HYDRATION OF IONS IN THE GABPHASE
1475
Hydration of the Halide Negative Ions in the Gas Phase. 11. Comparison of Hydration Energies for the Alkali Positive and Halide Negative Ions by M, Arshadi, R. Yamdagni, and P. Kebarle Che?niatm Department, Universitzl of Alberta, Edmonton, Canada
(Received September 8, 1968)
+
The AH,-l,,, AGn-l,n, and ASn-l,,, for the gas-phase reactions X-(H,O),-1 H20 = X-(H$O), where X- = = 1 to n = 4 or 5. The method of measurement depends on mass spectrometric sampling of the ions X-(H20), emerging from an ion source containing water vapor. Comparison of the enthalpies of X-(HaO), with the enthalpies of the isoelectronic alkali M+(HzO), shows that the isoelectronic positive ion gives stronger hydration interactions for small n. The difference between AH,+, for the positive and negative isoelectronic ions decreases as n increases. Electrostatic calculations of the potential energies of Xd(H20), indicate that the relatively stronger interactions of the negative ions at high n are probably due to a gradual change-over in the attachment mode of the water molecules to the negative ion, For small n the water molecule “touches” the ion with both H atoms; at higher n crowding is relieved by attachment through only one of the H atoms. The determined enthalpies for the halide and alkali ions are shown to be consistent with the total single ion hydration energies based on the Randles Volta measurements,
F-, C1-, Br-, I- were measured for n
Introduction The gas-phase hydration energies for the alkali positive ions are described in the preceding paper’ of this issue. The present work deals with the hydration energies of the halide ions in the reactions (n - 1,n) occurring in the gas phase where X- = F-,
C1-, Br-, and I-. The principle of the determination of the hydration equilibria and the temperature dependence of the equilibrium constants Kn-1 ,n was the same as that used in the preceding paper.‘ The present work is a continuation of an earlier study2 of the halide ions. In the earlier study equilibrium determinations were done only a t room temperature so that no AHn-~,,,values could be obtained. Also the set of (n- 1,n) reactions observed was more restricted. The study of the halide ions is a logical continuation of the alkali ion investigation. Both sets represent spherically symmetrical ions with noble gas electronic shells. However, since the orientation of the water molecules is different in the positive and negative ions, the hydration energies might show some specific differences. I n an earlier comparison2 of the hydration of the alkali and halide ions, which was restricted by the availability of a complete set of AGOa,a data only, we concluded that the gas-phase hydration energies are consistent with the single ion hydration energies based on Volta measurements by RandlesS3 The present results which
are more detailed allow interesting elaborations to be made on the above conclusion. The gas-phase hydration equilibria of the halide ions should also be of primary interest in the many fields of study involving ions at pressures from about Torr to atmospheric pressure. Thus in electrical phenomena in the troposphere and ionosphere, drift and mobility experiments with gaseous ions, gas discharges, ionic reactions induced by ionizing radiation, flames, etc., water, and other polar molecules are often natural constituents, deliberate admixtures, or chance impurities. Clustering of the polar molecules around the ion occurs in such systems and has important effects on the mobility, recombination coefficients, and reactivity of the ions.
Experimental Section Most of the measurements were made with a magnetic mass spectrometer incorporating a high-pressure ion source, A 2000-eV electron beam was used as ionizing medium. Both ion source and electron gun were mounted in separate ports of an %in. pumping lead (Figure 1). The electron beam produced by a thoriated iridium filament is electrostatically focused by an electrode system similar to that employed i n cathode ray tubes. The ion source machined out of (1) I. Di‘idio and P. Kebarle, J . Phys. Chem., 74, 1466 (1970). (2) P.Kebarle, M. Arshadi, and J. Scarborough, J . Chem. Phys., 49, 817 (1968); 50, 1049 (1969). (3) J. E. Desnoyers, in “Modern Aspects of Electrochemistry,” Vol. 5 , J. 0. M. Bockris, Ed., Plenum Press, New York, N. Y., 1969, Chapter 1.
Volume 74,Number 7 April 8, lQ70
M. ARSHADI,R. YAMDAQNI, AND P. KEBARLE
1476
time which an ion spends in the ion source is some 2-3 mec. One can calculate on the basis of clustering reaction rate constants for the hydration of the proton determined recently5 that clustering equilibria in that system are achieved in less than 100 psec at water pressures larger than. 0.2 Torr. Assuming that the rate constants for the clustering equilibria of the halides are of a similar order of magnitude, it follows that the equilibria for these ions are also achieved within the source residence time of the average sampled ion. All clustering equilibria measurements were made under continuous electron irradiation and ion deteotion since under these conditions the intensity of the d e tected signal is highest.
Figure 1. Electron beam high-pressure ion source: 1, electron filament; 2-6,electrodea for electrwtatic focusing of electron beam; 7,8, deflection electrodes; 9, magnetic and electrostatic shielding of electron beam; 10, ion source with copper heating mantle; 11, electrostatic shielding of ions; 12, electron entrnnce slit; 13, electron trap; 14, copper lid holding ion exit slit flange; 15, gas inlet and outlet; 16-18, ion source supports and insulation; 19-26, ion beam acceleration and focusing; 27, mass spectrometer tube to 90' magnetic sector.
I I
stainless steel had a port carrying the electron entrance slit (2 X 0.015 mm) and another port a t right angles carrying the ion exit slit (2 X 0.015 mm). The vertical distance between the plane of the electron beam and the ion exit slit wa8 4 mm. All parts of the ion Hource were sealed with gold gaskets. This allowed operation of the source up to 500'. The ion source block was sumunded by a thick copper mantle which carried the heater wells. The ions escaping from the exit slit were accelerated to the first cone electrode (Figure 1) where they entered a differentially pumped acceleration and focusing r e gion. Mass analysis was obtained in a No,15-em radius magnetic sector tube which was also differentially pumped. The electron pulses produced in a secondary multiplier were counted with a counting system. The above arrangement of ion source and electron gun is very similar to that described in an earlier publication by Durden, Kebarle, and Good.' An improvement in the present setup is the high-temperatnre capability of the ion source. The electron beam could be pulsed and the ion detection could be gated in a manner similar to that used in the Durden apparatus. Shown in Figure 2 is the detected total ion intensity with time after a 5O-~secelectron pulse. The ion source contained 3 Torr of water vapor. It can be seen that the average The Jmrrnol of Phydool C h a w
2
3
4
5
6
7
8
9
TIME, ~ . I O C .
Figure 2. Total ion intensity detected with maas spectrometer after electron pulse of 50-mec duration. Curve shows that ion residence time of the average ion is considerably longer than 100 psec.
Some of the measurements were made with the 01particle mass spectrometer which has been described previously.2 In order to be able to increase the temperature of the ion source without increasing the temperature of the 01 source a modification was made to the earlier apparatus. The 01 source was mounted in a separate hermetically sealed compartment which was not in physical contact with the ion source. Both the 01 particle compartment and ion source 01 entrance port were sealed by 0.0001-in. stainless steel foils. The arrangement is shown in Figure 3. The measurement of water pressure and other experimental conditions were very similar to those d e scribed in previous publications. The compounds used to produce the halide ions were the same as those used in the earlier work.z (4) D. A. (1869).
Durden, P. Keharle. and A. Good, J . Chem. Phys.. SO. 805
(5) A. Good, D. A.
Durden, and P. Keharle, W.. in press.
1477
HYDRATION OF ION@ IN THE GASPHASE I
I
I
I
I
1
C 7
I
C
Y
'
0
0 0 -.1
-1
Figure 3. Lu-Particle high-temperature ion source: 1, 01 source in double container with two foil windows and two porous stainless steel plugs for pressure equalization; 2, copper rod carrying 01 Bource container and allowing vertical motion of LY source; 3, insulation; 4, double gas inlet for allowing gas circulation; 5, copper heating mantle; 6, ion source; 7, ion exit slit; 8, shielding electrode and copper bottom of ion source.
-2
2.5
2.9
3.3
1 0 ~ 1 ~ 0 ~ Figure 5. van't Hoff plots of the equilibrium constants K n - ~ , n for the gas-phase hydration of C1-: 0, electron beam mass spectrometer; 0, 01 particle mass spectrometer.
I
,n
-0
1
c
V
-1 - 1 8 7 " "
2
v
3
4
5
6
H20 PRESSURE torr Figure 4. Plots of log k , z for the gas-phase hydration of GI- at various constant temperatures us. pressure of HtO.
Results and Discussion A . Results for the Halide Ions. An example of some typical determinations of the equilibrium constan t a Kn-itn is given in Figure 4 which shows K1,z for C1- as a function of water pressure and reaction temperature. The equilibrium constants were determined from the measured ion ratio In/In-l and the known water pressure p using the equation Kn-l,% = I,/ (In-lp). The data in Figure 4 demonstrate t h a t the equilibrium constants do not change with water pressure. van't Hoff plots of the equilibrium constants of C1- are given in Figure 5 showing the straight lines obtained whose slopes lead to the determination of AHn-~,n. Results of similar appearance were obtained also for the other halides. The experimental AHn-l,,, AGO,-,,, and AS",+,, for the halide ion hydrations are summarized in Table I and Table 11. The AH,-l,, of the halide ions are also shown in Figure 6 plotted us. 12. The figure shows that the -A€€n-~,nare highest for F- and lowest for I- as would be expected from the relative size of the ions. The variation of AHn-l,n with n will be considered below in connection with electrostatic calculations. The consistency of the relative AH,-l,, values for the different halides with available thermodynamic data is checked in Figure 7 which gives a plot of A H o , ~ (I-) - A H o , ~ ( X - )us. n, where X - = F-, C1-, Volume 74, Number 7 April 9, 1970
M. ARSHADI,R,YAMDAGNI, AND P. KEBARLE
1478
Table I : Experimentally Determined Enthalpies and Calculated Potential Energies for Hydration Reactions of the Halide Ions.' X-(H20),-1 HzO = X-(HzO),
+
23.3 16.6 13.7 13.5 13.2
...
...
18.8 16.9 13.3 10.5 5.8 2.1 2.46 5.06
x
12.6 12.0 10,6 9.5 8.3 7.2 3.05
13.1 12.7 11.7 11.1
13.2 12.3 10.5 9.2 6.3 4.2 2.92
...
... ,
I
,
8.7 8.4 7.7 7.1 6.4 5.8 3.48
12.6 12.3 11.5 10.9 ,
.
I
...
...
2.746 X lo6
104
12.7 11.9 10.3 9.0 6.3 4.4 2.97 3.445
x
8.4 8.1 7.4 6.9 6.2 5.7 3.54
10.2 9.8 9.4
... ..,
..,
...
9.7 9.2 8.2 7.5 5.6 4.5 3.37
6.4 6.2 5.8 5.4 5.1 4,7 3.92
1.181 X 106
10'
All energy values in kcal/mol. R corresponds to the distance between the centers of the negative ion and the water molecule 1. 0 Value of constant in term AR-lZ used for electronic repulsion between hydrogen atom of water molecule and halide ion.
for the case 12
Table 11: Gas-Phase Free Energies and Entropies for Hydration Reaction of Halide Ions.a X-(Hg0),-1
-.
- AGnn-ln, kcal/mol n-1,n
F-
c1-
Br-
I-
091
18.1
8.2
7.0
5.4
172 2,3 3,4
11.0 7.6 5.5 7.1
6.5 4.5 3.4
5.5 4.1 2.9
4.2 3.1
4.15
...
.
.
I
I _
17.4 (22.5)* 18,7 20.4 36.9 30.7
... I
,
,
a Standard state 1 atm, T = 298°K. Values in parentheses correspond to frequencies, based on electrostatic calculations.
and Br-. It is to be expected that for large n the above difference should approach the difference between the single ion heats of hydration AHh(I-) AHL,(X-). Indicated on the figure are the values for these differences obtained from the single ion hydration enthalpies of Latimer, Pitzer, and Slanski and Randlesaa The A H n - ~ , nvalues used in the plot are those directly measured when available or extrapolated values from Figure 7. The plot shows that the present determinations are consistent with the single ion hydration enthalpies since the AHo,, differences extrapolate approximately to the single ion hydration differences. For F- and C1- the single ion hydration differences calculated from the Latimer and Randles data are quite close. However, for the case of Br- there is an appreciable difference. This difference should be due to the use of different values for the electron affinity of Br in the Born cycles involved in the evaluatiomBE It will be noted in Figure 7 that the Br difference curve crosses the Latimer line and is asymptotic to the Randles line. Therefore the present results are consistent with the Randles data which were evaluated with use of more recent and better electron affinities. The Journal of Physical Chemistry
c1-
F-
+ HzO = X-(H$O),
- AS0,-l,,, ~~--------Br -
1-
16.5 (20.9) 20.8 23.2 25.8
18.4 (20.0) 22.9 24,8 26.8
16.3 (17.7) 19.0 21.3
...
...
. .
- ASollcalculated
I
,
,
using bond distances and vibrational
B. Electrostatic Calculations for the Negative Ions and Comparison of Calculations with Experimental Results. Electostatic calculations of the potential energy E, of the clusters X-(H20), were made since it was believed that a comparison of the calculations with the AH,-1,, will help in the interpretation of the experimental results. The potential energy E , was expressed according to eq I as a sum of the attractive potential energy
E,
=
EDIP
+ EPOL + EDIS + RDIP + REL
(I)
terms EDIP, EPOL, and EDIS standing for the iondipole, ion-induced dipole, and ion-water molecule dispersion forces interactions. The repulsive interactions considered were R D I P and REL standing for the dipole-dipole repulsions between the water molecules and the repulsion between the charge clouds of the ion and the water molecules. The procedures followed in the calculations were the same as those given in the preceding paper.' All water molecules were placed in equivalent positions. For the negative ions, two orientations of the water molecules may be considered. I n one orientation the negative ion lies on the extension of the bisector of the HOH angle
HYDRATION OF IONS IN THE GASPHASE
1479
kdF-
-60 -70
8
20
1
del-
:--
oIc
n
a, . -
Figure 8. Comparison of calculated potential energy A&,. and experimental AH,,, for Cl-(H20),: X, AHo,,; 0, AEo,, (sym); 0, AEo,* (nonsym).
2
:
-12-
\
-ij - I O -
~
12
0,1
4,5
3,4
2,3
5,6
U
Y
Figure 6. AHn-1,,
us. n for
-a
hydration of halide ions.
-
-6 -4
-2
-
t
L
,
0,l
I
1,2
I
I
2.3
3,4
4,5
56
(n-l,n)
Figure 9. Comparison of calculated potential energy A E , - ~ . . and experimental AHn-1,, for Cl-(HgO),: X, AH--I,*; 0, A%+ (sym); 0, AE,-I,, (nonsym).
I
I
1
2
3
4
5
6
7
8
n
Figure 7. Comparison of experimental AHo,, wit,h total single ion heats of hydration of Latimer, Pitaer, and Slanski (L) and Randles (R,).
and the two hydrogens are symmetrically ‘%ouching” the ion. This orientation we will call symmetric. In the second nonsymmetric orientation the negative ion lies on the extension of the H-0 bond with one hydrogen atom touching the ion and the other rotated around the X---H-0 axis to a position of minimum potential energy.
The electronic repulsion energies REL were calculated under the assumption that only the repulsions between the ion and the hydrogen atoms “touching” it are important. The repulsive term REL was set equal to 2A/R12 for the symmetric structure and A/R12 for the nonsymmetric structure. R is the distance between the ion and hydrogen nuclei. The selection of the constant A was obtained by the procedure outlined in the Appendix of the preceding paper.‘ As distance parameters for Figure 9 of the Appendix, in ref 1, the Stokes van der Waals radii were used for the halide ions: F- (1.909 A), C1- (2.252 A), Br- (2.298 A), I- (2.548 A), and the van der Waals radius for hydrogen H (1.2 A). The resulting values for A are given in Table I. Volume 74, Number 7
April 2, 1970 /
1480
M, ARSHADI,R, YAMDAONI, AND P. KEBARLE probably comes about from an F-H bond formation. Thus the electronic structure of the monohydrate is probably a hybrid of the mesomeric structures I, 11, and 111. The fact that this effect does not occur
0
E , -20 0
U
-14. -12
'
I
- 8-
I
I
1
0,l
1,2
I
4
3,4 ( n - 1,n)
2,3
I
45
5,6
Figure 10. Comparsion of Calculated potential energy and experimental AH%-,,%for F-(HzO),: X, AH%-,,,, 0, AEn-i,%(sym); 0, (nonsym).
The results of the calculations are given in Table I and Figures 8, 9, and 10. In Figure S a comparison is made between the experimental AHo,, and the calculated AEo,, (sym) and (nonsym) for the medium sized ion C1-. The figure shows that there is very good agreement between the AH,,, and AHo,z and the calculated symmetric values. For higher n, the calculated AEO,n(sym) become somewhat smaller than the experimental results. The - AE,,, (nonsym) are considerably lower for all n. However, the falloff in slope with increase of n in the nonsymmetric case is slower than that of the symmetric case. This tendency is shown more clearly in Figure 9 which gives AH,-l,, and The fall-off of the -AE,-l,, (sym) is much faster than that of the experimental or the nonsymmetric values. The slower fall-off observed for the nonsymmetric case must be due to the fact that the nonsymmetric arrangement allows more molecules to be fitted around an ion of given radius, ;.e., this arrangement minimizes the repulsions between the water molecules. Probably in the actual clusters, the first water molecules go in the symmetric positions, but as the cluster grows some molecules assume synimetric and others nonsymmetric positions or positions intermediate between symmetric and nonsymmetric. The calculations for the larger ions Br- and Ireveal trends which are very similar to the trends in the C1- ion; therefore they will not be discussed. However, the F- ion shows an interesting deviation which should be mentioned. In Figure 10 one finds that the -AHo,, is considerably larger than the calculated -AEoal. Since the symmetric AEo,l were in good agreement with AH,,,, for all other ions, the discrepancy observed in the F- case indicates that the bonding in F-.H20 is not well approximated by the electrostatic model. The additional bonding
-
The Journal of Physical Chemistry
m
II
to such a large extent with the other halides is easily understood. The tendency for H-X bond formation is by far the largest for fluorine. This is illustrated by the very high bond dissociation energy in hydrogen fluoride D(H-F) = 139 kcal/mol as compared with D(H-Cl) = 103 and D(H-I) = 71 kcal/mol. The close agreement between the absolute values of the calculated A E O J and AEl,z(sym) and the corresponding experimental A H O J and AHI,~is probably not significant. We do not believe that the electrostatic calculation is capable of producing such close agreement with experiment. In the preceding paper' dealing with the alkali ions, rather poor agreement was found between the electrostatic calculations and experiment. In that place reasons were given as to why the A values selected by the procedure used in the Appendix of ref 1 might be effectively too low for the positive ions. If these reasons are valid, the A values selected for the negative ions should be too low and thus lead t o - A E o , ~ which are too low. We think that absolute values of the electrostatic calculations for positive and negative ions do not have any great significance and that only the relative changes with .n are instructive. C. Compavison between the Hydyation Eneygies of the Alkali and Halide Ions. The experimental enthalpies AH,-,,, for the alkali and the halide ions are shown together in Figure 11plotted us, (n 1, n). The hydration interactions of these spherical ions are probably best examined if one compares the hydration energies of isoelectronic pairs like I(+ and C1-, Rb+ and Br-, etc. Since the nuclear charge of the negative ion in the isoelectronic pair is two units lower, the size of the electron cloud of the isolated negative ion will be definitely larger than that of the positive ion. Therefore, if one considers only the effect of ionic size (in vacuo) one would definitely predict that the positive isoelectronic ion should have higher - AH,-j ,n. Examining the enthalpies of the larger ions like E(+ and C1-, R b + and Br-, and Cs+ and I-, for which the effect of any covalent bonding t o water should be small, we notice (Figure 11) that in all cases the isoelectronic positive ion has considerable higher - AH,-, ,%. Thus the prediction based 0 1 1 1 ~ on the size of the ions is borne out at least qualitatively
-
HYDRATION OF IONS IN THE GABPHABE
1481
required in the various steps of the cycle. Two sets of data which have found wide acceptance are those \ of Latimer, Pitzer, and Slanski and Randles.a Data \ \ from these two sets were used earlier in the paper for a correlation of the relative heats of hydration of negative ions. Examining the values that the Latimer 25 set gives for the alkali and halide ions, one finds that the -AHh for the negative ion is substantially larger than that for the positive isoelectronic ion. Thus -AHh (Br-) = 81.4 kcal/mol while -AHh ( R b t ) = 69.2 kcal/mol. Therefore Latimer’s heats of hydration are exactly of opposite magnitudes to those expected from the standpoint of electron cloud size of the gaseous alkali and halide ions. Two basically different reasons have been put forward to explain the Latimer data. The first explanation which exists in several variations6 proposes that the arrangement of water molecules around the negative ion and (or) in the transition from the hydrated ion to the bulk of the liquid is more favorable. The second suggestion has been that water molecules have an electrical quadrupole moment which is of such a size that it leads t o an attraction with negative and repulsion with positive ions.’ On the basis of the present results which give higher energies of interactions for the I I I 1 0,1 1,2 2,3 3,4 405 positive ions, it is possible to eliminate the quadrupole n-l,n theory since the effect of the quadrupole should be particularly large exactly at close range, ie., in the Figure 11. Comparison of AH,-^,, for hydration of alkali gaseous clusters, It should be pointed out that the positive and halide negative ions. present results do not prove that a quadrupole moment is completely absent. They only show that a water by the results. It is interesting to note that the quadrupole moment of the magnitude required to difference between the AHn-~,nof the isoelectronic explain the Latimer data cannot be present. In any pairs decreases as n becomes larger and that in the event, as is shown in the subsequent discussion, the cases of Na+ and F-, K+ and C1-, Rb+ and Br- a present results cannot be reconciled with the very crossover is observed within the range of the figure strong hydration interaction for negative ions prein which the - A H n - I ! n of the negative ion becomes dicted by the Latimer data. higher. Furthermore, the smaller the size of the ions The Randles total hydration energy set assigns a the sooner does the crossover occur. For the Na+, slightly higher - A H h for F- than for Na+ but for F- it occurs at about n = 4,for K+,Cl- at n = 5 5 the larger ions the - A H h of the positive isoelectronic and for Ru+,Br- at n = 6. These observations can ions are somewhat larger than those of the negative be explained on basis of the electrostatic calculations ions, The Randles data are thus closer to expectaAHn-~,n tions based on the present results. A correlation of which indicated that the slower decrease of of the negative ions is due to the ability of the water the present data and the single ion hydration energies molecules to assume nonsymmetric positions in which of Latimer and Randles is given in the composite only one of the hydrogen atoms “touches” the negative Figures 12a,b which shows plots of [-AHo,,(M+)] iou. These nonsymmetric arrangements result in [- AHo,~(X-)] for isoelectronic pairs. The plots are lower water-water repulsions for ligands in the same based on the experimental AH,-I,, whenever these shell and become of importance when the shell bewere available (low n). For higher n, values extrapcomes crowded. Of course crowding occurs sooner olated on basis of Figure 11 were used. Also inin the smaller ions. dicated in Figure 12 (as two horizontal lines) are the It is of interest to examine at this point the correladifferences of the total single ion hydration energies tion of the present results with the total single ion hydration enthalpies. Values for the total enthalpies of hydration have been obtained by several authors (6) (a) E. T. Verwey, Rec. Trav. Chim., 61, 127 (1942); (b) D. R. Rosseinsky, Chem. Rev.,65, 467 (1965). on the basis of thermodynamic cycles and experi(7) A. D. Buokingham, Discusshns Faraday Soc., 24, 151 (1957); mental and semiempirical evaluations of trhe energies F. Vaslow, J. P h y s . Chem., 67, 2773 (1963). \
‘\
-------
I
-
‘Volume 7 4 , Number 7 April 9, 1970
1482
M. ARSHADI, R. YAMDAGNI, AND P. KEBARLE
I
-
-201 0.1
I" U - 2 W
L
01
'
0.2
'
0,2
1
0,5
'
0.3
'
0,4
'
04
1
0,5
'
0.5
'
"
1
0,6
0.7
G6
0,7
'
03
'
0,8
'
0,P
'
0 ~ 1 ~
0,lO
Figure 12. Comparison of AH^,^ hydration of alkali and halide ions with total enthalpies of hydration of Latimer, Pitzer, and Blanski (L) and Randles (R).
for the isoelectronic pairs based on the data of Latimer and Randles, It can be seen that the AHo,, differences are in all cases much closer to the Randlev differences; moreover, the AHo.%differences seem to extrapolate for high n into the Randles differences. Of course by definition the AHo,% differences should become equal t o the AHt, differences for very high n. We can summarize the observations on positive and negative isoelectronic pairs as follows. In the initial hydration interactions (n small) the positive ion gives higher energies of interaction as would be expected from its smaller size. As the cluster grows, interactions in the negative ion become gradually more favorable (Figures 11 and 12). This is probably due to the ability of the negative ion to pack the water molecules more closely without too large water-water repulsions. Extrapolation of the data to moderately
T h e Journal of Physical Chemistry
high n seems to lead to an asymptotic approach to the Randles data. Thus the present results are in support of the Randles data and also indicate that the decisive interactions determining the total heats of hydration occur during the attachment of the first 8-12 molecules. One may consider the further path toward the formation of a liquid solution as a single step in which the large cluster8 are fitted into the bulk of the liquid. The present results indicate that the hydration energy for this final "step" will be quite similar for a positive or negative cluster containing the corresponding isoelectronic ion. D. Entyopies of Hydvation Reactions. The experimentally determined entropies are summarized in Table 11. The Table also includes values for which were calculated from the translational, rotational, and vibrational entropy changes in the 0,l reaction using the well known forniulas of statistical mechanics. The rotational entropies were determined on basis of the X--H20 distances obtained from the electrostatic calculations. The vibrational entropy changes were calculated by assuming three new vibrational modes in the complex X--HzO, The force constants for these vibrations were obtained from the electrostatic calculations. The procedure was essentially identical with that used for K+(OHt) which has been described in greater detail in ref 8. Comparing the experimental and calculated ASo,g one finds that the agreement is only fair. The theoretical - AS0,1 are generally larger. The agreement between calculated and experimental values for the alkali hydrates was very much better.l It is difficult to say whether the differences between the present calculated and experimental results reveal structural features in the complexes not taken into account by the calculation or whether they are due to experimental error in the AS0,l determinations. Unfortunately, the AS determinations are obtained from the differences of two large terms AG and AH and are therefore subject to greater error. Examining the changes of ASn-1,%with increase of n, one finds that the - A S values increase as n increases. The same trend was observed with the alkali hydrates. The increase of the negative entropies should reflect the gradual loss of freedom of the water molecules in the complex due to crowding in the cluster.
Aclcnozcledgments. This work was supported by the Canadian National Research Council. Figure 2 in the text was obtained by Rfr. J. Payzant, a graduate student in our laboratory. (8) S. K.
Senrles and P. Kebarle, Can. J . Chem., 47, 2619
(1909).
