THERMOCHEMICAL INVESTIGATIOKS OF WATER-ALCOHOL SOLVENT SYSTEMS
699
Thermochemical Investigations of the Water-Ethanol and Water-Methanol Solvent Systems. I. Heats of Mixing, Heats of Solution, and Heats of Ionization of Water
by Gary L. Bertrand, Frank J. Millero, Ching-hsien Wu, and Loren G. Hepler Department of Chemistry, Carnegie Institute of Technology, Pittsburgh, Pennsylvania
(Received August 3, 1966)
Differential heats of solution (L)of water and ethanol in various solvents ranging from pure water to pure ethanol have been determined by measuring heats of solution of small quantities of pure water and ethanol in large quantities of the various solvents. Partial molal entropies, based on the pure liquids as standard states, have been calculated for ethanol in water and water in ethanol. The standard (hypothetical 1 m solution) partial molal entropy, heat of formation, and free energy of formation have been calculated for aqueous ethanol. The entropy data show that addition of small amounts of ethanol to water increases the structuredness of the solutions. Heats of solution of NaCl(c) have been determined in various water-ethanol mixtures. Heats of solution of aqueous HC1 and aqueous NaOH have also been determined and used in calculating AH values for solution of HCI(g) and XaOH(c) in the various solvent mixtures. The AH values for solution of NaCl(c), NaOH(c), and HCl(g) all show maxima in the water-rich region, while those for HCl(g) also show a minimum in the ethanol-rich region. Heats of reaction of NaOH with HCI have been measured and used in calculating heats of ionization of water in the various solvent mixtures. The resulting AH values show a small maximum in the water-rich region. Some similar work has been done on water-methanol systems.
Introduction Although water-alcohol solvent systems have been much used in a variety of chemical investigations involving determinations of acid ionization constants and rates of reactions as well as synthesis, there are few thermochemical data available for these important systems. Part of our interest in water-alcohol solvent systems has developed from a general interest in the relations between structure and thermodynamic properties of hydrogen-bonded liquids and their mixtures. I n this connection it is important to know some of the thermodynamics of mixing and also the thermodynamics of solution and reaction of various substances in wateralcohol mixtures. The experimental investigations reported here were concerned with determinations of enthalpies for some of these processes. The results permit us to calculate such quantities as excess en-
tropies of mixing and partial molal entropies, which yield structural information about these solutions. Our interest in water-alcohol solvent systems is also derived from recent investigations of the thermodynamics of ionization of organic acids and linear free energy relations. -5 Since experimental investigations of heats and entropies of ionization of organic acids in water have contributed to our understanding of these processes and related linear free energy relations, it seems likely that similar investigations of other solvent systems will prove similarly useful. Knowledge of heats and entropies of ionization may (1)
L. G. Hepler, J. Am. Chem. SOC.,8 5 , 3089 (1963).
C. D. Ritchie and W. F. Sager, Progr. Phys. Org, Chem., 2 , 323 (1964). (3) L. G. Hepler, Symposium on Linear Free Energy Correlations, Durham, N. C., 1964. (4) C. D. Ritchie, see ref. 3. (5) L. G. Hepler, J. Phys. Chem., 6 8 , 2645 (1964). (2)
Volume 70. h-umber S
March 1966
700
also be expected to lead to better understanding of the solvent dependence of Hammett p values and to understanding certain specific solvent effects. As a first step in determining heats and thence entropies of ionization of organic acids in water-ethanol mixtures, we have determined the heats of ionization of water in various water-ethanol mixtures and report these results here. Experimental Section The calorimeter is patterned after one previously described,6 except that a Leeds and n'orthrup Mueller G-2 bridge and HS galvanometer were used with a nickel wire resistance thermometer for temperature measurements. - b o , the resistance thermometer and calibration heater were contained in a glass spiral filled with mineral oil rather than wound on a silver cylinder. All of the calorimetric work reported here was carried out with 950 ml of water, alcohol, or wateralcohol mixture in the calorimeter dewar a t 25.00 f 0.15". Water-ethanol mixtures were prepared by weight in 950-ml lots from distilled water and U.S.P. 95% ethanol. Experiments with 95-100% ethanol were done with solvent prepared from Reagent Quality U.S.I. absolute ethyl alcohol. Water-methanol mixtures were prepared from either Commercial solvent (minimum purity 99.85%) methanol or 99.8% methanol from Baker. Samples used for heat of solution measurements were 99.8% methanol from Baker. Aqueous solutions of NaOH and HC1 were prepared and standardized by common procedures. Baker reagent grade NaCl was dried and then used without further purification. Calibrated pipets were used to obtain aliquots of various solutions for heat of solution and heat of reaction experiments.
Results and Discussion We have determined heats of solution of small quantities (about 5 ml) of pure water and pure alcohol in large quantities (950 ml) of water, alcohol, and wateralcohol mixtures. The measured heats very closely approximate differential heats of solution from which we obtained L quantities and integral heats of mixing as discussed below. The results are given in Tables I and 11. Each value in Tables I-IV is based on at least two measurements. Uncertainties in L, values range from *1 cal mole-' in the water-rich region to about lt4 cal mole-' in pure alcohol. Uncertainties in E, and IIn values range from about f10 cal mole-' in pure water to *1 cal mole-' in the alcohol-rich regions. I n these tables and the following discussion, T h e Journal oj Physical Chemistry
G. BERTRAKD, F. MILLERO, C. Wu, AND L. HEPLER
Table I: Partial Molar Heats of Solution of Water and Ethanol in Water-Ethanol Mixtures -
LF. Xe
0.0 0.0335 0.0725 0.0944 0.118 0.144 0.175 0.204 0.239 0.321 0.328 0.370 0.490 0.507 0,563 0.649 0.667 0.751 0.768 0.875 0,938 1.0
cal mole-'
0 -8 - 48 - 80 - 120 - 164
-216 - 223 - 251 - 248 - 243 -223 - 208 - 198 - 157 - 132 - 138 - 161 - 239 - 459
-
Le, cal mole-'
- 2380 - 1990 - 1340 - 906
-316 - 170
+26 +43 +51 22
+
+5 - 13 - 25
- 25 0
Table 11: Partial Molar Heats of Solution of Water and Methanol in Water-Methanol Mixtures -
LW,
X,
cal mole-'
0.0 0.129 0.241 0.307 0.399 0.499 0.560 0,568 0.627 0.641 0.761 0.773 0.784 0.828 0.871 0.912 1.0
0 - 60 - 165 - 207 - 241 - 281 - 288 - 294 -318 -318 - 396 -407 - 416 - 461 -513 - 573 -719
-
Lm, oal mole-'
- 1756 - 795 - 336 -211 - 144
- 92 - 73 - 43
-25 -7 0
mole fractions are represented by X , and subscripts w, e, and m refer to water, ethanol, and methanol, respectively. We have taken the pure liquids to be reference states so that the differential heats are (6) W. F. O'Hara, C. H.Wu, and L.G . Hepler, J. Chem. Educ., 38, 512 (1961).
THERMOCHEMICAL INVESTIGATIONS OF WATER-ALCOHOL SOLVENT SYSTEMS
400
0
1
I
1
I
0.2
0.4
0.8
0.8
xz.
energies obtained from vapor pressures, we know of no relevant vapor pressure data that are accurate enough to justify such a calculation. However, the vapor pressure data of Dobson” for the water-ethanol system at 25” have been shown by Guggenheim and Adams12to be internally consistent, and we have used these data as follows. Taking the pure liquids as standard states, we calculate the difference between the partial molal entropy of either component and the partial molal entropy that component would have in an ideal solution of the same mole fraction, which could be called an excess partial molal entropy, from the equation
1.0
z,
(water) Figure 1. Illustration of internal consistency of and (ethanol) values. Directly measured values are represented by circles and Zvalues calculated graphically by means of the Gihbs-Duhem equation from E values for the other component are represented by crosses.
z2
equal to the corresponding L quantities. An illustration of the internal consistency of our data for the water-ethanol system is shown in Figure 1, where some directly measured L values are represented by circles and 1values calculated graphically from other L values and the Gibbs-Duhem equation are represented by crosses. Kumerous workers have determined the heat of solution of ethanol in water, corresponding to our 1,a t X , = lo, and have reported798 values close to -2.4 kcal mole-l, in satisfactory agreement with our value. Boseg has measured heats of mixing in the water-ethanol system at 17 and 42”. Linear interpolations of his data yield integral heats of mixing to form one mole of solution that are in good agreement with values calculated from our data in Table I by means of the equation AHmiX = XlLl
+ XJz
701
(1)
Our 1 , and Le values are more precise than those calculated by differentiation of Bose’s integral heats of mixing. Integral heats of mixing in the water-methanol system that are calculated from our E, and E , data in Table 11are in good agreementwith the directly measured integral heats of Benjamin and Benson.lo Although heats and entropies of mixing can be calculated from the temperature dependence Of free
The results of these calculations, shown in Figure 2, demonstrate that addition of a little of either component to the other pure component has a structureforming influence in the water-ethanol system. Although some considerations might suggest that addition of a nonelectrolyte to water should result in a decrease in molecular order due to interference of the solute molecules with the normal hydrogen-bonded structure of water, these entropies show clearly that ethanol molecules increase the structuredness of the water, in agreement with the “iceberg” picture of Frank and Evans.I3 The positive slope of the SeE curve in Figure 2 shows that the effectiveness of a given molecule of ethanol in promoting structure decreases with increasing alcohol concentration, possibly owing to the resulting overlapping of “icebergs” or highly disordered regions between “icebergs.” For thermodynamic calculations involving reactions in which aqueous ethanol is a reactant or product, it is desirable to have the standard free energy and heat of formation and the partial molal entropy in terms of the hypothetical 1 m solution. To this end we have used Dobson’s data” for evaluation of the Henry’s law constant on the molality scale for aqueous ethanol and thence evaluated the standard free energy of solution of gaseous ethanol in water. From this AGO value and the standard free energy of gaseous (7) “Selected Values of Chemical Thermodynamic Properties,” National Bureau of Standards Circular 500, C. S. Government Printing D. c,,1952. (8) E. M. Amett, W. G. Bentrude, J. J. Burke, and P. M. Duggleby,
J. A m . Chem. Soc., 87, 1541 (1965). (9) E.Base, 2. Physik. Chem. (Leipzig), 5 8 , 585 (1907). (10) L.Benjamin and G. C. Benson, J . P h w . C h e w 67,858 (1963). (11) H. J. E.Dobson, J. Chem. SOC.,2866 (1925). (12) E.A. Guggenheim and N. K. Adams, Proc. Roy. SOC.(London), A139, 231 (1933). (13) H. s. Frank and M. w. Evans, J . Chem. Phys., 13, 507 (1945).
Volume 70,Number 9 March 1966
G. BERTRAND, F. MILLERO,C. Wu, AND L. HEPLER
702
0
-a -8
- 2.0
I
h
-4.0
T
c
4
bJla
-6.0
-8.0
1
-1
using our heats from Table I1 with vapor pressure data a t 25".14 Figure 3 shows values of SwEand Using tabulated values7for AGfo,AHro, andS" (allat298" E()for CH30H, wecalculated AGt" = -41.89kcal mole-1, AHr" = -58.78 kcal mole-', and 3,"= 31.6 cal deg-1 mole-' for aqueous methanol in the hypothetical 1 m standard state. The entropy data for water-methanol systems confirm the expected similarities to waterethanol systems, Investigation of thermodynamics of ionization of acids in water-alcohol mixtures possibly should begin with measurements leading to data for ionization of the most acidic component of the solvent mixtures. To this end we have made heat of solution and reaction measurements that permit us to calculate the heats of ionization of water in various water-ethanol mixtures. These measurements also yield thermal data on HCI, XaOH, and NaCl in these mixtures that are relevant to recent work by Arnett, et al.* Some similar measurements have been made in water-methanol systems. Our measurements on HCl in water-ethanol were designed to yield data to be used in calculating the heat of ionization of water and to yield AH values for
I 0.2 0.4 0.8 0.8 1.0
0.0
Xe. Figure 2. Excess partial molal entropies (eq 2) for water (BWE)and for ethanol (&.E).
HCI(g) = HCI(S)
1 0.0
I 0.2
I
I
0.4
0.8
I 0.8
1 1.0
where (S) indicates that the preceding substance is dissolved in some designated solvent. Both aims were reached by way of determinations of heats of solution of aqueous HC1 in various water-ethanol mixtures. Combination of our measured heats (&) with already known heats of solution' (AH,) of HCI(g) in water and our Lwvalues from Table I permits calculation of AH values for processes represented by eq 3. The equation used in making these calculations is
Xm.
Figure 3. Excess partial molal entropies (eq 2) for water (&E) and for methanol (BmE).
ethanol,? we have calculated AGt" = -43.4 kcal mole-' for aqueous ethanol in the hypothetical 1 m standard state. Combination of our heat of solution of ethanol in water (Table I) with the heat of formation of liquid ethanol' gives AHf' = -68.74 kcal mole-1 for the standard heat of formation of aqueous ethanol. These data have been combined with the entropy of pure ethanol? to give S," = 35.9 cal (deg mole)-' for the standard partial molal entropy of aqueous ethanol. Calculations similar to those described in the three preceding paragraphs and shown in Figure 2 have been carried out for the water-methanol system, The Journal of Physical Chemistry
(3)
A H 3 = - +QA H h H , - - n , w nHc 1 nHCI
(4)
where nHcl and nw refer to the number of moles of HC1 and water in the small portion of aqueous HC1 added to a much larger amount of water-ethanol mixture, Measurements with various amounts (1-10 ml) of aqueous HCl of various concentrations (1-5 m) were made to enable us to extrapolate AH3 values to zero concentration of HCl. Concentrations of HC1 in the final solutions ranged from 0.001 to 0.025 M . The results of all these measurements and calculations are summarized as AH3' values in Table I11 and displayed in Figure 4. Estimated uncertainties in J. A. V. Butler, D. W. Thomson, and W. H. Maclennon, J. Chem. SOC.,674, (1933); K. A. Dulitskaya, J. Gen. Chem. USSR, (14)
15, 9 (1945).
THERMOCHEMICAL INVESTIGATIONS OF WATER-ALCOHOL SOLVENT SYSTEMS
-16.0
703
rrj
-22.0
J
I
I
I
1
0
0.2
0.4
0.6
0.8
1.o
0
0.2
Xe.
Figure 4.
0.8
1.0
Xm.
Heats of solution of HCl(g) in water-ethanol.
the derived AH30e values indicated in Figure 4 are mostly due to uncertainties in the nwIjw/nHC1term in (4) and heats of dilution.
Table 111: Heats of Solution (AH,",) of HCl(g) in Water-Ethanol Mixtures
- AHa'e,
- AHa's,
Xe
kcal mole-1
X.
kcal mole-'
0.0 0.0336 0.0727 0.0948 0.145 0.206 0.240 0.328
17.96 17.4 16.9 16.9 17.20 18.00 18,80 19.0
0.372 0.567 0.653 0.757 0.881 0.935 0.938 1.0"
19.5 20.6 22.1 22.7 22.4 22.4 22.4 20.7
' The initial solvent was pure ethanol, but the final solution contained water (-0.5%)
0.6
0.4
from HCl(aq) dissolved.
accounts Although the explanation by Arnett, et for the maximum in the water-rich region of Figure 4, this explanation is not applicable to the minimum in the ethanol-rich region. Bezman and Verhoek's observed a similar minimum in the equivalent conductance of HC1 in the same ethanol-rich solutions and have suggested an explanation which may be applicable to our heat data. Slansky16has measured heats of solution of HCl(g) in water-methanol mixtures, but made no measurements between X , = 0.64 and 1.00. We have therefore determined heats of solution of aqueous HC1 in the water-methanol system and have used eq 4 along with our previously given E , values in the water-
Figure 5 . Heats of solution of HCl(g) in water-methanol. Our data are represented by vertical lines showing estimated uncertainties while Slanky's results are indicated by crosses, without estimated uncertainties.
methanol system to calculate heats of solution of HCl(g). These measurements were made a t various concentrations and extrapolated to zero HC1 concentration to obtain the AH30m values given in Table IV and shown in Figure 5 with Slansky's results.
Table IV: Heats of Solution (AH3",) of HCl(g) in Water-Methanol Mixtures
- AHs'm, Xm
0.0 0.129 0.242 0.307 0.400 0.499 0.554 0.569 0.627
kcal mole-'
18.1 17.4 17.7 17.7 18.6 19.0 19.5 19.7 19.8
- AHaom, Xm
kcal mole -1
0.639
19.7
0.758 0.773 0.790 0.828 0.871 0,912 1.0"
19.8 20.6 20.2 20.0 20.5 19.7 17.6
a The initial solvent was pure methanol, but the final solution contained water (-0.5%) from HCl(aq) dissolved.
The disagreements between our data and those of Slansky'G in solvent mixtures with X , > 0.3 are greater than the sums of estimated uncertainties. Since Slansky16 had experimental difficulty because of slow attainment of equilibrium and our final AH30, values Bezman and F. H. Verhoek, J . Am. Chem. Soc., 67, 1330 (1945). (16) C. M. Slansky, ibid., 62, 2430 (1940). (15) I. I.
Volume 70,Number 3 March 1966
G. BERTRAND, F. MILLERO,C. Wu, AND L. HEPLER
704
are afflicted with uncertainties from heats of dilution and the nwLm/nHCIterm in (4), we cannot choose definitely between the two sets of results. We have, however, separately verified our method of measurement involving solution of aqueous samples as follows. We have measured the heats of solution of KBr(c) and KBr(aq) in water-methanol solutions having X , = 0.641 to compare with Slansky's16 AH = 3.80 kcal mole-' for solution of the solid. Our measurements gave AH == 3.6 kcal mole-' for solution of the solid. Combination of our measured heats of solution of aqueous KBr in water-methanol (X, = 0.641) with the heat of solution of KBr(c) in water' and our Ew value from Table I1 in an equation like (4) leads to AH = 3.7 kcal mole-' for solution of NBr(c) in this solvent mixture. We have measured heats of solution of various amounts of aqueous NaOH of various concentrations in water-ethanol mixtures. Calculations using the resulting data in the appropriate modification of eq 4 lead to AH values for solution of NaOH(c) in the various solvents. These AH values for different NaOH concentrations were extrapolated to zero S a O H concentration to yield the A H o values listed in Table V. As for HC1 and also for electrolytes investigated by Arnett, et ai.,*the heat of solution of SaOH(c) goes through a maximum in the water-rich region. There is no evidence for a minimum in the ethanol-rich region. Table V: Heats of Solution ( A H ' ) of NaOH(c) in Water-Ethanol Mixtures -AHo,
-AHo,
Xe
kcal mole - 1
Xe
kcal mole-1
0.0 0.0336 0.0727 0.0948 0.145 0.174 0.240
10.2 10.3 9.8 9.7 9.4 9.5 9.8
0,372 0.507 0,566 0.757 0.881 0.938 1.0"
10.7 11.7 12.2 13.5 14.0 14.8 15.9
were also made for reaction of small volumes of concentrated aqueous HCl with 950 ml of dilute S a O H in water-ethanol mixtures. Combination of these measured heats with previously measured heats of solution of concentrated aqueous S a O H and HCl in water-ethanol mixtures gave AH values for the neutralization process represented by H+(S)
+ OH-(S)
HZO(S)
(5)
Since these AH values were obtained for solutions having different concentrations, we could extrapolate to zero concentration of both S a O H and HCl to obtain A H o values for the ionization of water (reverse of reaction 5 ) in the various solvent mixtures. These A H o of ionization values are listed in Table VI. ~
~~
Table VI: Heats of Ionization ( A H " ) of Water in Water-Ethanol Mixtures
X,
0.0 0.0336 0.0727 0.0948 0.145 0.174
AH', koa1 mole-]
13.3 13.6 13.6 13.6 13.3 12.8
AHO,
Xe
0,240 0.372 0 . ,566 0 . i'5i 0.881 0.93s
kcal mole-'
12.0 10.3 8.0 5 3 5.2 5.1
Measurements of heats of solution of SaCl(c) in water-ethanol mixtures had the dual purpose of giving thermal data for a typical 1: 1 electrolyte (not involving either H f or OH- ions) and also permitting another means of evaluating heats of ionization of water in these solvent mixtures. We have therefore measured the heats of solution of various amounts of SaCl(c) in water-ethanol mixtures with X , < 0.57 and heats of solution of aqueous XaC1 in mixtures with X , > 0.57. The results, extrapolated to zero SaCl concentration, are given in Table VI1 as A H o values for
a The initial solvent was pure ethanol, but the final solution contained water (-O.SCr,) from NaOH(aq) dissolved.
Table VII: Heats of Solution ( A H " ) for NaCl(c) in Water-Ethanol Mixtures
In order to determine heats of ionization of water in water-ethanol mixtures, we have measured heats of reaction of solutions of HC1 with solutions of IYaOH. Excess NaOH was used in every experiment to minimize effects of traces of carbonate impurity. Heats were measured for reaction of small volumes of concentrated aqueous KaOH with 950 ml of dilute HC1 in various water-ethanol mixtures. A few measurements The Journal of Physical Chemistry
AH0, kcal
AHO,
X,
mole -1
X,
kea1 mole-'
0.0 0.0336 0.0948 0.145 0.174
0.91 1.34 2.18
0.240 0,372 0.566 0.SSl 0.938
2.57 2.10 1.35 0.7 0.4
2.58
2.64
THERMOCHEMICAL INVESTIGATIONS OF WATER-ALCOHOL SOLVENT SYSTEMS
NaCl(c)
=
Na+(S)
+ C1-(S)
(6)
These AH" values go through the usual maximum in the water-rich region and exhibit no minimum in the ethandl-rich region. We have combined the AHo of solution values and E , values already reported in this paper with AH" = 42.5 kcal mole-' (ref 7) for the reaction NaCl(c)
+ HzO(l) = NaOH(c) + HCl(g)
(7)
to obtain AHoof ionization values for HzO(S)
= H+(S)
+ OH-(S)
(8)
from the relation A H s " = 42.50
- A H O N ~ C I- E , + AH"NaOH
+ AH"Hc~ (9)
These values at 0.1 mole fraction intervals are compared in Table VI11 with the values obtained from heat of neutralization experiments that were summarized in Table VI. We estimate that the uncertainties to be associated with the AH" values in Table VI11 range from less than kO.1 kcal mole-' in pure water to not more than 0.5 kcal mole-' in the alcohol-rich region. These heats of ionization of water in water-ethanol mixtures are required for subsequent calorimetric investigation of ionization of organic acids in these solvents. Combination of these heats with free
*
705
Table VIII: Comparison of Heats of Ionization (AH') of Water in Water-Ethanol Mixtures AHo,
AH0,
X.
koal mole-la
koal mole-lb
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
13.4 13.7 12.6 11.4 10.2 8.8 7.4 6.1 5.3 5.3
13.3 13.6 12.6 11.3 10.0
8.7 7.4 6.2 5.2 5.1
' These A H o values for reaction 8 were calculated from eq 9.
' These A H o values for the same reaction were obtained by interpolation of the values determined from heat of neutralization experiments and listed in Table VI.
energies that can be obtained from determination of the ionization constant of water in these mixtures will give entropies of ionization that should contribute to understanding of the water-ethanol solvent system.
Acknowledgment. We are pleased to thank E. M. Arnett and D. McKelvey for their helpful discussions and the National Science Foundation and National Institutes of Health for their financial support of this research.
Volume 70,Number 3 March 1966
