Hamilton, D.; Stokes, R. H. J. Soln. Cl7em. 1972. 1. 213. 16. Millero. F. J. Chem. Rev. 1971, 71, 147. 17. Lankford, J. T.; Holladay. W. T.; Criss. C. M. J. Soln. Chem. 1984, 13, 699. 18. French. R. N.; Criss, C. M. J. Soln. Chem. 1981, 10. 713. 19. Eley, D. D. Trans. Faraday Sot. 1939, 35, 1281; 1939, 35. 1421. 20. Uhlig. H. H. J. Pl7.w. Chem. 1937, 41, 1215. 21. Edward. J. T.; Farrell, P. G.: Shahidi, F. J. Chem. Sot. Faraday Trans. Il977, 73, 705. 22. Edward. J. T.; Farrell, P. G. Can. J. Chem. 1975, 53, 2965. 23. Stillinger, F. H. J. Soln. Chem. 1973, 2. 141. 24. Masterson, W. L. J. Chem. Phvs. 1954, 22. 1830. 25. Dutta-Choudhury. M. K.; Miljevic, N.; Van Hook, W. A. J. Phys. Chem. 1982, 86. 171 I. 26. Franks. F.; Ravenhill. J. R.; Reid, D. S. J. Soln. Chem. 1972, I. 3. 27. Franks. F.: Quickenden, M. A. J.; Reid, D. S.: Watson, B. Trans. Faraday Sot. 1970, 66. 582. 28. Stuehr. J.: Yeager, E. Physical Acoustics, Principles and Merhods. Masson. W. P.: editor. Academic Press: New York. 1965. 29. Gucker. F. T. Chem. Ret,. 1933, 33. 111. 30. Longsworth, L. G. J. Phys. Chem. 1%3, 67, 689.
Apparent molar volumes, isobaric expansion coefficients, and isentropic compressibilities for some non-aqueous carbohydrate solutions a PEDRO
J. BERNAL*
and W. ALEXANDER
VAN HOOK
Chemistry Department, University of Tennessee. KnoxviIle Tennessee 37996-1600. U.S.A. /Received Ii June 1985; in revised,form
28 January 1986)
The molar volumes and isentropic compressibilities of a number of carbohydrates and some of their deuterated isomers have been determined in several non-aqueous solvents (dimethyl sulfoxide, dimethyl formamide, ethylene glycol, and methanol) at several temperatures. The results are compared with similar measurements in aqueous solvents. A correlation of the limiting apparent molar volumes with solvent compressibility is discussed.
1. Introduction Bernal and Van Hook’” have commented on recent efforts devoted to the study of aqueous carbohydrate solutions. Some of the interesting effects observed in aqueous sugar solutions, such as stereospecific solute-solvent interactions, have been attributed to structural features which are presumably unique to water.“’ To test this view we thought it appropriate to perform measurements in non-aqueous solutions because the comparison might highlight the effects peculiar to aqueous solutions. Also the measurements are of interest since non-aqueous solvents, especially dimethyl sulfoxide (DMSO), are being increasingly used in spectroscopic and chemical-reactivity studies involving carbohydrates.
2. Experimental D( + )-glucose, myo-inositol, IX- and P-methyl-D-glucosides were obtained from Sigma Chemical Co. High-purity glucose was supplied by Chemical Dynamics Corp., and galactose by Aldrich Chemical Co. About 0.3 kg of special-production high-purity sucrose was a gift of Professor Andrew Van Hook of Holy Cross College. All compounds were dried under vacuum at about 350 K for several days and used without further purification. ” Abstracted from part of a PhD. thesis of P. J. Bernal, University of Tennessee, 1984. * Present address: Chemistry Department, University of Oklahoma, Norman OK 73019, U.S.A. OOZl-9614/86/100969+
IO $OZ.OOjO
Ft 1986 Academic Press Inc. (London) Limited
P.J.BERNALANDW.A.VANHOOK
970
Gold label (greater than 99.9 moles per cent) dimethyl sulfoxide (DMSO) was obtained from Aldrich Chemical Co. Ethylene glycol, NJ-dimethyl formamide (DMF), and methanol (certified ACS grade), obtained from Fisher Chemical Co., were dried over molecular sieve and further purified by distillation under reduced pressure. Density and speed of sound measurements were made using a Mettler Paar DMA 601 HT vibrating densitometer ( f 0.002 kg. m- 3, and Nusonics Solution monitor SSM 6105 or CA 6080 respectively (LO.02 rn. s-r). The techniques have been described elsewhere and we have also quoted equations to obtain apparent molar volumes V,. @, or apparent molar isentropic compressibilities ks, 2,9 from the measurements.‘”
3. Results We have previously reviewed the influence of anomeric interconversion on the density of aqueous carbohydrate solutions.“) Other processes, like furanose-topyranose interconversion, might also affect densities even though the effect may be impossible to quantify because of the presence of competing equilibria. While the influence of these processes on the density of non-aqueous solutions is probably negligible, it is nonetheless important to specify which species are present. In water and in DMSO, glucose exists in two anomeric forms and at room temperature the equilibrium composition is about the same in the two solvents (0.36a-glucose + 0.64&glucose). The furanose and open-chain forms only make up about 0.003 mole per cent of the glucose present. (3) In DMF, however, the solution contains about 4.5 moles per cent of the furanose form at 343 K,(4) and in ethylene glycol the behaviour of glucose has been described as “abnormal”(5~ although we are not aware of any study about the equilibrium composition. The effect of temperature on the anomeric equilibrium is small.@ In water, galactose, unlike glucose, exists in more than two isomeric farms.(3) An aqueous solution of galactose at equilibrium is approximately (0.32a-D-galactopyranose + 0.63l3-D-galactopyranose and O.OScr- and (3-D-galactofuranose).(‘) In DMSO, furanose increases to about 0.15.@) In this case a temperature increase favors the formation of more furanose. Sucrose is a disaccharide and is not capable of the configurational changes common to monosaccharides. It can, however, form intramolecular hydrogen bonds and undergo rotation about the glycoside linkage.‘@ While the conformation of sucrose in aqueous solution is still a subject of controversy,“’ it is clear that disaccharide conformation does depend markedly on solvent.‘@ The relative densities (p -p:) were fitted with the equation: (P-d)
= ~(~,l~l~l)+~(~,l~l~l~2+C(~,l~,~l)3.
(1)
where n2 and n, are the amounts of substance of solute and solvent, respectively, M, is the molar mass of solvent, and p: and p are the densities of pure solvent and solution. The coefficients of equation (I), the variance 0’ of fit, and the number N of points per run are given in table 1.
6.o. (av,,,laT),. AND km OFNON-AQUEOUS
CARBOHYDRATES
971
TABLE 1. Coefficients of equation (1)
n21hMI) mol.kg-’
N
A
kg2.m-3.molF’
B
7 5 7 7 7 6 6 6 6 5 6
298.15 K 67.096 56.740 72.489 67.209 67.07 1 125.601 53.484 52.172 75.851 66.494 82.595
7 7 6 6 7 6 6
313.15 K 67.738 67.689 126.787 126.324 54.641 52.616 76.461
- 9.096 - 30.254 -27.348 -9.533 - 7.592 - 10.642
0.07 to 0.40 0.04 to 0.18
7 6 6
288.15 K 74.774 141.645 140.666
-9.872 -49.623 - 32.798
hX'OSe+DMF
0.07 to 0.40 0.04 to 0.18
r-Methyl glucoside + DMF Glucose +ethylene glycol r-Methyl glucoside+methanol
0.03 to 0.35 0.15 to 0.33 0.03 to 0.25
6 6 6 6 6 6 6
298.15 K 74.713 141.896 141.013 66.522 57.309 79.437 78.675
-9.397 -48.516 -33.348 -9.261 -6.300 - 18.783 - 10.146
6
313.15 K 79.345
- 11.879
G1ucose + UMso-d, Glucose-d, + DMSO Galactose + DMW
0.07 0.06 0.07 0.07
to to to to
0.65 0.29 0.49 0.65
Sucrose + UMSO a-Methyl glucoside + UMSO B-Methyl glucoside + UMSO Myo-inositol + DMSO Myo-inositol+ DMso-d, Myo-inositol-d, +DMSO
0.03 0.07 0.10 0.06 0.05 0.05
to to to to to to
0.49 0.60 0.64 0.30 0.30 0.18
Glucose + DMSO Galactose + DMW Sucrose + UMSO
0.07 to 0.65 0.07 to 0.65 0.03 to 0.49
z-Methyl glucoside + UMSO P-Methyl glucoside + uMS0 Myo-inositol+ DMSO
0.07 to 0.60 0.10 to 0.64 0.06 to 0.30
Glucose + UMF
GlucOSe
+ DMSO
SUCrOSC+l>MF
Glucose + DMF
a-Methyl glucoside + methanol 0.03 to 0.15
C
- 9.827 - 8.666 - 11.595 - 9.336
- 8.667 - 30.686 - 7.690 -9.291
10Jd -?1
kg3.m-3.mo]-’
kg2.m-h
1.189
0.24 2.76 0.2X 0.19 0.70 0.24 3.05 0.92 1.71 0.23 0.2X
3.163 0.724 4.538 1.995
- 9.920
- 9.668 - Il.841
1.65 2.74 I .02 4.22 0.28 3.00 0.05
- 8.838
4.089 1.931
2.74 0.9x 3.20
63.972
1.17 0.60 2.46 1.20 1.14 0.67 2.77
57.672
24.811
13.98
Values of V2.@were least-squares fitted with the equation:
vZ.9= 1/;1~+S,(n,/nIMI)+L,(n,lnIMl)2. Coefficients of equation (2) are reported in table 2. Comparison with results in the literature is possible only in three cases. Sears er ul.‘l”) have measured densities of glucose and sucrose solutions in DMSO at 298.15 K and the agreement with the present results is excellent. Dack”” has measured V2.,+ of sucrose solutions in DMF but with low precision (f 1 or 2 x 1O-6 rn3. mol-‘). The present results fall within his error band. While on the
972
P. J. BERNAL TABLE
2. Coefficients
of equation
AND (2):
W. A. VAN
V2,+ = l/,“Pm+Sv(n,/n,M,)+L,(n,/n,M,)*
106V” 2.4 m3,mol-’
HOOK
106S, kg.m3,mol-*
298.15 K GhlCOSC+DMK3
Glucose-d, Galactose
+ DMSO + DMso
SUCrOSCfDMSO
cc-Methyl glucoside + DMSO P-Methyl glucoside f DMSO Myo-inositol + DMSO Myo-inositol-d, + DMSO Myo-inositol+ DMso-d, GhCOSe+DMKJ-d,
108.56 108.74 108.42 207.67 132.61 133.92 101.11 101.12 101.01 108.55
1.4369 1.4512 1.3155 2.7114 0.5622 0.7386 2.0202 2.4179 2.2097 1.8516
0.29 1.79 0.39 3.53 2.09 0.70 0.14 1.66 0.46 2.80
1.5226 1.7757 2.5945 1.0685 0.8769 2.3418
I .30 0.60 0.78 2.03 0.34 0.16
313.15 K
a-Methyl glucoside + DMSO P-Methyl glucoside + DMSO Myo-inositol+ DMSO
108.56 108.59 208.07 132.96 134.45 101.21
GhCOSC+DMF SUCrOSCf DMF
106.24 202.9
Glucose + DMF Glucose + ethylene glycol a-D-Methyl glucoside + DMF a-D-Methyl glucoside + methanol
106.47 115.70 130.50 118.6 203.1
GhlCOSC+DM%l
Galactose
+DMso
&lCrOSC+DM%3
288.15 K 5.9793 29.894
-5.165 - 85.29
2.40 8.90
298.15 K
SUCl'OSC+DMF
6.0437 -0.6591 6.1491 17.493 28.916
- 5.848 -8.861 - 37.61 -78.21
1.70 3.90 1.30 3.30 9.40
313.15 K a-D-Methyl
glucoside
+ methanol
118.0
9.427
18.40
subject of error we emphasize that the limiting values VZy+reported in table 2 for DMF and methanol solvents are not as reliable as those in water and deuterated water,“) or DMSO, because the extrapolation to infinite dilution is complicated by a good deal of curvature in the non-aqueous solvents. More precise limiting values will require more density measurements on dilute solutions. To exemplify the quality of the results, plots of V,, + against nz/(nI M,) for glucose and galactose at 298.15 and 3 13.15 K in DMSO, and for glucose at 288.15 and 298.15 K in DMF, and at 298.15 K in ethylene glycol are shown in figure 1. Expressions relating isentropic compressibilities K~ to speeds of sound u and defining the apparent molar isentropic compressibility k,, 2, + have been presented earlier.‘” For non-electrolytes Hemmes et ~l.,“~’ Rao,‘13’ and Gucker and Haag”*’ have reported that the relative change in speed of sound in dilute solution is a linear
6s. (av,,,PT),, AND kz.+
OF NON-AQUEOUS
973
CARBOHYDRATES
FIGURE 1. Plots of V2,+ against (n,/n, M,) in different solvents at various temperatures: *, glucose in at 288.15 K; A, glucose in DMF at 298.15 K; 0. galactose in DMSO at 298.15 K; IJ, glucose in DMW at 298.15 K; n , glucose in DMSO at 313.15 K; 0. galactose in DMSO at 313.15 K: A. glucose in ethylene glycol at 298.15 K.
DMF
TABLE
3. Parameters
of equation
(3) for some solutions
Warn) m~s~‘~kg.rnol
’
7
102Q m.s-‘~kg.mol-’
K
Glucose + H,O’ Fructose + H,O Sucrose + H,O Myo-inositol+ H,O
68.51 kO.01 74.42 k 0.61 99.36kO.06 86.45 kO.01
4.61 5.08’ 6.78 5.90
288.15 288.15 288.15 288.15
Glucose+H,O Fructose + H,O Sucrose + H,O Myo-inositol + H,O Myo-inositol+ D,O
62.06 f 0.0 I 66.5120.47 91.42kO.07 79.15 k 0.08 92.34kO.3
4.15 4.44 c 6.11 5.29 6.59 4.91 5.21 7.92 3.58 3.73 3.43 3.73
298. I5 298.15 298.15 298.15 298.15
b
GhCOSC+DMW‘+
Sucrose + ~xw~ a-D-Methyl glucoside O-D-Methyl glucoside GhCOSe+DMFP
” For H,O du,(298.15 “~~(298.15
+ +
DMSO DMXI
72.83 +0.04 74.65 kO.05 113.56kO.05 53.13*0.01 55.34_io.o1 51.28_+0.01 54.27kO.01
solutions (see reference 1); b u&298.15 K) = 1400.59 rn. s- I; c Infinite K) = 1483.91 m.s-‘; ~~(313.15 K) = 1433.94m.s-*. K) = 1494.96m.s-‘; u,(313.15K) = 1455.56m.s-‘.
dilution
298.15 313.15 313.15 313.15 298.15 288.15 298.15 values,
974
P. J. BERNAL TABLE
4. Coefficients
of equation
AND
W. A. VAN
(4) for several
HOOK
compounds
10’5k” s. 2.4 m3.Pa-‘~mol-’
in non-aqueous
solutions 10-2 m6~Pa-*~mol-’
1015L m3.k$.mol’3.pam1 288.15 K
-22.12
GhlCOSCfDMF
9.642
- 5.992
2.75
-6.711
0.33 4.78 0.07 0.66
298.15 K -28.44 - 15.25 9.42 9.36
GhlCOSCfDMF
Glucose + DMSO a-D-Methyl glucoside P-D-Methyl glucoside
+ DMSO + DMKI
10.548 2.808 -0.017 0.033 313.15 K
-20.71 -21.28
GhlCOSC+DMKI
Sucrose + DMSO
3.742 1.745
5.62 0.56
function of molality: wu = Qh/n,M,)~ (31 and carbohydrates are no exception to this rule. In table 3 values of 6u/u and Q are reported for aqueous and non-aqueous solutions. These values are useful because Q has been regarded as a qualitative measure of solute-solvent interaction. Values of k,, 2, + were least-squares fitted with the equation: (41 plots of compressibility
ks.,,+ = k~,.,+S,(n,ln,M,)+L,(n,ln,M,)‘, and the coefficients are reported in table 4. Representative are shown in figure 2. 4. Discussion
The values for I& reported in this and the previous paper”’ vary widely with solvent. Some solvent properties which might influence I’,. ,+,are listed at 298.15 K in table 5. They include the cohesive energy density, AU,/V,. the internal pressure Pi, the molar volume V,, the isothermal compressibility tiT, and the dielectric constant -i5
I
-14-
E 72 -16-
I
+.+
+’
I
1
I
10
.-
-----+
I
9-@
z -,8‘+CI P-x -2 -2o-
I
I
I
0
”
rl /* 0
0.1
0.2
0.3
0.4 (nzln,
9I 0.5
8o
I
I
q u
I 0.1
u
u I 0.2
1 0.3
I 0.4
I 0.5
I 0.6
0.7
M,)l(mol.kg-‘)
FIGURE 2. Plots of kS.2.0 a g ainst (n,/n,M,) in different solvents: A. sucrose *, glucose in DMSO at 313.15 K: f. glucose in DMSO at 298.15 K: 0. P-D-methyl 298.15 K; 0. r-D-methyl glucoside in DMSO at 298.15 K.
in DMSO at 313.15 K; glucoside in DMSO at
b.r. (a%&T)p. AND ks.l.+OF TABLE
VMF Methanol
6. Apparent
molar
volume
at 298.15
536 548 172 518 477 297
as a function
of solvent 298.15 K
Solvent
55.93 39.89 18.07 71.33 77.44 40.74
892 1575 2302 705 582 874
compressibilities
for several
10”Vz~d(m3. glucose
3.7 4.1 4.6 5.3 6.5 12.6
Ethylene glycol Formamide Hz0 VMSO VMP
Methanol ’ Reference
K
J.rne3
3.7 4.1 4.6 5.3 6.5 12.6
VMSO
properties
CARBOHYDRATES
106p,
Pa-’
Ethylene Glycol Formamide HZ0
TABLE
5. Solvent
lo’%,
Solvent
NON-AQUEOUS
26; b reference
sucrose
compounds
at
mol-‘) myo-inositol
galactose
37.1 109.5 78.5 48.5 36.7 32.6
methylglucosides Z-D-
B-D-
133.2" 132.61 130.50 118.6
135.5 133.92
115.70 218.9h 211.45 207.67 203.1 187.0b
111.99 108.56 106.47 93.7' 11: ’ reference
110.7" 108.42
100.78 101.11
30.
E. The only clear correlation is that V2,+ decreases with or as shown in table 6 and plotted in figure 3 for all non-electrolytes in the table except sucrose. The table and figure show that V2,+ is not a simple linear function of K= in spite of the claim made by Dack (rl) for sucrose and urea. More precise results for urea”” clearly show curvature like that reported here for glucose and sucrose. I
136-
I
I yo +
12x7 5 E “’
120:
0
‘I
+
.s
‘- 112xci L. 5 104-
B n
0
** WII 2
I
4
I 6
,
/
8
I(1
,: 0 I2
IO”‘K ,/Pa? FIGURE 3. Results f, a-D-methyl glucoside; see tables 5 and 6.
for V’z.+ plotted against q.: 0, glucose; Cl, S-D-methyl glucoside. The compressibility
a. galactose; *, myo-inositol; is varied by changing solvents.
976
P.J.BERNALANDW.A.VANHOOK
The correlation between V,,, and i+ is better documented for electrolyte(‘6.‘7’ solutes than it is for non-electrolytes. However, in 1972 Hamilton and Stokes’15) noted the existence of the correlation for urea dissolved in six polar solvents and their approach was further explored by Dack. (rl) More recently French and Crisso8) refined ideas dating back to Eley”” and Uhlig(*” qualitatively to rationalize the correlation. Similarly Edward and Farrell’21.2’) using a model proposed by Stillinger (23’ have shown that a volume contraction of the solvent cavity results when a hydrophilic solute is dissolved in a polar solvent. The shrinkage is expected to be proportional to tiT because solvents with low compressibilities and high packing densities are not susceptible to further volume reduction due to hydrogenbond formation (solvation). If for hydrophilic solutes in polar solvents, the value of V2,$ reflects a process of cavity formation followed by volume contraction due to solventtsolute interaction, then one would expect V2,+ to depend on the magnitude of K~ in each of these two processes. Both cavity formation and volume shrinkage are expected to be easier in solvents of high compressibility. (18) The inverse correlation which is observed between V2,s and K~ indicates control by volume contraction instead of cavity formation. However, such arguments are applicable only to hydrophilic solutes dissolved in polar solvents, because otherwise there is no mechanism to produce marked volume contraction. For non-polar solutes exactly the opposite behaviour has been observed. Thus V,, + for benzene is higher in methanol than in water.‘24-26’ Such behaviour is expected of solutes where V2,+ is governed by cavity formation. Myo-inositol, for which there are only two points (in H,O and DMSO), appears to be an exception to the rule. This seems reasonable in view of the very large negative value of V2,4 for myo-inositol in water. (l) This indicates an unusually large increase in packing density around the solute. The volume reduction is apparently enough to compensate for the slightly higher compressibility of DMSO. If the correlation between V,. + and K~ is more than coincidental then one expects the temperature dependencies of V2.+ and K~ also to be related. (The results show the expansivities of carbohydrates in non-aqueous solution to be very low. The expansivity of cl-D-methyl glucoside in methanol is negative.) In pure DMSO, DMF, and methanol an increase in temperature leads to an increase in xr. which, according to the arguments above, should result in a reduction of V2,+ in the carbohydrate solutions. Of course this decrease will be countered by the effect of thermal expansion of solute and solvent. The two effects tend to cancel, the result being low values for (av2ya7-),, as observed. According to this argument, negative (aV,q?,/aT), in methanol results because K~ increases with temperature fast enough to more than compensate for the thermal expansion of solvent and solute. The discussion can be extended to aqueous solutions. For H,O below 322 K, KT decreases with temperature, and according to the model this should cause less cavity shrinkage and hence an increase in V2,+. That increase will be complemented by thermal expansion of solute and solvent and will result in large values for (a vi:+iaT),, as observed. It is also in agreement with the observation that the addition of OH groups to the solute renders (aV2T,/aT), larger.‘26, 27) Such simple arguments have, we think, even more explanatory power. Consider for example, the increase in slope observed at low temperatures in a plot of V2,* against T in aqueous
K,,, (W.,/aT),. AND ks.2.~OF
NON-AQUEOUS
CARBOHYDRATES
917
solutions. This is predicted by the present model, the temperature coefficient of compressibility of H,O increases rapidly as temperature falls. It also rationalizes the inverse H,O/D,O isotope effect on (av&@T), as a consequence of the inverse isotope effect on the temperature coefficient of K~ of these two solvents. Arguments of the type set forth in the preceding few paragraphs are an oversimplification. Other factors are at work including the very important and better documented structural effects unique to aqueous solutions. Still, it is comforting to see a simple model based on a well characterized solvent property produce a high degree of qualitative agreement in both aqueous and non-aqueous solvents. Finally in this section dealing with volumes it is appropriate to comment on changes in I’*,+ p reduced by stereochemical differences. Table 1 shows that 1/2.4 of c1-and @D-methyl glucosides are not identical in DMSO. The assumption is that such differences are a consequence of structural effects. Certainly they cannot be rationalized in terms of models like the kind above which are designed to rationalize differences for the same solute in different solvents, not for different solutes in the same solvent. It is interesting that the difference between the methyl glucosides is much smaller in DMSO than it is in water.““’ Values of k,, 2. + for glucose in DMSO and DMF, and for sucrose in DMSO, are large and negative indicating a high degree of solute-solvent interaction. Values of k&b for c1- and B-D-methyl glucosides are positive and nearly identical. Methyl . substltutlon thus renders k; 2, + more positive in DMSO than it does in water. The similarity of the values indicates that DMSO is not as sensitive as H,O in distinguishing between closely related molecular conformations. The temperature dependence of kz 2, + in the non-aqueous solvents is smaller than in H,O. This behavior is similar to that of (av2;,/aT),. Furthermore (i?k,, 2,a/i3T), is negative, as is the temperature coefficient of the compressibility of the pure solvents. Recently Criss and co-workers (l’) have reported that for electrolytes k,, 2.+ becomes more negative as the isothermal compressibility of the solvent increases. This observation is implied in the equation commonly used to calculate hydration numbers nh from compressibility measurements;(z8’ (5) ks . 2.+ = nh Vl*xT. Equation (5) is derived assuming an incompressible solvation shell and is therefore not expected to be quantitatively correct for non-electrolytes. However it is qualitatively useful in showing that the temperature dependence of k,,,,+ should reflect that for K~. Thus in non-aqueous solvents an increase in temperature increases K~ and results in a more negative k,,,+ In water exactly the opposite effect is observed. An increase in temperature lowers tiT rendering V, + more positive, as observed. The situation is complicated by the large difference in V,, of the solvents being compared. We have not presented enough results to establish a correlation, but for the two organic solvents of similar molar volume the expected trend is observed. The dependence of k; 2,+,on I+. can also be rationalized from the inverse relation between k’;, + and K= commented on previously; kg 2.,+is the negative of the pressure coefficient of V2y+: ki’t 2. $I = -(a h:ml+)T. (29) Therefore a negative kc 2,4 implies that
978
P. J. BERNAL
AND
W. A. VAN
HOOK
I/& must increase with pressure which can only occur if rcT decreases as the pressure is raised. This is the normal situation for most liquids including H,O, DMSO, and DMF. For most liquids l/~~ varies linearly with p provided that p is not too high. At 298.15 K in DMSO the glucose/glucose-d, isotope effect, (AV,Jm = {VT&H)-VT+(D)} = -0.18 x low6 m3.mol-‘, as compared with the effect in H,O/D,O which varies from 0.41 to -0.18 x 10e6 m3.mol-’ between 288.15 and 328.15 K.(r) This is just the effect one would expect were solvent structure making a significant contribution in the aqueous but not in the non-aqueous case. (The structural contribution in water is expected to fall markedly as temperature increases.) For myo-inositol both solute and solvent isotope effects on limiting apparent volumes at 298.15 K were determined in DMSO. The solute effect is negligible, the solvent effect positive, but small, (AV,,,)m = 0.1 x lO-‘j rne3. mol-‘, as compared with (AV’,,,)m in H,O/D,O where effects of 0.88 (288.15 K) and 0.56 x 10m6 (298.15 K) are observed. Again the isotope effect is much larger in aqueous solvent, generally regarded as more structured. This research was supported by the National CHE 81-12965 and CHE 84-13566.
Science Foundation
under grants
REFERENCES 1. Bernal, P. J.; Van Hook, W. A. J. Chem. Thermo&namics 1986, 18. 955. 2. Suggett. A. Water-A Comprehensive Treatise, Vol. 4. Franks, F.: edition. Plenum Press: New York. 1973. 3. Wolfram. M. L.; Tipson, R. S.: editors. Advances in Carbohydrate Chemistry, Vol. 24. Academic Press: New York. 1%9. 4. Reine. A.; Hevding. J. A.; Kjolberg. 0.; Westbye. 0. Acfa Chem. Stand. 1974, 28, 690. 5. Dzhundubaev, K. D.; Kozhakhmetova. R. I.; Sarybaeva, R. I. Izv. Akad. Nuuk. Kirg. SSR 1966,69. 6. Franks, F. Phil. Trans. Roy. Sot. London B 1977, 278, 581. I. Shallenberger, R. S.; Birch, G. G. Sugar Chemistr.v AVI Publishing: Westport. CT, 1975. 8. Mackie. W.: Perlin. A. S. Can. J. Chem. 1966, 44, 2039. 9. Mathlouthi, M.; Vinhh Luu. D. Carbohydrate Res. 1981, 91. 113. IO. Sears, P. G.; Siegfried, W. D.; Sands, D. E. J. Chem. Eng. Dafa 1964, 9. 261. I I. Dack. M. R. Aust. J. Chen7. 1976, 29, 779. 12. Hemmes, P.; Mayevsky. A. A.; Buckin, V. A.: Sarvayan. A. P. J. Phw. Chm7. 1980, 84, 699 13. Rao, M. R. Current Sri. 1940, 9. 534. 14. Gucker. F. T.: Haag, R. M. J. Acoust. Sri. Am. 1953, 25. 470. 15. Hamilton, D.; Stokes, R. H. J. Soln. Cl7em. 1972. 1. 213. 16. Millero. F. J. Chem. Rev. 1971, 71, 147. 17. Lankford, J. T.; Holladay. W. T.; Criss. C. M. J. Soln. Chem. 1984, 13, 699. 18. French. R. N.; Criss, C. M. J. Soln. Chem. 1981, 10. 713. 19. Eley, D. D. Trans. Faraday Sot. 1939, 35, 1281; 1939, 35. 1421. 20. Uhlig. H. H. J. Pl7.w. Chem. 1937, 41, 1215. 21. Edward. J. T.; Farrell, P. G.: Shahidi, F. J. Chem. Sot. Faraday Trans. Il977, 73, 705. 22. Edward. J. T.; Farrell, P. G. Can. J. Chem. 1975, 53, 2965. 23. Stillinger, F. H. J. Soln. Chem. 1973, 2. 141. 24. Masterson, W. L. J. Chem. Phvs. 1954, 22. 1830. 25. Dutta-Choudhury. M. K.; Miljevic, N.; Van Hook, W. A. J. Phys. Chem. 1982, 86. 171 I. 26. Franks. F.; Ravenhill. J. R.; Reid, D. S. J. Soln. Chem. 1972, I. 3. 27. Franks. F.: Quickenden, M. A. J.; Reid, D. S.: Watson, B. Trans. Faraday Sot. 1970, 66. 582. 28. Stuehr. J.: Yeager, E. Physical Acoustics, Principles and Merhods. Masson. W. P.: editor. Academic Press: New York. 1965. 29. Gucker. F. T. Chem. Ret,. 1933, 33. 111. 30. Longsworth, L. G. J. Phys. Chem. 1%3, 67, 689.