THERMODYNAMICS OF AQTJEOUS SOLUTIONSOF NOBLEGASES
trations of the various forms. In addition, the examination of the chemical potentials of the various forms is simpler than the evaluation of the partition function of the system since it requires less detailed information on the structure of water.
VI. Conclusion The thermodynamic behavior of aqueous solutions of noble gases was discussed in terms of a “two-structure” model for liquid water. It was shown that a satisfactory qualitative explanation of the entropy and enthalpy of solution can be given by regarding the thermodynamic functions of solution as composed of two parts, the static and the relaxation one. This division proves to be helpful also for interpretation of
3245
experimental results. The occurrence of the relaxation part was based on the assumption that liquid water contains large compact clusters of water molecules connected by hydrogen bonds. This property is one which distinguishes water from other liquids. The penetration of solute molecules into the cavities of the relatively open structure of the clusters was shown to enhance the Stabilization effect but, by no means, is the essential cause for it. Acknowkdgments. The author wishes to express his thanks to Professor G. Stein and Dr. S. Baer for suggesting the problem and for numerous helpful discussions on the subject. Indebtedness is expressed to Dr. A. Treinin for discussion on different parts of this work.
Thermodynamics of Aqueous Solutions of Noble Gases. 11. Effect of Nonelectrolytes
by A. Ben-Naim Department of Physiccll Chemistry, The Hebrew University, Jerusalem, Israel
(Received March 11, 1966)
The solubility of argon was m w e d in water and in dilute aqueous solutiom of nonelectrolytes : methanol, ethanol, 1-propanol, 1-butanol, glycerol, dioxane, glucose, and sucrose. The entropy and enthalpy of solution of argon were calculated from the temperature dependence-of the solubility. The difference in these quantities in solution of nonelectrolyte and in pure water is interpreted in terms of a “two-structure” model for liquid water and is attributed to the difference in the degree of crystallinity of the various solvents.
Introduction
cerned with the effect of nonelectrolytes. A qualitaThe thermodynamic behavior of aqueous so~utions tive interpretation of the results, based on a “twofor liquid water, is of noble gases reveals many anomalous properties when structure” compared with other ~olvents.l-~I n an attempt to (1) D.D.Eley, Trans. Faraday SOC.,35,1281 (1939). find their origin we examined in detail the effect of (2) H.8.Frank and M. M. Evans, J. Chem. Phys., 13,607 (1945). added solutes on the thermodynamic functions of solu(3). (e) A. Ben-Naim, J. phy8. Chem.,69,1922 (1965); (b) A. Bentions of argon in water. This investigation is conN-, ibid., 69,3240 (1965). Volume 69,Number 10 Odobm 1066
A. BEN-NAIM
3246
Experimental Section and Results The solubility of argon was measured in pure water and in dilute solutions of nonelectrolytes. The details of the method have been described elsewhere.' Measurements were done at five temperatures between 5 and 25". Several measurements were performed at each temperature, and the mean values obtained we recorded in Table I in terms of the Ostwald absorption
In y/yo
-RT
Apto
where yo and y refer to a solution of argon in pure water and in a solution of a nonelectrolyte, respectively. PO and p are the corresponding densities of the solvents.
Table I: Values of y x lo8for Argon in Water and in Aqueous Solutions of Nonelectrolytes
Pure water Methanol x = 0.015 Ethanol x = 0.015 1-Propanol x = 0.015 1-Butanol x = 0.015 Glycerol x = 0.015 p-Dioxane x = 0.015 Glucose 0.5 m Sucrose 0.5 m
20
26
39.56 41.35
36.63 38.45
34.08 35.96
45.05
41.30
38.33
35.85
48.45
44.05
40.55
37.75
35.45
48.00
43.55
40.10
37.25
34.90
43.80
39.80
36.70
34.10
31.93
46.24
42.40
39.35
36.96
35.00
41.55
37.93
34.90
32.45
30.40
38.80
35.47
32.75
30.60
28.85
5
10
48.07 49.60
43.36 45.00
49.80
b
55 -10 -20
I
I
I
I
1
I
sol-
The value of y for pure water at 10' was found to be slightly lower than that published previo~sly.~Distilled water and Analar grade materials were used. During outgassing, a small change of concentration might have occurred; however, no correction for this was t&en into account.6 As we were primarily interested in the changes of the thermodynamic functions of solution upon adding the solute, we found it convenient to plot Apto us. T, where Apto is defined by Apto = Apso
-
-30
Temp., "C. 16
(in water 3- nonelectrolyte) Apso
-
(in pure water)
Apeo is the standard free energy of solution of argon given by' Apso = -RT In y and y is the Ostwald absorption coefficienL6 Values of Asto and ato were calculated from the slopes of the curves (measured with an accurate tangentimete?) in Figure 1 and are given in Table 11. The pertinent relations are (for more details see the Appendix)
The Journal of Physieal C h m k t r y
\ = "=. 9 mt-
0
I
5
I
io
I
15
I
20
I
25
tOC Figure 1. vduea of Apt" 88 a function of temperature for the tranafer of argon from pure water into an aqueous solution of nonelectrolyfes (z is the mole fraction of the nonelectrolyte)$ a, methanol (z = 0.015); b, ethanol (z = 0.015); c, 1-propanol (z = 0.015); d, 1-butanol (z = 0.015); e, glycerol (z = 0.015); f, pdioxane (z = 0.015); g, glucose (0.5 m ) ; h, sucrose (0.5 m).
(4) A. Ben-Naim and 8. B a a , Trans. Faraday Soc., 59, 2736 (1963). (6) J. H. Hildebrand and R. L. Smtt, "The Solubility of Nonelectrolytee," 3rd Ed., Reinhold Publishing Gorp., New York, N. Y., 1960,p. 4. (6) A. Ban-Naim and S. Baer, Trans. Faraday Soc., 60, 1936 (1964). (7') R. P.Bell, ibid., 33,496 (1937). (8) H.J. G.Hayman, F. Deutach, and H. Tabor, J . Sci. Instr., 34, 307 (1967).
THERMODYNAMICS OF AQUEOUSSOLUTIONS OF NOBLE GASES
The calculated thermodynamic functions correspond to the process argon (in pure water) + argon (in water
+ nonelectrolyte)
at an equal molar concentration of argon in the two liquids. Table 11: Values of Apt" (cal./mole), A s t o (cal./mole deg. ), and Uto (cal./mole) for the Transfer of Argon from Pure Water into the Various Solutions of Nonelectrolytes
Apt" Asto
ARt
O
Apt " Ast
hRt
O
Methanol, x = 0.015 -17.8 -21.9 -26.0 -29.2 1.00 0.91 0.73 0.55 260 236 184 132
-31.5 0.37 79
1-Propanol, x = 0.015 -23.3 -8.7 -14.2 -18.7 1.00 0.98 0.92 0.87 274 268 251 236
ARt "
0.9 0.87 243
1-Butanol, x = 0.015 -11 -2.3 -7.7 -14.2 0.64 0.82 0.73 0.59 230 202 176 162
Apt" Asto ARto
Glycerol, x = 0.015 51.6 48.0 43.0 40.2 0.68 0.47 0.24 0.75 ado 240 118 111
Mt " Apt" Asto
p-Dio;nane, x = 0.015 12.8 3.2 -6.4 1.8 1.8 1.8 522 522 521
38.4 0.08 62.2
ARt "
21.5 1.8 522
Apt" Asto ARt
80.4 1.19 417
Glucose, 0.5 m 74.9 71.7 0.87 0.55 321 230
69.0 0.37 177
67.6 0.32 163
AM" Asto
118.4 1.14 435
Sucrose, 0.5 m 112.9 107.9 1.05 1.00 410 396
103.3 0.96 385
98.7 0.87 358
Apt ASt"
d t "
the properties of pure liquid water, yet it seems that it furnishes a satisfactory explanation for some anomalous properties of pure water and aqueous solutions of nonelectrolytes. Liquid water is regarded3 as being composed of monomeric water molecules (p) and "icelike" clusters of water molecules (c), containing n molecules linked together by hydrogen bonds. The "chemical" reaction is cI rnP Let np and nc be the number of moles of the two species, respectively. If the solution contains n, moles of gas (ie., argon) and nW moles of water (nn, np = n,) then the partial molar quantity E,, corresponding to any extensive function E , can be represented by
+
Ethahol, x = 0.015 -29.7 -18.7 -21.9 -25.1 -27.9 0.73 0.64 0.55 0.46 0.37 81 184 159 133 107 -4.1 1.05 288
Apt" Asto
3247
-15.5 1.8 521
(The pressure and temperature are held constant and are omitted from the notation.) The static term, Es*l refers to a solution where the equilibrium between the two forms is "frozen in," takes into account the while the relaxation term, a,', change in the distribution of water molecules between the two forms. For the sake of comparison with experimental results, the interpretation of the relaxation terms should be considered. The "two-structure" model is useful for detecting the origin of the anomalous thermodynamic behavior of aqueous solution of noble gases. However, liquid water consists of clusters of different size and shape. The relaxation term should thus be modified so as to take into account the change in the concentration of the various clusters present. In the following discussion, we still use a single relaxation term. In fact, it expresses the change of the thermodynamic functions due to the change of the concentration of all the clusters present. The static term retains its usual meaning; it refers to a solution where the equilibrium between all kinds of clusters is frozen. Entropy and Enthalpy of Transfer of Argon from Pure Water into a Solution of a Nonelectrolyte. Table I1 shows that Asto and are always positive for nonelectrolyte solutions although the effect on the structure of water might be different for each nonelectrolyte. A qualitative interpretation can be given by defining the quantities
Anto
Discussion It has been p r e v i o u ~ l yfound ~ ~ ~ convenient to divide the partial molar quantities of the gas into two parts: a static and a relaxation part. This was done using a "two-structure" model for liquid water. This model is, no doubt, the &nplest one by which one can describe
(9) A. Ben-Naim, J . C h a . Phge., 42, 1512 (1965).
Volume 69,Number 10 October 1966
3248
A. BEN-NAIM
at* = H.*
(in water
+ nonelectrolyte) H,* (in pure water)
AH:
=
AH: (in water
+ nonelectrolyte) -
Table III : Approximate Values of ASt* (cal./mole deg.) and of AStr (cal./mole deg.) for the Transfer of Argon from Pure Water into the Various Solutions of Nonelectrolytes (2: Is the Mole Fraction of the Nonelectrolyte)
AH: (in pure water) ASt* = S,* (in water
+ nonelectrolyte) S.* (in pure water)
AS:
=
AS: (in water
+ nonelectrolyte) AS,' (in pure water)
so that the following relations hold
AS," AI&" =
AH:
A&*
+ AS:
AH$*f AH: =
TAS;
(Note that ASt*, ASe', AHt*, and AH: refer to the same standard state chosen for A s t o and a t " . ) These three relations contain four unknownsASt*, hst', AHt*, and AH;-of which AHt* seems the simplest to interpret. We assume, following Eley's view,l that most of the gas molecules occupy empty cavities in both pure water and in dilute solutions of a nonelectrolyte. Since the major part of AH,*is determined by the interaction energy between the gas molecule and its cavity, we should expect that the difference between AH,* in pure water and AH,* in dilute solutions of a nonelectrolyte will be very small. Thus, if we put AHt* = 0 the last relations can be solved to obtain AS:
=
5
0.06 0.94
0.07 0.66
10
Temo.. _ . OC. 15
20
Methanol, x = 0.015 0.08 0.09 0.1 0.83 0.64 0.45 Ethanol, x = 0.015 0.08 0.09 0.56 0.46
0.095 0.37
25
0.1 0.26 0.1 0.27
0.015 1.04
1-Propanol, x = 0.015 0.031 0.05 0.063 0.97 0.93 0.86
0.078 0.79
-0.003 0.873
1-Butanol, x = 0.015 0.008 0.027 0.037 0.81 0.7 0.6
0.047 0.54
-0.185 0.935
Glycerol, 2 = 0.01.5 -0.17 -0.15 -0.14 0.85 0.62 0.38
-0.075 1.87
p-Dioxane, x = 0.015 -0.045 -0.011 +0.022 1.84 1.81 1.78
-0.13 0.21 0.052 1.73
-0.29 1.48
Glucose, 0.5 m -0.26 -0.25 1.13 0.8
-0.23 0.6
-0.22 0.54
-0.42 1.56
Sucrose, 0.5 m -0.40 -0.37 1.45 1.37
-0.35 1.31
-0.33 1.2
AR,"/T
A&* = A s t o
- AS:
Values of ASt* and AS: calculated on the basis of this assumption are given in Table 111. These values, although approximate, seem to have a significant meaning. First, we see that the sign of ASt* is positive for methanol, ethanol, 1-propanol, and 1-butanol solutions, while negative for glycerol, glucose, and sucrose solutions. If we assume again that the major part of ASt* is determined by the change in the total number of cavities, the sign of ASt* for the first four solutes might indicate that these solutes increase the number of cavities while glycerol, glucose, and sucrose reduce the number of cavities. This conclusion is in accord with the view that solute molecules containing inert groups "stabilize the structure of water'' while the other solutes have an opposite effect. (An exception is the behavior of pdioxane. Using a different set of measThe Jollrnal of Physical Chemistry
urements, we concluded that pdioxane probably has a destabilizingeffect on the structure of water.10) It should be noted that ASt* refers to the transfer of argon from pure water into an aqueous solution of a nonelectrolyte, the molar concentration of the gas being the same in the two solvents. Thus, if we take the same volumes of pure water and of the aqueous solution of nonelectrolyte, the total number of water molecules in the latter will be less than that in pure water, and we might expect that the total number of cavities will also be reduced by the presence of the added solute. The sign of ASt* for the first four solutes indicates that for a low concentration of these solutes the stabilizing effect of the structure of water is even larger than the above-mentioned opposite effect, so that the net effect is that the total number of cavities (10) A. Ben-Ndm and G. Moran, Trans. Faraday Soc., 61, 821 (1965).
THERMODYNAMICS OF AQUEOUSSOLUTIONS OF NOBLEGASES
increases. Obviously, for a high concentration of solutes the destabilizing effect would be the predominating one. As for the relaxation term, Table I11 shows that for all the solutions its sign is positive. Now, since we have shown3 that AS: is negative for a noble gas in pure water, the above result means that the absolute value of the relaxation term in the solution is smaller than that in pure water. This seems to contradict the conclusion we have drawn p r e v i o ~ s l ythat ~ ~ ~the relaxation term is greater the greater the “degree of crystallinity” of the solvent. However, it should be emphasized that the above conclusion was drawn for pure water only, using a two-structure model ( i e . , one kind of clusters), and this must not be the case if the change of the “degree of crystallinity” is due to the presence of an additional solute. A proper interpretation of this result should take into account some factors which might change when passing from one solvent to another. Let us write ASt’ in the form3
Appendix Derivation of the Thermodynamic Functions for the Transfer of Argon from Pure Water to an Aqueous Solution of Nonelectrolyte. Let paBand p: be the chemical potential of the gas s, in the gas and liquid phases, respectively. Assuming ideal behavior in the two phases, one can write
+ RT In c,‘ pnol+ RT In c,‘
pag= p l o g 1
pa =
p,Og
=
Acknowledgment. The author wishes to express his thanks to Professor G. Stein and Dr. S. Baer for their continuous interest in this work.
(2)
lim[pne- RT In c , ~ ]
(3)
car+0 p,ol
= lim[p,’ c a l 4
- RT In c,’]
(4)
One usually proceeds to interpret pao1and pBogas being the chemical potentials of s at a hypothetical ideal state of c: = 1 and ceB= 1, respectively. However, for the purpose of interpretation, a simpler significance can be related to the difference Apso =
p:
- paog.
To do this let us recall that at equilibrium we have = pag,and thus from (1) and (2) we get Apn0 =
-RT In ( c ~ ~ / =c ~-RT ~ ) ~n ~ ~y
(5)
where y is the Ostwald absorption coefficient. By substracting (2) from (1) and using (5) we get ps1 - pag= Apno RT In ( C : / C , ~ ) =
+
Conclusion From the temperature dependence of the solubility of argon in water and in aqueous solutions of nonelectrolytes, we calculated that the entropy and enthalpy change accompanied the transfer of argon from pure water into the corresponding nonelectrolytic solution. The division of Asto and of AI%’ into two parts was found to be useful for the interpretation of the experimental results. A qualitative correlation with the “degree of crystallinity” of the solvent was found. The results obtained in this manner lead to a classification of the various nonelectrolytes into two categories: those which stabilize the structure of water and those which destabilize it.
(1)
where cae and :C are the molar concentrations of the gas s in the two phases, respectively. p.Og and pao1 are formally defined by
paO1
All the factors in the last bracket might be affected by the addition of the solute. Moreover, for treating a real case, one should consider the sum of such terms over all kinds of clusters present. Thus, an interpretation of the sign of AS: seems to be impossible at this stage.
3249
-RT In y
+ RT In
(C;/C,~)
We immediately recognize that Apso = -BT In y is the change of free energy which accompanies the transfer of the gas s from one phase to the second whenever c;/csB = 1. This is true no matter what the values of the concentrations, c: and cap, provided that they are low enough to ensure the validity of (1) and (2) and that they are equal to each other. In the same manner one can consider the transfer of s from one solvent, 11, to a second solvent, 12,and get Apto
pao1z
-
- paoB)-
= (cl.olz (P(.Ol1
- paog)
=
-RT
(yz/~i)
where y1 and y2 are the Ostwald absorption coefficients in the two solvents, respectively. Apto is simply the change of free energy which accompanies the process Volume 69,Number 10 October 1066
A. BEN-NAIM AND M. EOEL-THAL
3250
argon (in solvent 11)
argon (in solvent 12)
where the molar concentration is the same (low enough) in the two solvents; ie., cp = c:. In the same manner by differentiation (1) and (2)) with respect to the temperature and by substituting c? = we get the changes of entropy and enthalpy which accompany the same process mentioned above.
Asto = R#
a
a
In ( Y 2 I Y d ) - RF$h
@to
Apt’
(PZIPl))
+ TAB*”
The term RT[b In (pz/pl)]/aT which arises from the volume change of the solvents has, in most cases, a negligible value.
Thermodynamics of Aqueous Solutions of Noble Gases. 111. Effect of Electrolytes
by A. Ben-Naim and M. Egel-Thal Department of P h y s k ’ l Chemistry, The Hebrew University, Jerusalem, Israel
(Received March 11, 1966)
The solubility of argon was measured at five temperatures between 5 and 25’ in water and in aqueous solutions of electrolytes: LiCl (1 m), NHGl (1 m), NaCl (1 m), KC1 (1 m), KBr (1 m), NaI (1 m), and K I (1, 2, and 4 m). The entropy and enthalpy of solution of argon were calculated from the temperature dependence of the solubility. The difference in these quantities in solution of electrolytes and in pure water is interpreted in terms of a “two-structure” model for liquid water and is attributed to the decrease of the “degree of crystallinity” of the water caused by the added electrolytes.
Introduction Effects of electrolytes on the structure of water have been extensively studied both theoretically and experimentally. On the other hand, aqueous solutions of noble gases reveal some anomalous thermodynamic behavior, the origin of which has been related to the special structure of water.’-* It is, therefore, interesting to examine the effect of electrolytes on the thermodynamic functions of solution of the gases in water. The solubility of gases in electrolytic solutions was studied by many authors who were primarily interested in “salting-out” effects of the various salts. The temperature dependence of the solubility in these solutions was rarely Frank and Evans,2 in a discussion of the anomalous The Joumal of Physieal Chembtry
thermodynamic behavior of aqueous solutions of noble gases, calculated some values of the entropy change on transferring the gas from pure water to an aqueous electrolytic solution. However, their conclusions rest upon earlier experimental results which seem to be insufficiently accurate for this purpose, Their interpretation was based on the “icebergbuilding” idea. The change of the thermodynamic (1) D. D. Eley, Truns. Furoduy Soc., 35, 1281 (1939). (2) H.8.Frank and M. M. Evans, J . C h . Phys., 13, 607 (1946). (3) A. Ben-Naim, J . Phys. C h . , 69,1922,3240 (1966). (4) A. Euoken and G. Herzberg, 2. phySik. C h . (Leipzig), 195, 1 (1960). (5) T.J. Momson and F. Billett, J . C h m . Soc., 3819 (1952). (6) T.J. Morrison and N. B. B. Johnstone, ibid., 3665 (1966). (7)F. A. Long and W. F. McDevitt, C h m . Rep., 51,114 (1952)
