2345
Partial Molar Volumes of Nonionic Solutes
Contribution of Hydrogen Bonds to the Partial Molar Volumes of Nonionic Solutes in Water Seijl Terasawa,* Hidenori Itsukl, and Satoshi Arakawa Department of Chemical Engineering, Faculty of Engineering, Tokyo Institute of Technology,Ookayama, Meguro-ku, Tokyo 152, Japan (Received September 12, 1974; Revised Manuscript Received July 25. 1975) Publication costs assisted by Tokyo Institute of Technology
Partial molar volumes of 1,2-dimethoxyethane, diethylene glycol dimethyl ether, ethyl sulfide, ethyl, npropyl, and allyl bromide, methyl, ethyl, n-propyl, n-butyl, n-pentyl, and allyl alcohol, and ethylene, trimethylene, tetramethylene, and pentamethylene glycol were measured in water at 25.0°C. Values obtained were correlated with the Bondi's van der Waals volume. It was shown that the partial molar volume is composed of the van der Waals volume and the void partial molar volume. An experimental equation for the partial molar volume was proposed, which includes three terms, i.e., the van der Waals volume, the void partial molar volume of a hydrocarbon having the same van der Waals volume as the solute, and the solute-solvent interaction partial molar volume. It was shown that the values of the three terms can be determined experimentally. Through the discussion of the solute-solvent interaction partial molar volume for the alcohols and glycols, the contribution of hydrogen bonds between the solutes and the surrounding water molecules to the partial molar volume was estimated.
Introduction It is well known that the formation of a hydrogen bond results in the decrease in the molar volume due to shortening of the interatomic distance. Pimentel and McClellanl showed that the molar volumes of hydrogen bonded compounds are smaller than those of nonassociated compounds of similar molecular size. Fishman and Drickamer2 measured infrared spectra of n-butyl alcohol in carbon disulfide under 1,5820, and 11,300 atm, and estimated the average volume change of the association from 1to 5820 atm t o be -4.6 ml/mol from the effect of pressure on the characteristic hydrogen bond absorption. Kabachnik, Yakushkina, and Kislyakova3 measured the effect of pressure on the keto-enol tautomerism of ethyl acetoacetate in various solvents, and found that the volume change of the tautomerism in water is -7.5 ml/mol, while in the other organic solvents the values are in the range from -3.1 to 3.2 ml/mol. They interpreted the smaller volume change in water as due to the formation of hydrogen bonds between the enol form of the ester and the surrounding water molecules. Whalley4 mentioned that the formation of a hydrogen bond almost certainly causes a decrease of volume, but this may sometimes be compensated by the formation of a fairly open structure if the forces are strongly directed. The purpose of this study is to attempt to clarify the contribution of hydrogen bond formation to the partial molar volume of nonionic solutes at infinite dilution in water. Experimental Section Materials. Methyl, ethyl, n-propyl, n-butyl, n-pentyl, and allyl alcohol used were commercial guaranteed reagents, purified by distillation, refluxed on freshly burnt caustic lime, and redistilled. The samples thus purified were refluxed further on aluminum amalgam prepared from aluminum and a small amount of mercuric chloride: and were rectified two times. All the above preparations were performed in a stream of nitrogen at atmospheric or
reduced pressure thus excluding carbon dioxide and moisture. The vapor phase chromatography of each purified sample showed a single peak. The ethylene, trimethylene, tetramethylene, and pentamethylene glycol used were commercial reagent grade samples, purified by drying with anhydrous sodium sulfate and distilling fractionally under reduced pressure in a dry nitrogen stream. The VPC of each sample showed only a single peak, but the water content, less than 0.02%, was determined by the Karl Fisher titration method. The commercial guaranteed reagents of 1,2-dimethoxyethane, diethylene glycol dimethyl ether, and ethyl sulfide were used without further purification. The VPC of each of these showed a single peak. Ethyl, n-propyl, and allyl bromide were commercial extrapure reagents, which were used after purification by washing with water, drying with anhydrous potassium carbonate, and distilling. Analysis of each sample by VPC showed less than 0.01% impurity. Water was distilled and passed through a deionizing resin column, and used for the experiments after redistillation in an apparatus which excluded carbon dioxide in the atmosphere. The conductivity of the water used was less than 1.5 X lo-' 0-*cm-l at 25OC. Measurements of Partial Molar Volume. The apparatus and method for the determination of partial molar volumes were essentially the same as those described by Hyne and his collaborators.6 The dilatometer, having a capacity of about 200 ml, with a capillary of 1 mm i.d. and with a microsyringe for solute injection, was dipped in a water thermostat regulated at a temperature of 25.0 f 0.002°C. The amount of solute injected from the microsyringe into the dilatometer was accurately determined from the density of the solute at the room temperature. The apparent molar volume, &, of each solute was calculated by the following equation = 6V/n where 6V is the increment of volume caused by an addition of n lnoles of a solute. The Journal of Physical Chemistry, Vol. 79, No. 22, 1975
2346
S. Terasawa, H. Itsuki, and S. Arakawa
&'s for the alcohols, glycols, 1,2-dimethoxyethane, and diethylene glycol dimethyl ether, all of which have high solubility in water, could be measured even within 5 min after the injection, since the & observed was independent of time. On the other hand, for the solute having a low rate of dissolution, such as ethyl sulfide and alkyl bromides, the value observed after the injection, &Obsd, was found dependent on time, as shown in Figure 1. &Obsd just after the injection was close to the molar volume of the pure solute, and steeply decreased with increasing the running time from 5 to 30 min. After a steep decrease, &Obsd for ethyl sulfide and ethyl or n-propyl bromide reached a stationary value, but for allyl bromide it continued to decrease slowly. For the alkyl bromides, such decreases of &obsd might be attributable to the progress of their hydrolysis. When the conversion of the solute hydrolyzed is 0, may be expressed by the intrinsic value of & and the volume change of the hydrolysis, Avo, as follows: &Obsd
=
85
? I
0
vo.
Results a n d Discussion Partial Molar Volumes. The obtained values of Po for the ethers, sulfide, alkyl bromides, alcohols, and glycols a t 25.0°C in water are tabulated in Table I. The values for methyl, ethyl, n-propyl and n-butyl alcohol, and ethylene, trimethylene, and tetramethylene glycol are in good agreeThe Journal of Physical Chemistry, Vol. 79,No. 22, 1975
2
9
I
L
o
5
time,hr molar volume
+ PAV0
Then, the change in the concentration of hydrogen bromide, one of the products, was followed by the conductimetric method by using a pair of platinum electrodes inserted into the dilatometer, simultaneously with the determination of &obsd. (3 at the respective running time could be determined from the concentration of hydrogen bromide for allyl bromide, as shown in Figure 1 (the initial concentration of the solute; about 0.002 M ) . As a first approximation, the value of & was determined by the linear extrapolation of the &Obsd vs. time curve to the time of injection (0 = 0 ) within the region of the slow decrease. A v o was calculated from $v thus estimated and Vo of water,7 allyl alcohol (Table I), and of hydrogen bromide.s &'s calculated by subtracting PAVo from &obsd at the respective times were found constant, as shown in this figure, and agreed with the value estimated by the first approximation above, within an experimental error of f O . l ml/mol, so that this value was adopted as &. In the cases of both ethyl and n-propyl bromide, @ at 24 hr after the injection was less than 2.5%. Therefore, the steep decrease of &obsd just after the injection is not attributable to hydrolysis but to the volume decrease accompaning mixing. It was found that ethyl sulfide, which is actually not hydrolyzed in the neutral aqueous solution, showed a similar steep decrease of &Obsd. Hence, &Obsd during the stationary state is adoptable to the value of & as a first approximation. Since A v o was calculated to be -4.9 ml/mol for ethyl bromide and -5.2 ml/mol for n-propyl bromide, bAVo during each stationary state was found to be less than -0.13 ml/mol, which is comparable to the experimental error. Therefore, the value during the stationary state was adopted as dV in the homogeneous solution. The cumulative injection of a solute either to the same solvent or to a solution with a known concentration was carried out. The value of dV remained constant in the concentration range from about 0.001 to 0.01 M. The obtained value of +v is equal to the partial molar volume of solute at the infinite dilution,
1
110
5 ,-+---0
10
20
go
bo
310
900
t i m e , min
Figure 1. Time dependence of
&Obsd
and 0.
TABLE I: Partial Molar Volumes (p)of Ethers, Sulfide, Alkyl Bromides, Alkyl Alcohols, and Glycols in Water at 25.0"C -
Vo,ml/mol
Solute
Other This work works
1,2-Dimethoxyethane Diethylene glycol dimethyl ether Ethyl sulfide Ethyl bromide n- Propyl bromide Allyl bromide Methyl alcohol Ethyl alcohol n- Propyl alcohol n- Butyl alcohol n- Pentyl alcohol Allyl alcohol Ethylene glycol Trimethylene glycol Tetramethylene glycol Pentamethylene glycol a
95.6 131.6 99.5 66 .7 82.2 77.6 38.1 55.1 70.3
85.9 102.3 64.3 55.6 71.6 88.2 104.1
38.68" 55.08" 70.66" 86.676 55.4= 71 .6c
88.2~
Reference 9. Reference 10. Reference 11.
ment with those in the literatureg-ll determined by density measurement. Correlation of with Carbon Number. The additive property of and the interaction between a solute molecule and the solvent molecules have been discussed in terms of the measurements of Vo for nonelectrolytes in
vo
Partial Molar Volumes of Nonionic Solutes
2347
water.gJOJ2-14 Alexander: for instance, assumed the additivity of for groups, and estimated the contributions for of CH2, CH3, and CHzOH by using the increment of for a series of n-alkyl alcohols and the value of for trimethylene glycol. On the other hand, the solute-solvent interaction has been examined by means of either the comparison of among the solutes with a same carbon number12 or that between ITo for the systems of the solutions and the molar volume for the pure system of the solute itself.1%13714 Plots of obtained in the present work against the carbon number are shown in Figure 2, including the values for methane, ethane, and propane obtained by M a ~ t e r t 0 n . l ~ For the individual series of hydrocarbons, n-alkyl alcohols, or glycols, are linearly related to the carbon number. If the additivity holds for and if the contributions of the terminal groups, such as, CH3 and CHzOH, are independent of the carbon number, the slopes of the straight lines in this figure must correspond to the increment of CH2 in VO. By way of trial and error, the contributions of CH2, CH3, and CH20H were evaluated in the four cases as follows: (case 1) after the contribution of CH2 for the hydrocarbons is estimated from the slope, for ethane and propane are used to calculate the contribution of CH3 for the hydrocarbons; (case 2) the contribution of CH2 for the glycols estimated from the slope is used to calculate that of CH20H for the glycols; (case 3) the contribution of CH2 for the alcohols is estimated from the slope for the n-alkyl alcohols, and then that of CH3 for the hydrocarbons from case 1 is used to evaluate that of CHzOH for the alcohols; (case 4) the contribution of CHzOH for the glycols from case 2 is used to calculate that of CH3 for the alcohols. The contributions of these groups to thus evaluated, are summarized in Table 11. The contribution to of CH2, CH3, or CHzOH shows little difference for the hydrocarbons, glycols, and n-alkyl alcohols; an additive property for these homologs fairly appears on The contribution of CHzOH for the n-alkyl alcohols and glycols is greater than that of CH3, which seems to be inconsistent with the expectation that the smaller contribution of CH20H may be present because of the associative property of OH. In addition, comparing Poamong the solutes having the same carbon number, we can see from Figure 2 that the are in the order ethyl sulfide ethers N alkyl bromides > glycols > alcohols > hydrocarbons. It may be difficult to relate this order in to the molecular properties of the solutes. Therefore, even though are correlated with the carbon number, no further information may be obtained. van der Waals Volume and Void Partial Molar Volume. It has been considered that Po’s for ions in solutions are composed of the crystal volume and the other contributions (the disorder, electrostriction, and cage effects).s With respect to for nonelectrolytes, Franks and his coll a b o r a t o r ~pointed ~~ out that Poreflects mainly the intrinsic volumes of the solutes and usually contains only a minor contribution due to changes in molecular interactions. It was, however, not clarified what was used as the intrinsic volume. Recently in a study on the volume changes for ionization in water, King16 used the crystal volumes for ions and Bondi’s van der Waals volumes for nonelectrolytes. Similarly in the present text, the authors will attempt to adopt the van der Waals volume to a measure of the intrinsic volume. The van der Waals volume has been defined by Bondi17 as the volume occupied by the solute molecule itself, i.e., the volume impenetrable to the solvent molecules
vo
v
vo
140
v
120
100
v
vo
v’s
80
60
$ *
LO
IC
vo,
vo”s
v,
vo’s
vo’s
vo
2
3
,
I
I
4
5
6
carbon number
Flgure 2. Correlation of partial molar volume (i“)with carbon number in water at 25%: (1) methane; (2) ethane; (3) propane; (4) 1,2dimethoxyethane; (5) diethylene glycol dimethyl ether; (6) ethyl SUIfide; (7) ethyl bromide; (8) n-propyl bromide; (9) allyl bromide; (10) methyl alcohol; (11) ethyl alcohol: (12) n-propyl alcohol; (13) n-butyl alcohol; (14) *pentyl alcohol; (15) allyl alcohol; (16) ethylene glycol; (1 7) trimethylene glycol; (18)tetramethylene glycol; (19) pentamethylene glycol: (4-19) this work; (1-3) results reported by Ma~terton.’~
TABLE 11: Contributions to P of CH2, CH3, and CHzOH Groups
V o ,ml/mol
v
vo.
vo
1
Case Case Case Case
1 2 3
15 .O
4
115.9
25.8
16.2
27.8 28.8 (27.8)
(25.8) 26.8
with a certain thermal energy. Bondi calculated the van der Waals volume, V,, for a variety of molecules by assuming that the atoms in a molecule are spheres with the intermolecular van der Waals radii estimated from crystallographic data, and that a molecule or a functional group is an assembly of the covalently bonded sphere segments. From Bondi’s tables, the value of V, for a solute with no hydrogen bonds can be calculated as the sum of the values of the functional groups of which the solute molecule consists. vo’s are plotted against V , as shown in Figure 3, which again includes the results for the hydrocarbons.15 In Figure 2, Poof allyl alrohol (no. 15) is out of position from the line of the n-alkyl alcohol, Le., its Po value is smaller than n-propyl alcohol (no. 12) even though the former has the same carbon number, while for allyl alcohol is on the straight line for the n-alkyl alcohols in Figure 3. Similar result is obtained for allyl bromide (no. 9). of ethyl sulfide (no. 6),which is greater than that of 1,2-dimethoxyethane (no. 41, tetramethylene glycol (no. 181, and n butyl alcohol (no. 13) in Figure 2, is found on the line for the hydrocarbons as well as the ethers. The simple regularity in Figure 3 compared to that in Figure 2 may show that V, is much more useful than the carbon number in the
v
v
The Journal of Physical Chemistry, Vol. 79, No. 22, 1975
2348
S.Terasawa, H. Itsuki, and S. Arakawa
TABLE 111: v v " l d and v v ( , l d / V w forCHZ,CH3,and CH20H Groups
14@
Vvoid,
Case 1 Case 2
alcohols
Case 4 Case /'
mi/moi
CH,
CH,
4.8 6.0
12.1
1 5'7
(12.1) 13.0
'void/
CHZOH 9.5 10.0 (9.5)
1
CH,
CH,
0.47 0.59
0.89
Oe5'
/' /' /'
t L,/'
/' /*" I
L
0 0
10
20
30
vY ,
LO
59
60
70
80
ml/rnol
ed. The results are compiled on Table 111. v v o i d / V w of CHzOH for the alcohols and glycols are smaller than that of CH3. It is concluded from these results that the more hydrophilic the group is, the smaller v v o i d it creates. Franks and his collaborator^^^ compared Poamong solutes having similar molecular dimensions and conformations in order to examine the contribution to of the molecular interaction. They described that in the comparison of between furfuryl alcohol and 2-methyltetrahydrofuran the increment due to OH is much smaller than due to CH2. When the alcohols and the hydrocarbons having a same carbon number are compared in the present results (Figure 2), the difference of p, for example, between ethyl alcohol (no. 5) and ethane (no. 2), 3.9 ml/mol
measure of Po,and furthermore shows that V, may be in closer relation to than the carbon number. Pofor a series of the hydrocarbons, alcohols, or glycols can be expressed as the following linear equation with respect to v,:
vo
vo= aV, + b
(1)
where a and b are constants. The ethers and sulfide seem to behave as the hydrocarbons in water. The values of the constants obtained are as follows: a = 1.534 and b = 9.9 ml/mol for the hydrocarbons (including the ethers and sulfide), a = 1.558 and b = 4.5 ml/mol for the alcohols, and a = 1.585 and b = -2.3 ml/mol for the glycols. In the case of alkyl bromides a similar linear relation seems to exist, but only three data are available in the narrow range of V,, so that the constants, a and b, are not estimated. If V, is assumed to remain unchanged in water, the difference, PO - V,, may be the volume of the actual void space created by the addition of 1 mol of the solute to the solvent. Therefore, this is referred to here as the void partial molar volume, v v o i d . Pois expressed as
vo= v w + v v o i d From the point of view that v0 consists of v,
(2)
and v v o i d , the following information is given on the v v o i d . If it can be assumed that the contributions of CH2, CH3, and CH2OH to PO are constant and independent of the carbon number for the respective series and that the slope corresponds to the increment of for an addition of the CH2 group to the molecule, v v o i d for these groups of the solute molecules can be determined by subtracting V,of the corresponding groups from their_contributions to VO in Table 11. The ratio of v v o i d to v , , Vvoid/Vw, can also be calculat-
vo
The Journal of Physical Chemistry. Vol. 79, No. 22, 1975
v,EtOH
- vO,CzH6 = ( VwEtOH
Figure 3. Correlation of P with the Bondi's van der Waals volume (V,.,) in water at 25.OoC: solute numbers in Figure 2.
CH,OH
0.52 (0.89) 0.55 0.95 (0.52)
vo
/
V 'I
vo
- VwCzH6) + ( vvoidEtOH - vvoidCzH6)
is divided into the differences of V,, 4.6 ml/mol, and of vvoid, -0.7 ml/mol. It is concluded that the order of shown in Figure 2, glycol > n-alkyl alcohols > hydrocarbons, is mostly determined by V, for these solutes. The comparison of vo's a t a same V, (Figure 3) will be examined in the following. First, the difference of between two solutes, A and B, is modified as
vo
vopA - POpB= ( VwA- VwB)+ ( vvoidA - v v o i d B ) If VWA= VWB,the difference of vois equal to that of v v o i d vo,A- Po*B= ( v v o i d A - vvoidB) VwB Here, vo'sare compared a t a certain value of V,. For exVwA=
ample, when p of ethyl alcohol (no. 5) is compared with that of the hydrocarbon, it is not able to compare ethyl alcohol directly with ethane (no. 2) but with the imaginary hydrocarbon that has the same van der Waals volume as ethyl alcohol. p of this imaginary hydrocarbon is regarded as being on a straight line for the hydrocarbons determined experimentally. In such comparison, v 0 of ethyl. alcohol is found to be smaller by 3.7 ml/mol than that of the hydrocarbon, and v v o i d of ethyl alcohol to be smaller by the same quantity than of the hydrocarbon. v v o i d for the solutes are plotted against V, as shown in Figure 4, which is essentially the same as Figure 3, since it corresponds to the upper part of the straight dashed line (VJ= V,) shown in Figure 3. By comparing two kinds of solutes a t a certain V, in Figure 3 or 4, the following clear facts are found. or v v o i d of the alkyl bromides are slightly smaller than of the hydrocarbons (the ethers and sulfide). The alcohols are smaller than the hydrocarbons. The glycols are further smaller than the alcohols. It is noted that these facts suggest the more hydrophilic molecule creates the smaller vv_oid. The correlation of Vvoid with the carbon number, as plotted in Figure 5, is also expressed by a few linear lines.
vo
2349
Partial Molar Volumes of Nonionic Solutes
\alcohol
the difference of V, between ethane and the imaginary hydrocarbon for ethanol, which is not due to the difference of molecular properties of these solutes. Therefore, such a direct comparison of v v o i d for two kinds of solutes having different V, is inadequate to discuss the difference of the molecular properties. KinglG attempted to correlate the packing density ( V,/ Po)with V, in order to examine how ions and molecules are accomodated in cavities of liquid water. The van der Waals volume of alcohols, however, were used after the hydrogen bond corrections (-VH). Therefore in his figure, the packing density, (V, - V H ) / P O > ~ Oof~ an , alcohol was plotted against V, - VH, and then it was compared with the packing density, (V, - V H ) / ~ O , of ~ ~a ,hydrocarbon having V, - VH. This treatment means that is composed of V, - VH and vv,,,dRoH(Vw) + VH ( v w and PvoidRoH(Vw) in Figure 3 or 4) and is composed of - VH and PvoidHC(Vw-VH) (the same as in Figure 3 or 4), where the superscripts in the parentheses refer to the respective van der Waals volumes. Thus, he directly compared PvoidRoH(Vw) VH with ~ v o i d H c ( v w - v H ) . NOW,this direct difference between them can be expressed as follows: (PvoidROH(Vw) + vH)- v v o i d H C ( V w - V ~ ) =
v0sRoH
line
v0rHC
v,
+
Figure 4.
Correlation of
with V,.,: solute numbers in Figure 2.
( vvoldROH( Vw)
- vvOldHC(Vw)) + ( v v o i d H C ( Vw) vvvoidHC(Vw- VH))
n-alkyl alaohols
3
1
4
5
6
oarban number
Figure 5.
Correlation of
vvold
with carbon number.
Vvoid’S are in the order, hydrocarbons > n-alkyl alcohols > glycols, corresponding to the hydrophilic molecular properties, while for the ethers, sulfide, and n-alkyl bromides the Vvoid’S are greater than the hydrocarbons. In addition, allyl alcohol and bromide are smaller than n-propyl alcohol and bromide,, respectively. Furthermore, comparison of v v o i d of ethyl alcohol with that of ethane will be shown as follows. When the imaginary hydrocarbon having the same van der Waals volume as ethyl alcohol is denoted as HC(Et0H) PvoidEtOH - vvoidCzH6 =
-
+
( vvoidEtoH vvoidHC(EtoH)) VwEtOH= VwHC(EtOH) ( iivoidHC(EtoH) vvoidCZHs) VwHC(EtOH)tv,CZH~
-
The first term on the right-hand side of this equation (-3.7 ml/mol) corresponds to the decrease of v v o i d by changing the hydrophobic hydrocarbon into hydrophilic ethyl alcohol. However, the second term (3.0 ml/mol) refers to the difference of Pvoid between two hydrocarbons caused by
+ VH
The first term on the right-hand side is due to the difference of the molecular properties of these solutes proposed in the present paper. The second term depends on the difference of the interactions of two hydrocarbons with water. The third term depends on the hydrogen bond interaction between alcohol molecules. Hence, the direct difference includes the contributions other than due to the difference of the molecular properties. This is the reason why in his figure the packing densities of the alcohols appear in close proximity to those of the hydrocarbons. Hydrocarbons as Standard Materials and Solute-Solvent Interaction Partial Molar Volumes. The hydrocarbons are considered to be an appropriate standard materials to compare v v o i d or Bo.Organic compounds are the derivatives from the hydrocarbons. In addition, the hydrocarbons do not interact strongly with solvent water molecules. Hence, the solute-solvent interaction partial molar volume, V,-s(HC),is defined here as the following equation, so that v v o i d (or Po)of a solute is compared with that of the hydrocarbon, PvoldHC (or Po,HC), having the same van der Waals volume, VWHC,as the solute V,. vs-s(Hc)
= ( vvoid -
vvoldHC) Vw=VwHC
- (9’ - P ~ H C ) ~ w = ~ w H C
(3)
Since there exists generally no hydrocarbon that has the same VwHCas the solute v;lvoidHC (or Po,HC) for a solute is interpolated from a plot of v v o l d (or 9’) vs. for a series of hydrocarbons which can be obtained experimentally. I t is considered that though the relation between v v o i d and V, for homologous solutes has a different linearity from that for-the hydrocarbons or even shows a nonlinear correlation, VS-s(HC)can be evaluated in the same manner. The physical meaning of may refer to the additional void partial molar volume which is caused by the hydrophilic molecular property of a solute, compared to the hydrocarbon with exactly the same dimension as the solute. Therefore, may become one of the measures for solute-solvent interactions. In addition, when the various sol-
v,,
v,
v,+,(HC)
vsls-s(HC)
The Journal of Physical Chemistry, Vol. 79, No. 22, 1975
S.Terasawa, H. Itsuki, and S. Arakawa
2350
vs-S(HC)
vents are used for a certain solute, must depend on the differences of the molecular properties of solvent. From eq 2 and 3, can generally be expressed by the following equation:
vo
vo= + v w
vvoidHC
+ P,-,(HC)
The values of the three terms on the right-hand side can be determined as follows. The term, vvoidHC, can be known by the interpolation from the experimental values of for the hydrocarbons as mentioned above. When the plot of pvoid (or Po)against V , for the hydrocarbons is approximated to a straight line, it can be calculated more easily by the following equation (from the eq 1)
vo
vvoidHC
TABLE IV: V,, v v v o , d H C ,and Vs-s(HC) of Ethers, Sulfide, Alkyl Bromides, Alkyl Alcohols, and Glycols in Water at 25.0"C
- v, + bHC
= (aHC 1)
where aHC and bHC are constants for the hydrocarbons. Therefore, the term can be determined from the measurable values of and vvoldHC, and the value of V, calculated by Bondi's method. Furthermore, when the slopes of the plots of Pvoid (or Po)against are equal for a series of hydrocarbons and of homologous solutes, and then the assumption is valid that the contributions of CH2, CH3, and a functional group attached to the solute molecules are constant and independent of the carbon number, Vs-8(Hc) can be regarded as the difference of Pvoid (or Po) between the functional group and the part of hydrocarbon molecule (part of CH3) that is imaginary but has the same V, as the functional group, and can represent the property of the functional group itself. The values of V,, vvoidHC, and for each solute in water a t 25°C thus determined are tabulated in Table IV. From this table, it is concluded that while the absolute values of Vs-s(Hc) show trends of slight decreases with lengthening the alkyl group or adding a methylene group for the alcohols and glycols, the average values are -4.4 and -9.6 ml/mol, respectively. For the alkyl bromides, P,-,(HC)'~ are as small in the absolute values as -1 to -2 ml/mol. for a Many authors have discussed the behavior of certain solute in various s ~ l v e n t s . ~ ~On - ~ the ~ J *other hand, there are fewer papers trying to examine the behavior of ii0 for solutes in a certain solvent even qualitatively, as mentioned before. The discussion in the present paper is considered to develop a new method that can quantitatively examine how the molecular property of a solute in a certain solvent reflects on the value of V. Electrostriction. As has been mentioned frequently, the volume change by the electrostriction, Pes,is considered to be included in the value for vS-,(HC) of the alcohols and glycols, naturally. P,, for a spherical dipole can be estimated by the following equationlg derived from the Kirkwood equation: aDpe' =-Nw2 302 r3 ( 2 0 + 1)2($)T where I.L is the dipole moment, r the radius of spherical dipole, and D the dielectric constant of the solvtnt (water). The probable maximum absolute value of V,, for the alcohol may be calculated by using a spherical model, V, = 4Nnr3/3, and r of methanol which is the smallest among those of the alcohols. The estimated value of p,, is -0.02 ml/mol, which is much less than the-experimental error in the measurement of Po. Therefore, V,-s(HC)'~for the alcohols and glycols are not due to the electrostriction, substantially.
v,-,(HC) vo
v,
v,-,(HC)
The Journal of Physical Chemistry, Vol. 79, No. 22, 1975
1,2-Dimethoxyethane 55.2 39 ' 4 1'0 Diethylene glycol di79.4 52 '3 -0.1 methyl ether Ethyl sulfide 58.6 41., -0 '3 Ethyl bromide 38.3 30.4 -2 .o n- Propyl bromide 48.5 35., -2 Allyl bromide 45 .O 33 '9 -1.3 Methyl alcohol 21.7 -5 .I 21 '5 Ethyl alcohol 31.9 26., -3.7 n-Propyl alcohol 42.2 32.4 -4 '3 n- Butyl alcohol 52.4 37 '9 -4 '4 n- Pentyl alcohol 62.6 43 '3 -3 '6 38.7 Allyl alcohol 30., -5 .o 36.5 Ethylene glycol 29.4 -10 '3 46.8 Trimethylene glycol 34., -10.1 Tetramethylene glycol 57 .O 40., -9 .I Pentamethylene glycol 67.2 45., -8 - 9 a Tables X v and XVI in ref 1 7 . b Experimental equation for hydrocarbons: V v o , d H C = (uHC- l ) V w + b H C . c Vs.s(HC' = - V -
.,
W
VWldHC.
Hydrogen Bonds. The volume change due to the formation of a hydrogen bond has been calculated as -1.08 ml/ mol by Bondi.17 The division of for a hydroxyl group by this value may correspond to a number of the hydrogen bonds of 4.2. Whalley4 and WealeZ0suggested that there is almost certainly a volume decrease due to the decrease of the internuclear distance (such as calculated by Bondi), but if hydrogen bonds are strongly directed, their formation may create a fairly open structure and the net volume contraction may be negligible. This leads to a number of hydrogen bonds more than 4.2. However, since the hydroxyl group of an alcohol molecule has one hydrogen atom and two lone pairs of electrons, it might not be expected to form more than three hydrogen bonds with water. Therefore, the observed must include additional causes of the volume decrease. Recalling its definition, the observed Vs-s(HC)refers to the difference between vvoid of a hydroxyl group and a part of a hydrocarbon molecule that has the same V , as the hydroxyl group. Therefore, v v o i d of the hypothetical non-hydrogen-bonding state of the hydroxyl group assumed by Bondi, Whalley, and Weale is found to be less than that of the corresponding hydrocarbon. In other words, there is a volume decrease from a hydrocarbon to the hydroxyl group at the hypothetical non-hydrogen-bonding state. In contrast to the treatment adopted by them, Hamannz1calculated the volume decrease due to the formation of a hydrogen bond by using a cylinder model as 3.8 ml/ mol, which may include the other volume decrease in the space other than the van der Waals spheres. The physical meaning of this space decrease due to the formation of a hydrogen bond has not been clarified. The difference between the space decrease of the Hamann's value for the formation of a hydrogen bond and that of Bondi, (-3.8) (-1.08) = -2.72 ml/mol, seems to be related partly to the volume decrease from the hydrocarbon to the hypothetical non-hydrogen-bonding state described above.
v,-,(HC)
vs-.s(Hc)
Partial Molar Volumes of Nonionic Solutes
The volume decrease from the hydrocarbon to the hypothetical state, thus discussed, may be explained qualitatively by the concept of the ice-like structure of water22 as follows. The addition of a hydrophobic molecule to water causes an increase of the bulky ice-like structure.23 On the other hand, the introduction of a hydrophilic molecule lea+ to a partial destruction of the water structure so that the hydrophilic hydroxyl group does not increase the icelike structure so much as a hydrophobic hydrocarbon moleThus, the volume decrease from the hydrocarbon to the hypothetical state, suggested above, seems to be related reasonably to the volume decrease due to the melting of the bulky ice-like structure by the change of a hydrophobic molecular property to a hydrophilic one. King16 also presented similar qualitative discussion with respect to his observation that different classes of solutes have different packing densities. The more rigid or quantitative explanations of this decrease will be one of the subjects left to be clarified in the future. In brief, it is concluded that by treating Po to be composed of and Pvoid, Pvoid of a solute containing a hydroxyl group was found to be less by 4.5 ml/mol than that of the hydrocarbon with the same V, as the solute in water. It is further suggested from the observed Pvoid(HC) that a hydroxyl group even a t a hypothetical non-hydrogen-bonding state decreases its Vvoid from that of the hydrocarbon.
v,
Acknowledgment. The authors wish to thank Professor
T. Keii and Associate Professor A, Morikawa in Tokyo Institute of Technology for kind discussions.
References and Notes (1) G. C. Pimentel and A. L. McClellan, "Hydrogen Bond", W. H. Freeman, San Francisco, Calif., 1960, p 53.
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The Journal of Physical Chemistry, Voi. 79,No.22, 1975
