Determination ol Partial Volar Volumes of Monovalent Ions
1099
olumes of Ions in Organic Solvents from Ultrasonic Vibratio Density Measurements. 11. Ethanol and Dimethylforrnarnide awaizumi and R. Zana* C N.R S , Centre de Recherches sur les Macromolecules, 67083 Strasbourg-Cedex, France
(Received November 16. 1973)
The partial molal volumes of monovalent ions in ethanol and dimethylformamide (DMF) have been obtained from ultrasonic vibration potential data and density data for solutions of uni-univalent electrolytes. The use of Hepler’s equation has permitted us to split ionic partial molal volumes into geometric and electrostrictive contributions. The results obtained in this work together with those previously reported for ions in water and methanol indicate that the parameters which determine ionic partial molal volumes are (1) the size of solvent molecules, (2) the degree of steric hindrance of the poles of the dipole of the solvent molecule, and (3) the properties of the layer of atoms 3-4 A thick around ions. The geometric contribution depends on 1 and 2 while 2 and 3 appear to determine the contribution of electroStriction.
Introduction In the first paper1 in this series, partial molal volumes of monovalent ions in methanol were obtained from the combination of ultrasonic vibration potential (uvp) data and density data for solutions of uni-univalent electrolytes. ‘The purpose of this paper is to report similar data in ethanol and dimethylformamide (DMF). As will be seen below these data show that the empirical methods of Mukerjee2 and of Conway, et u L . , ~ for obtaining ionic partial molal volumes do not hold in DMF. They also provide new informations about the parameters which determine ionic partial molal volumes. The apparatus and the experimental procedures used in this work have been proviously described.l
Partial Molal VoWumes of 1-1 Electrolytes at Infinite Dilution in Ethanol aind D M F Density data for ellectrolytes in ethanol and DMF are quite scarce in the literature. For this reason, as a part of this work measurements of density as a function of concentration were performed for solutions of ten 1-1 electrolytes in ethanol and thirteen 1-1 electrolytes in DMF. The apparent molal volume cpz of the salts have been calculated using eq 3 in ref 1. The partial molal volumes vzoof the salts at infinite dilution were obtained by extrapolating to zero concentration the curves cpz = f(c112), where e is the concentration, according to Masson’s e q ~ a t i o n . ~ The results are shovvn in Figures 1-4. They indicate an overall error of about *l cm3/mol on Vzo values. The error on v(Cs1l) in ethanol may be larger because the limited solubdity of Cis1 prevented the investigation of a sufficiently large range of concentration (the extrapolation f ( c 1 l Z ) the was performed by assuming for the line cpz same slope as for Rbl). Within the experimental error we found that small additions of water resulted in negligible changes of cpz and (see Figure 3). The values of V 2 O and of the slopes S , ’ of the lines cpa = f(clI2) are listed in Table I where are also giveh the results of other worker^.^^^ The result of Butler and Lees5a for LiGl in ethanol is in good agreement with that found in this work. For DMF differences well above the experimen-
vzo
tal error appear between the results of Gopal, et c ~ l . and ,~ those found in this work. It must be pointed out, however, that the results of these authors6 were obtained a t 35”. They are cited in Miliero’s review? as a “private communication” but have not appeared in the Chemical Abstracts up to now. We were thus unable to find thoc. source of these discrepancies. For this reason our results were preferred when calculating ionic partial molal volumes. The results of Table T indicate that within the experimental error the values of V 2 O obey the additivity rule.’ A number of results listed in Table I were obtained using this rule because the solubility of several electrolytes (mostly chlorides in ethanol) is too low to permit measurements of density with the accuracy required for apparent molal volume determination. Ultrasonic Vibration Potential of Electrolytes in Ethanol a n d D M F The results of the measurements performed in the range 3 x to 3 x M for most of the electrolytes of Table I are given in Table [I. The sign of the uvp @ was assigned as previously rep0rted.l-8 Small additions of water (up to 17’0) were found to have no effect on the measured uvp. As for electrolytes in methanol, in all instances but LiN03, the uvp show a decrease a t Concentrations above 3 X to l o w 2M . These decreases are relatively small for bromides and nitrates but become significant for iodides thus showing the same trend as that observed for electrolytes in methano1.l Two processes may be responsible of these variations of @: (1) ion-pair formation which occurs a t lower concentrations in organic solvent than in water, owing to their lower dielectric constant (as pointed out in ref 1 ion pairs may give rise to dipole vibration potent i a l ~ )(2) ; ~ formation of complex ions such as triple ions.’O The concentration of ion pairs and complex ions increases with the electrolyte concentration c One may therefore expect an influence of these two processes on the measured uvp at higher c, as is experimentally found. At this point it is worth recalling that in some soap solutions is concentration dependent bot,h in the submicellar and
+
The Journal of Physicai Chernistry. Vol. 78. No 11. 1974
F. Kawaizumi arid R. Zana
Figure 1. Apparent molal volumes of alkali metal and ammonium todiaes vs (molar concentration) in ethanol at 25"
r--
1
0.1
0.2
0.3
0.1;
0.6
0.5
Figure 3. Apparent molal voiumes of ammonium, rubidiu m , potassium, sodium, and lithium nitrates and lithium chloride vs. (molar concentration)'!* in DMF ( A ) and in 99% DMF-1% H 2 0 ( V )at 25".
J
i
G
0.1
0.2
0.3
0.4
Figure 2 , Apparent molal volumes of NHhN03, NHdCI, NaBr, LiNO:,,, and LiCi (our results, A , results from ref in ethanol at 25". The 5a, 0 ) vs. (molar inner concewiration :scale is for LiCI. 0
in the micellar ranges of concentrationll because of submicellar association and micelle formation. The reisurts of Table 11 show that in most instances @ varies only slightly with c in the range 3 x to 3 X 1.0-3 M . Foi, this reason the values of @ listed in column c in 'Table 11 and which were used in calculating ionic partial molal volumes have been taken in this range.
Calculation of Iontic Partial Molal Volumes The calculation of partial molal volumes of anions ( Y - 0 ) and cations (9,O) a t infinite dilution makes use of eq 1 and 2 in ref 1.. I t involves the knowledge of the cation and anion tyansport numbers t , and t - = 1 - t - and of the amplitude of the velocity of ions in the ultrasonic field. The transport numbers have been obtained from the 1imit.ing eqkivalent conductivities of ions in ethanol and DMF compiled b y Kratochvil and Yeager,12 and the values of t - are listed in Table I. At the onset it must be The Journal of Physrcai Chemistry. Vol. 78. N o . 1 7 . 7974
0.1
0.2
0.3
0.4
Apparent molal volumes of alkali metal iodides, ammonium iodide, and potassium and sodium bromides in DMF at 25'. vs. (molar
Figure 4.
pointed out that transport numbers in DMF are less accurate than in water, methanol, and ethanol. For example, Prue and Sherrington13 results, which were adopted in this work, yield t o ( K + ) = 0.359 in KCI solution while data from other workers14 give 0.342 for the same quantity. This fact introduces an additional error of up to 2 cm3/ mol in the calculation of ionic partial m Q l d volumes in
DMF. For ions in ethanol, aEtOHwas determined using the same graphical procedure as for methano1.l Its average value was found to be 11.1 cm/sec. Table I11 gives in column a the ionic partial molal volumes in elhano). calculated using aEtOH= 11.1 cm/sec and the vzfl and Q data of Tables 1 and 11. For each ion the value in column a is an average over the results for all of the electrolytes of Table
Deterrinatioi? of Partial Molar Volumes of Monovalent ions
1101
TABLE 1: Partial Molal Volumes of Electrolytes and C a t i o n Transport N u m b e r s a t Infinite Dilution in E t h a n o l and DMF a t 25" Ethanol
__ V20,
DMF
__
cm3/mol
____
V20,cm3/m01
_ I _ _
HCl LiCl LiN03 NaCi NaRr NaI NaN03 KC1
This work
Other works
- 5.2 5* 1
-4.48
&', cm3/mo1"2
0.733 0.438 0.390 0.482 0.480 0.430 0.432 0.518
3.0a
12 15.3
4:~Oa
20.5 15.5
E;. 1 17.2 151.3~
This work
t+C
12.6n
-4.4 6.9 5.96 6.6 23.1 17.2 13.0" 14.1 30.5 24.3 18.9O 34.9 30.3 17.0. 34.0 28.3
MBr 26.8
KL KNOB NFI4C1 NH41 N 134N 0a RbCl RbI RbNBJ
21.8 35.0 33.1 18.4" 31.6 29.7fi
CSG1
26.2a
CSI CSN08
39.46
0.466 0.469 0.486 0.434 0.437 0.533 0.481 0.484 0.547 0.495 0.498
20
23.9a
13.5 15.7 15 24 23
37.5a
Other works
SV',
'
cm 3/moi8 2
t+C
0.312 0.304 0,352 0.358 0.364 0.343 0 359 0.365 0,371 0,350 0.413 0,425 0.403 0.370 0,383 0,361
9
14 13.5 21.3' 24.51
2.7
16 15.5
35.81
5
16 38.41 41.71
10 21
8
16.5
40.4 34.8~
9.3
0.397 0.376
Values obtained using the additivity rule. The error on ?n(CsI) is probably larger than for other salts owing to the low solubility of CsI in ethanol. The values of t-n(CsC1) arid ?o(CkNO8) in ethanol are likely to be affected by the same error. Values calculated using the results compiled in ref 12. Reference 5b. e Reference 5a. 1 Reference 6.
TABLE 11: Ionic Vibration P o t e n t i a l @ (in pV) of Uni-univalent Electrolytes at Various C o n c e n t r a t i o n s (in .M) in E t h a n o l and DMF a t 2 2 ' ~ Concentration
3
x
_________ Electrolyteh
FtOH
HC1 (l,Oj LiNOa (0,l) NaCl (2,l) NaBr (1,2) N a I (1,l) N a N 0 3 (4,2) KC1 (2,2) KBr (0,l) (12) KNO, (2,2) "4C1 (1,1) "41 (0,2) NH4NO3 (3,~) RbCI ( 2 , l ) R b I (1,1) RbNO, (l,1) CsCl (2,l)
-4.5
esa (l,h)
C S N O ~(3,l)
5 -23.5 -- 62 --
12 9.5
~-43
--5.5 -- 8
DMF
51.5
EtOH
DMF
-4 -22.5 14.5 - 25 -53.5 -8 14 - 14 ~
53 -8
-1.5 - 63
--22.5 - 17 42.5 36 --13.5 - 20 17.5 26.5 64 9
3
10 - 3
10-4
-4 49
x
EtOH
-4 - 22
3 -24.5 - 70 - 16 13
-- 24
8
EtOH
-16.5 47 -21.5 26.5 -4.5 50.5
DMF
DMF
Q'
_______ EtOH
DMF
- 22
-9
16 -24.5 -24 -68 -53.5 -14.5 -9 12.5d i 6 d - a4 -46.5 -53.5 -5d -8d -7 -3 3 d
-24
-58 -7 -9 -70.5
-51.5
- 62
-25.5
-18
-28
- 19
-20.5
-26.5 23
-24.5
- 34
-58
-9
-30.5 -78.5
-26 -67 -8
30 -- 16
- 14
71 5.5
10-2
-4d
-24.5 - 62 -7.5
-5.5 -6.5
EtOH
-12.5 -27 -73.5 -21
-47
x
-3.5 - 20
23 2.5 -24.5 -23.5 -66.5 - 53 -9.5 - 13 24.5 12.5 -13.5 - 46 -53.5 -4 -8.5 -7 -6.5 -70.5 39 -16.5 19.5 70.5
DMF
_ _ _3
10 -2
10-3
- 18
-60
-5
-65 -6.5
-7 - 72
18.5
- 74
-30
-20.5 15.5
--
68
-25 -17 39 45 -18.5 -21 19.5 26.5 71
-9 47.5
- 13
42
- 17
8"
31.5
-4.5d 49.5
Prior to measurements in organic solvents, measurements were carried out on aqueous solutions of CsCl and RbCl in order to obtain the value of the velocity amplitude ai>- in water.' The average value of aiy was found to be 10.35 cm/sec and the uvp's measured in organic solvents have all been mulkiplied by 10.3S/aiv to give 1.he .values of .P listed above. The numbers in parentheses represent the numbers of independent runs performed on each electrolyte; the first number is for to ethanol (EtOH) and the second for DMF. Values of .P selected for ionic partial molal volume calculations (see text). Salt for which the sign of the uvp has been obtained as explained in ref 1.
I involving this ion. The values of p ( N a + ) , P ( C l - ) , p ( N O , - ) and qO(I-! yield results in good agreement
v$'
with those which can be calculated from the data of Table I. For this reason the ionic partial molal volumes have been recalculated using these four values as references and the V z o data of Table I, yielding the set of values :listed in column b. The values of VO(Br-) in columns a and h differ by 5.7 cm3/mol while for all of the other ions the differences are below 2 cm3/mol, i.e., with-
in the experimental error which is estimated to be &2-3 cm3/mol for all ions except Cs' for which the error may be somewhat larger. For ions in DMF, a D M F was taken as 10.5 cm/sec. Indeed the use of eq 5 in ref 1 and the calibration of the apparatus with aqueous solutions of known uvp show that for DMF one should have 10.35 5 anMF5 10.7 crn/sec. The results of these calculations are given in Table IV, The values of the partial molal volume of a given ion, calThe J o u r n a l o f Physical Chernisfry \lo/. 78. No. 1 1 . 1974
1102
F.
BLE IEI: Ionic Partial Molal Volumes in Ethanol at !Go (can3/mol)
TABLE V: Ionic Partial Molal Volumes in DMF in cms/mol and at 25"
__
I _
This WOW
This workb
-9.8 (1.5) -2.5 6.8 15.2 7.0 12.3 (2.6) 20.8 26.7 (3.4) 2 3 . 8 (R.6)
-15.5 --19.2 -9.8 -0.4 5.5 13.3 8.9 12.5 15.1 26.7 23.8
Ion
Mukerjee's methodC
-20.2 -10.5 -1.9 3.9 11.7 6.8 15.0 16.6 27.7
Ion
Waterd
--5.7 -6.6 -6.9 3.3 8.4 15.6 12.2 23.5 30.4 41.9 34.7
Li + Na + K+ Rb + CS NHa + c1Br +
1NOZ(C&) 4N (C3H7)qN (C4Hs)qN (CsHd aN
+
The numbers i.n parentheses represent the root mean square deviations obtained as in ref 1, for iivelocity amplitude a E t O l i = 11.1 cm/sec. Average values calcuhted using f-"(GlP) = 12.5 cm3/mol, I.'o(Na+) - 9.8 cm3/mol, ?n(I-) = 26.7 2rn3,'mo:, ia(iNOy-) = 23.5 cm3jrno1, and the f 1 ~ 0 data of Table I. Values calcu1,nted using Mukerjee's method2 and the ?$ data of Table I. Vduf's obtained from the data compiled in ref 7 with T;o(Cl-) = 23.6 cma/mol (see ref 3 and 8 ) .
TABLE IV: DMF Ionic Partial Molal Volumes in cmz/mol and at Z!5" Calculated from the Data of Tables I and PI with ~ D I I F = 10.5 cm/sec
----Li iVa +
Chlorides
Bromides
Iodides
-22.4 -11.4 -9.2
M+ Rb + c:s
-25.4 -20.4
+
a"
+
-1.0
SaltsofZi+
Na'
K"
-26.4 -14.5 -13.3 2.2 -4.0 Rh+
Cs+
-24.1 -17.5 -7.1 -8.4 0.9 -2.1 NHa+
B. Results for Anions
c1Rr I NOd-
31.0
28.3 32.0 49.5 34 7
24.4 34.5 45.0 31.4
26.2 47.3 36.7
19.9 38.2 33.9
38.9 32.3
culated from the results for several electrolytes containing this ion, show a greater scatter than in the case of methanoll and ethanol For example, the calculated values of p ( I - ) range from 38.2 to 49.5 cm3/mol with an average values of 43.8 cm3/mol and a root mean square deviation of 4.5 cm3//mol. For NQ3-, however, the values of Vo(NOa-) calculated for the six nitrates studied in this work are quite consistent, ranging from 31 to 36.7 cm3/ mol with a mot mean square deviation of 2 cm3/mol from the mean or 33.3 cm3/mol. For this reason this value of pYO(NO3-) was adopted as reference and used together with the Vzo data of Table I to calculate the set of ionic partial mold volumes given in column b in Table V. For coniparison are given in column a the average ionic partial molal volunies calculated from the results of Table IV. The comparison of columns a and b shows that for Li+, K + , Cs+, NH4+, and C1 the difference between the two sets of data is less than 3 cm3/mol. For Na+, Rb+, and Ithis difference 1s about 5 . 5 cm3/mol. This last value is slightly above the estimated maximum error on ionic partial molal \.olumes in DMF (k4 cm3/mol). The case of Br- is more difficult t o understand. Indeed the difference between the resulrs of columns a and b is larger than 10 cm3/mol. The behavior of Br- in DMF is similar to that The Journal of Physical Chemistry Vol. 78. No. 7 1. 1974
+
+
This worka
This workb
-24.1 -22.1 (3.6) -11.0 (3.0) -10.3 (2.2) 1.6 - 2 . 4 (1.2) 24.7 (3.1) 33.3 43.8 (4.5) 33.3 (2.0)
-26.4 -16.3 -9.0 -5.0 1.5 -3.1 22.0 22.9 39.0 33.3 125. S e 19Se 266.4s 336, l e
Mukerjee's methodC
-19.4 ---9.1 -2.0 2.6) 8.5 3.9 15.0 15.9 32.3 26.
Waterd
-6.6 -6.9 3.3 8.4
15.6 12.2 23.5 30.4 41.9 34.7 143.4 208.7 270.1 333.5
a Average values calculated from the results of Table 111. For N a + and K + the results obtained with the bromides have not been taken into account
(see text). The root mean square deviations are given in parentheses. Calculated from the ?$ data of Table I with ?O(NQs-) = 33.3 cm3/mol. Calculated using Mukerjee'e method and the data of Table I. Obtained from the data compiled in ref 7 with Vo(Cl-) = 23.5 cm"mo1 (see ref 3 and 8) e Obtained from the ?$ data for tetraalkylammonium halides of Gopal, et al.,B cited in ref 7 with I.'O(I-) = 39 cm3/mol,
Nitrates
A. Results for Cations
+
Kawaizumi and R. Zana
observed in ethanol. The purity of the bromides used in the experiments is not involved as NaBr and KBr were both Merck purissimum compounds (purity >99.9%) and yielded identical values for V z o and when used without further purification and after an additional recrystallization. Before discussing ionic partial molal volumes in terms of geometric and electrostrictive contributions it is interesting to compare the "experimental" ionic partial molal volumes obtained in this work with those that can be calculated using the method of Mukerjee2 and the extrapolation procedure of Conway, et aL3 Mukerjee's method assumes the ionic partial molal volume Vio of an ion i to depend only on its ionic radius r,. The V,O's are then obtained by setting the value of the partial molal volume of a certain ion such that all other ionic partial molal volumes calculated from this chosen value and VzO data fall on a single curve when plotted as a function of r,3. Mukerjee's method can be used rn each instance where a sufficient number of values of VzO are known. When applied to the data of Table I in conjunction with Pauling's ionic radii, this met hod yielded the two sets of values listed in column c in Tables 111 and V. For ethanol the differences between the experimental results (column b) and those of column c are of about 1-2 cm3/mol, i.e , within experimental accuracy. For DMF, however, the differences are of about 7 cm3/mol. Thus Mukerjee's method does not apply in DMF in contradistinction to water,8 methano1,l and ethanol, This conclusion is discussed below. The extrapolation method of Conway, et makes use of the partial molal volumes of tetraalkylammonium (TAA) halides. An extrapolation to zero cation molecular weight then yields the partial molal voiume of the halide ion. There are no data available for TAA halides in ethanol. In DMF the use of Gopal. et a/ results extrapolated to 25" yields p ( I - ) = -4 f 5 cms/mol. This value is more than 40 cm3/mol below that in column b of Table V and shows that as for methanol1 the extrapolation method
Determination ot Partial
Molar Volumes
of Monovalent Ions
1103
does not hold for DMF. The same conclusion is likely to be true for ethanol.
iscussion As for ions i n methanol1 and water8 the equation proposed by H e p l d 5 will be used to split ionic partial molal v01umes in !DMF and ethanol into a geometric contribution and B contribution of electrostriction. This equation is given by15
VI0 = Ar,3 - B/r,
(1)
where A and E) are two constants. The first term in the right side of eq 1 represents the geometric contribution and the second term the electrostrictive contribution. This equation has been shown to give a good description of ionic partial molal volumes in water8 and methano1.l For these two solvents A and B have been found to depend only on r, and not on the sign of the ionic charge.'SX Figures 5 and 6 show the plots of Y,Or, us r,4 (Pauling's ionic radii) for ions in ethanol and DMF. For each solvent the points relative to alkali metal ions and halide ions define two straight lines (referred to as 1 and 2, respectively) as predicted by eq 1 For DMF the difference between lines 1 and 2 is well a,bove the experimental accuracy and there is a clear dependence of A and B on the sign of the ionic charge. For ethanol, such a clear cut conclusion cannot be reached on the basis of the results of Figure 5 . The difference betwwn lines 1 and 2 is larger than that found for methanol (see Figure 6 in ref 1). Moreover the slopes of lines 1 and 2 are different while in methanol these lines run parallel.' Nevertheless, Figure 5 shows that line 1' which corresponds to the results of column c of Table I11 (Mukerjee's method) is compatible with the experimental points for all of the alkali metal and halide ions (values in column b) if we assume a maximum error of f 4 cm3/mol for p ( C s + ) (owing to the limited accuracy on the value of ~ { C S I )and ) for p ( B r - ) (whose abnormal behavior has been pointed out above). With the same assumption the coirespondence method of Criss and Cobblel6 appears to hold for ions in ethanol and yields ( v l o ) ~ t = o ~0.72 (v2°)Hzo - 3. The values of A anti B for alkali metal and halide ions 01,s of Figures 5 and 6 and the results F calculated from the data of Gopal, Figure 6), are given in Table VI. For comparrson we have also given the results for ions in waters and methanol.' As will be seen now these results will permit us to find which parameters determine ionic partial molal volumes. The discussion which follows is restricted to the values of A and R obtained from line 1' both for ethanol and mt?thanol (see Figure 6 in ref 1). Discussion of the Values of A The results of Table VI show the thre:! folXowing salient features: (1)within experimental accuracy A is independent of the sign of the ionic charge for alkali metal and halide ions in water, methanol, and ethanol hut cepends on this parameter in DMF; ( 2 ) for the three organic solvents the values of A for alkali metal and halide ions are smaller than in water; and (3) TAA ions are charact d by identical values of A in water, methanol, and D These resulis can be interpreted in terms of size of solvent molecules and of specific interactions between ions and solvent dipolss Indeed, one may expect the contact between alkali metal ions and advent dipoles to occur at the negative
0
5
10
20
15
Figure 5. Variation of Piffri vs. ri4 for ions in ethanol. Lines 1 and 2 correspond to the results of column b in Table I l l and line 1' corresponds to the results of column c obtained by means of Mukerjee's method.
60
~
-1000 40-
-500 20.
i-4
- 20
J
(A4j
600
---i
0
5 10 15 20 Figure 6. Variation of Pior, vs. ri4 for ions in DMF, Lines 1 and 2 correspond to the results of column b in Table V and line 1' corresponds to the results of column c obtained by means of Mukerjee's method. The inner scales are associated with line 3 which shows the results for TAA ions.
pole of the dipole, 1.e , at the oxygen atom of the solvent molecule, for the four solvents of Table VI. On the other hand, for all of these solvent molecules there is only little steric hindrance about the oxygen atoms and those may be considered as equally accessible to cations. It is therefore meaningful to compare the geometric contributions to the partial molal volume of a given cation in these solvents. Table VI shows that for alkali metal cations A increases as the size of the solvent molecule decreases, Ie , as the average volume of the holes in the solvent structure decreases. Thus for a given type of ion-solvent dipole contact the perturbation of the packing of solvent molecules brought about by a given cation decreases as the size of the solvent molecule increases, resulting in smaller values OfA.
The same reasoning holds for halide ions in water. methanol, and ethanol where the contact halide ion-solvent dipole occurs at the hydrogen atom of the solvent hydroxyl group. It must be added that the hydrogen atom is The Journai o l Physical Chemistry 'dol 78 N o 1 7 1974
1184
F.Kawaizumi and 8.Zana
TABLE 'VI: Values of A (crn3/A3mol) and B (cm3A/mol) at 25" -
__
____I_
_ l _ l
Methanol
.___
A
Ethanol
- -
A
-
-
B
A
DMF
Water" -.___
B
A
A
H
l__l_l___
Halide ions Alkali metal ions T A A ions a
\\
3 . 5 =k 0 . 2
2 . 4 lt 0 . 2
17.5 i 2 90 rt 20
] 3.3 & 0 . 2
12 i 3
2 f5 ' 18 l t 3 ) 4.75 f 0 . 2 10 lt 2
32 .. 58 f 0o ., 43 2.4 i 0.2
100 i 20
2 . 4 f 0.2
15 i 5
From ref 8.
TARLE VI1 : Comparison between Experimental and Calculated Values of B for Water, Methanol, Ethanol, and DMF at 25" Solvent
a
D"
10"K~, cm2,fdyn
Water
78.4
l\&el,hanol
32.6
12.
Ethanol DMF
24.3
11.4a 6.20b
36.7
10"(d In D / d p ) , cmz/dyn
4.71"
4.57a
11.3c
From ref Z!. Calculated using eq 3 and 4 and the data in ref 22 and 24.
as accessibls? to anions as is the oxygen atom to cations and one s h o d d not expect important differences of organization of solvent molecules about, anions and cations in these three solvents. Therefore the A values should depend only slightly on the sign of the ion charge. In going to DMF thE; situation changes drastically. Indeed the nitrogen atorr is sterically very hindered and thus not accessible to halide ions. Important differences of organization of DMI' molecules about anions and cations must be therefore expected and this may very well explain the difference between the values of A for halide and alkali me.tal ions (see Table VI and Figure 6). One is also led to predict closl?r values of A for these two types of ions in formamidie where the P; atom is much less hindered than in DNlF ,and thus more accessible to anions. Ionic partial molal voiume determination in formamide thus appears worthwhile. In the above the concept of volume fraction statistics?7J8 which has permitted other worked8 to obtain the value of A for ions in water has not been used. Indeed, as already pointed out1 this concept, supposes (1) a mixture of two ';ypes of spherical objects while methanol, ethanol, and DMF molecules are not spherical and (2) that contacts beiiween the two types of objects occur a t random. This is clearly not the case, especially with DMF. Table VI Indicates that for TAA ions, A is independent of .the natuit of the solvent. With the radii of TAA ions given by Rc8binson and Stokes,19 A has been found to be very close ti, the value which can be calculated for a rigid sphere immersed in a continuous solvent, i . e . , 2.52 cm3/ The simplest explanation for this last result is to mol be found in the large size of TAA ions. Indeed the smallest TAA ion (tetramethylammonium ion) has approximately the same :size as DMF molecules, ie., the largest solvent of Twbie VI. I t must be pointed out, however, that if the experimental value of A depends on the choice of TAA ion radii, the fact that identical values of A were found for wster, methanol, and DMF is not affected by this choice. DiscussiorL of t h e Values of B. The expression of B for monovalent ions,20.21given by eq 2, provides a theoretical basis for discussing the values of B of Table VI. In eq 2, B The Journal o f Phys/cai Chemistry. Voi. 78. No. 11. 1974
B c n ~ ,
cm3 .%/mol
4.2
10 (alkali metal, halide and TAA
ions) 17 (alkali metal and halide ions) 90 (TAA ions) 12 (alkali meial and halide ions) 18 (alkali. metal ions) 2 (halide ions) 100 (TAA ions)
24.2 32.6 11.7
From ref 20 and 21.
is expressed in cm3 A/moP, D is the dielectric constant and P the pressure in dyn/cm2.
B
=
6.9 X 10l2 d In D _____
l _ _ l l
D
dP
B has been calculated to be20,214.2 and 24.2 cm3 A/mol for water and methanol, respectively, as the value of the derivative d In D / d P is known for these solvents. For ethanol and DMF this quantity is not known. However with an approximation of about 10% this derivative can be set equal to the isothermal compressibility M of the solvent. Indeed the values of d In D / d P and oi Krl given in Table VII check this approximation. KT is known for ethanol22 but not for DMF. For this solvent K- was calculated from the adiabatic compressibility K , using eqZ33 and 4 where
T i s the temperature, V the molar volume of the solvent, a the isobaric expansibility, C,, the molar heat a t constant pressure, d the density, and c the velocity of ultrasound. As all of these quantities are known22,24for water, methanol, and ethanol the validity of eq 4 was checked before using it to obtain K.r for DMF. The values of K r and of B,,,,, calculated by means of eq 2-4 are given in Table VII together with the experimental results, BexpL,from Table VI. The comparison between the values of Be,,,, and Bcalcd shows that the solvent continuum model does not permit the explanation of any of the experimental results. It is not possible however to decide whether this failure of the continuum model is due to the model itself or to the form used for the geometric contribution because the value of El obtained from eq 1 depends on this f o r a . Therefore the comparison of B in various solvents using eq I may not be correct if the geometric contribution is not proportional to r,5 in all solvents as previously pointed out by Millero.20b In this respect, the determination 01 the fraction of void space in a mixture of spheres (ions) and ellipsoids or cylinders (solvent molecules) in the same manner as in Robinson and Stokes1* work would be very interesting.
Determination of Partial Molar Volumes of Monovalent Ions In our study of ions in methano1,l we were led to interpret the values of B in water and methanol in terms of dielectric properties of .;he first layer of atoms, 3-4 A thick, in contact with the ion rather than in terms of dielectric properties of the solvent. in the bulk. The results obtained in this work g h e a strong support to this interpretation as is shown now. (I) For the four solvents of Tables VI and VI1 the layer of atoms in contact with dkaii metal ions contains essentially oxygen atomsz5 and hydrogen atoms which are either covalently bound (water, methanol, ethanol) or close (DMF') to oxygen atoms. Thus the content of this layer depends much less on the nature of the solvents than W O U ? ~appear li.oni their chemical formulas. This explains that the values of are all between 10 and 18 cm3 A/mo? while those of Bcalrdrange from 4 to 32 em3 A/ Wlol. ( 2 ) In wa'kr.. methano!, and ethanol. halide ions are in contact with hydroxylic hydrogen however, the hydroxylic oxygen atoms are in their close neighborhood. Therefore for these three solvents the layer of atoms 3-4 A thick., i.e , abont the diameter of a hydroxylic group or of' a methyl group, around halide ions has about the same content as around alkali metal ions. Owing to this behavior, QrxPt does iiot depend on the sign of the ionic charge for the three above solvents, In DMF, halide ions have a tendency to siarround themselves with nitrogen atoms. Howesver, 8.s poi:iitcd out above, these atoms are very sterically hindered ,-ompared to the oxygen atom of DMF. tance between halide ions and nitrogen rge and results in a smaller electrostriction than for illkali metal ions. These results are to be compared with those of LalibertB and Conway26 in their study of the electros-triction of water by R,H4-,N+ ions with 0 < x 4 . These authors have shown that when the steric hindram2 at the nitrogen atom is increased by increasing x 01 the length of the alkyl group R, the electrostriction of watw decreases rapidly because of the increasing average distance between water dipoles and the ion though a reverse situation occurs for where negative ions cannot get close to the positive pole of the solvent dipole the end result remains the same. Tho distance ion-dipole is too large to give rise t o a strong electrostriction. The small value of R,,,, for halide ions i n DMF indicates that these ions are teil." A similar conclusion was reached b y other w o r k e d 3 011 the basis of ionic limiting equiva:a
(3) The values of BiAxpt found for TAA ions in methanol anti DMF can be considered as equal within the experimental error. Orz the basis of the above model such a result is to be expected as in both solvents methyl groups tend to surrourd TA.A ions. In water however TAA ions are of neccwity in contact with OH groups. Therefore eq 4 when applied til the effective content of the layer of atoms in contact with 'FAA ions will yield much larger values of B for organic solvents than for water. This is because the dieleetric constant 0:: a system containing mostly OH groups is 1.arger than that of a system containing essentially C'Ha groups: the reverse is true for the quantity d In
llQ5
D l d P (compare D values and KT values for water and nalkanesz2). From the above one is also led to predict values of B practically identical for T vents containing methyl groups. However a different result should be obtained with formamide. This again ernphasizes the interest of measurements of ionic partial molal volumes in this solvent.
Conclusions The results obtained in parts I and I1 of our work on ionic partial molal volumes in organic solvents indicate that the parameters which determine the values of these quantities are (1) the size of solvent molecules and the degree of steric hindrance of the poles of the solvent dipole; and (2) the properties of the layer of atoms 3-4 A thick around ions. Our results also show the specificity of ion-solvent interactions and the necessity to use a molecular model to account for these interactions.
Acknowledgment. The authors are pleased to thank Dr. J. Francois for her assistance in the denslty measurements. References and Notes (1) F. Kawaizurni and R. Zana, J. Phys. Chem., 7 8 , 627 (1974). (2) P. Mukerjee. J. Phys. Chem., 65, 740, 744 (1961). (3) B. E. Conway, R. E. Verrall, and J. E:. Desnoyers, Trans. Faradav Soc.. 62. 2738 (19661: Z. Phw. Chem., 230. 157 ( 1965) .' D. 0 . Massan, Phil. Mag., 8, 218 (1929). (a) J. V. Butler and A. Lees, Proc. Roy. Soc,. Ser. A, 131, 382 (1931); (b) J. Sobkowski and S. Minc, Rocz. Chern., 35, 1127 (1959) R. Gopal, eta/., cited in ref 7 as private communication. F. J, Millero, Chem. Rev., 71, 147 (1971). R . Zana and E. B. Yeager, J. Phys. Chem., 71, 521, 4241 (1971). A. Weinmann, Proc. Phys. Soc. (London), 73, 345 (1959); 75, 102 (1960). J . 0 . Rockris and A. K. Reddy in "Modern Electrochernistry," Plenum Press, New York, N. Y . , 1970, p 450. R. Zana and E. €3. Yeager, J. Chim. Phys. Physicochim. Bioi., 65, 467 (1968); 66, 252 (1969). E . Kratuchvil and H. L. Yeager, FOrhChF. Chem. Forsch., 27, 1 (1972). J. Prue and P. Sherrington, Trans. Faraday Soc., 57, 1795 (1961). R. Paul, J. Singla, and S. Narula, J. Phys. Chem., 73, 74'1 (1969) L,6 .Hepler, J. Phys. Chem., 61, 1426 (1957) 6. Criss and .I,W. Cobble, J. Amer. Chem. Soc,. 86, 5385 (1964) R. J. Alder, J. Chern. Phys., 23,263 (1955). R. H. Stokes and R . A . Robinson, Trans. Faraday Soc., 53, 301 (1957). R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, Butiermorths, London, 1959, p 125. (a) F. J. Miilero, J . Phys. Chem., 75, 280 (1971); (b) /Did., 72, 3209 (196U). J. Padova a.nd I . Abraharner, J. Phys. Chem, 7 3 , 2112 (1967). J. Riddick and W. Bunger, "Techniques of Chemistry: Organic Solvents," Val. I / , 3rd ad, Wiley-lnterscience, New York, N. Y., 1970; "Handbook of Chemistry and Physics," 49th ed, The Chemical Rubber Publishing Co., Cleveland, Ohio. 1968. J. Lamb, "Physical Acoustics," Vol. I I A . W . P. Masan, Ed., Academic Press, New York, N. Y., 1965, p 212. W. Schaafs, "Molekularakustik," Springer ed, Berlin. G . W. Stockton and J. S. Martin, J. Amer. Ghern;. Soc., 94, 6921 (1972) L. ialibsrth and 8. Canway, J . Phys. Chem., 74, 4116 (1970).
The Journal of Physical Chemistry. Vol. 78. No. 1 7 . 1974
