2728
J. Phys. Chem. 1980, 84, 2728-2734
Acknowlednment. I thank Mr. E. P. Hunter for carrving out many of the measurements and electrostatic cal&lk tions and Professors F. H. Field and H. Gershinowitz for their interest in this work. This work was funded by a grant from the National Science Foundation.
(4) M. Meot-Ner (Mautner), Drecedlna uauer this Issue. (5) I. C. Lewis and C. S..Singer, J.-Chem. Phys., 43, 2712 (1965). (6) 0. W. Howarth and G. K. Fraenkel, J. Am. Chem. SOC.,88, 4514 I,,VU",. 4OICLI
(7) 8. Badger and B. Brocklehurst, Nature(London), 219, 263 (1968). (8) 8. Badger, 8. Brocklehwst, and R. D.Russel, Chem. Phys. Lett., 1. 122 (1972). (9) T. Chiang and A. W. Reddock, J . Chem. Phys., 52, 1371 (1970). (10) A. Kwa, S. Arai, and M. Imamura, J. phys. Chem., 78, 1119 (1972). (11) S. Aral, A. Kka, and M. Imamura, J. Chem. phys., 54, 4890(1971). (12) M. A. J. Rodgers, J. Chem. Soc., Faraday Trans. 1,68, 1278 (1972). (13) R. K. Rowell and R. S. Steln, J . Chem. Phys., 47, 2985 (1967). (14) S. L. Bennett and F. H. Field, J. Am. Chem. Soc.,94, 5188 (1972). (15) D.J. Evans and R. 0. Watts, Mol. Phys., 31, 83 (1976).
References and Notes (1) M. Meot-Nsr (Mautner), P. Hamlet, E. P. Hunter, and F. H. Fleld, J . Am. Chem. SOC., 100, 5466 (1978). (2) M. Meot-Ner (Mautner), E. P. Hunter, and F. H. Field, J. Am. Chem. SOC., 101, 686 (1979). (3) M. Meot-Ner (Mautner), J . Am. Chem. Soc., in press.
Adiabatic Partial Molal Compressibllities of Electrolytes in 0.725 rn NaCl Solutions at 25 OC Frank J. Mlllero," Ana Kembro, and Antonio Lo Surdo Rosenstlel Schwl of Marine and Atmospherlc Science, Unlversky of Miami, Mleml, FIOrhj8 33149 (Received: Merch 13, 1980)
The apparent molal adiabatic compressibilities ( 4 ~of) 29 electrolytes have been determined in the medium of 0.725 m NaCl from sound speed measurements. The values of C$K have been extrapolated to infinite dilution to yield partial molal adiabatic compressibilities (I?*O) in 0.725 m NaCl. The experimentally derived values of R*O are compared to those predicted from binary solution data by using the ionic strength principle, Young's rule, and the specific interaction model. For electrolytes with a common cation (Na+)or anion (Cl-) the specific interaction model and Young's rule predict similar values of I?*O (f2 X lo4 cm3mol-' bar-l) and better estimates than the ionic strength principle. The compressibilities of mixing electrolytes (AK,)are quite small (less than 2X cm3mol-l bar-'). The values of AK, for electrolytes with a common cation (NaX + .NaCl)and anion (MC1+ NaCl) at I = 0.725 determined from our results correlate reasonably with the volume of mixing. The compressibility and volume changes of transferring various ions from water to 0.725 m NaCl were found to correlate in a linear manner (lO4fltrmS = -0.5 + 4.517Avtr,, u = 1.8 X cm3 mol-' bar-').
Introduction A number of workers have used various ionic interaction models to estimate the effect of pressure on activity or the partial molal volumes (v) of electrolytes in ionic media (e.g.,jeawater).l& Four models have been used to estimate the V of electrolytes in ionic media: (1) the ionic strength princip1e;l (2) the ion pairing and hydration m0de1s;~J(3) the specific interaction m 0 d e 1 ; ~and ~ ~(4) ~ ~the Young's rule For simple ionic media like NaCl solution, the values of Y predicted by using the specific interaction and Young's rule models are similar and in better agreement with measured values than those predicted by using the ionic strength p r i n ~ i p l e . ~ For ? ~complex ionic media like seawater, the predicted values of 7 for anions that form strong interactions with Mg2+and Ca2+ (C032-,HC03-, OH-, etc.) must be corrected for ion pair f o r m a t i ~ n . ~ ? ~ In order to select the best method to estimate the partial molal properties of electrolytes in natural waters, one must have reliable experimental values of these properties. In a recent paper6we reported the P of 29 electrolytes in 0.725 m NaCl (the approximate ionic strength of average seawater). In the present paper we will present our experimental results for the adiabatic compressibility measurements of the same 29 salts in 0.725 m NaC1. These results will be used to examine the most reliable method that can be used to estimate the partial molal compressibility of electrolytes in an ionic media. Experimental Section The sound speeds were measured at 2 MHz to a precision of f0.02 m s-l with a Nusonics "sing around" vel0022-3654/80/2084-2728$01.00/0
ocimeter described in detail elsewhere.s The velocimeter was used to measure the relative sound speeds (u - u2) where u is the speed of sound in the mixed electrolyte solution and u2is the speed of sound in 0.725 m NaC1. The velocimeter was calibrated with pure water by using the sound speeds of Del Grosso and MaderSgMeasurements of the speed of sound in seawaters indicate that the accuracy of the system is f O . l m s-l. The densities of the mixtures were measured with a "vibrating tube" densimeter.1° The densimeter was calibrated with standard seawaterll and ion-exchange (Millipore Super &) water.12 The precision1°J3of the densities is f 3 X lo4 g C M - ~while the accuracy13is f5 X lo4 g ~ m - ~ . The measured densities were used to estimate (or check) the molalities of the mixtures by using the results from our earlier studies.6 The temperature of the bath containing the sound velocimeter was controlled to f0.002 "C with a Tronac thermoregulator and set to 25.000 f 0.005 OC with a NBS platinum resistance thermometer and G-2 Mueller bridge. All the salts (Baker reagent grade) were used without further purification. The salts that did not decompose (LiC1, NaCl, KC1, RbC1, CsC1, NaBr, KBr, NaI, KI, NaF, NaN03, KN03, NaHC03, KHC03, Na2C03,K2CO3, Na2SO4,K$04, NH4C1,and NH4Br)were dried under vacuum for at least 1 h, and stock solutions were prepared by weight in 0.725 m NaCl. Approximately 1 m stock solutions of the electrolytes that could not be dried (HC1, NaOH, KOH, KF, MgC12, CaC12, Sr2C12,BaC12, and MgS04) were made, and the molalities were determined by measuring the density. The NaCl was added to these
0 1980 American Chemical Society
The Journal of Physical Chemistty, Vol. 84, No. 21, 1980 2720
Adiabatic Compressibilities of Electrolytes
solutions to make thiB ionic medium 0.725 m NaC1. Dilute solutions of the salt mixtures (salt and NaC1) were prepared by weight dilutions with 0.725 m NaCl.
NaHCO,
n
Results and Calculations The relative sound speeds (u - u2)of 29 electrolytes at 25 OC and various molalities (mi) in 0.725 m NaCl are given in Tables I-X:YIX.14 As with binary solutions, it is convenient to examine the speed of sound (and adiabatic compressibilities) of ternary electrolyte solutions in terms of apparent molal properties. If n3 moles of the electrolyte (3) is considered to be dissolving in a solvent of electrolyte (2), one can define the apparent molal volume of 3 in the medium by 4VIk(3)= (v- V2)/n3
" d
00
, 06
08
IO
(1)
-
where Pi = --(l/VJ(dVi/dP) is the adiabatic compressibility. For a molal solution (n3= m3,the molality), the volumes of the solution (V) and the medium (V,) are given by V = (1000 + m2M2+ m & f 3 ) / d (3)
* Y
+ m2M2)/dz
0.4 (rn;)"
where V is the total volume of the mixture and V2 is the volume of the medium. The differentiation of eq 1 with respect to pressure at, constant entropy (8)yields the apparent molal adiabatic compressibility [9K,* = -(dd*v/ dP)s] in the ionic medium15 9K*(3) [ b v - @2VZl/% (2)
V2 =: (1000
02
IL
n 7-
-105
E n
E
-
t-
Na,CO, 0725rn NaCl
t
2 -115 8
0 -I75 --
i
0.0
0.2
(4)
where d and d 2 are, respectively, the densities of the mixture and medium, Mi is the molecular weight of electrolyte i, and m2 the molality of NaC1. Substituting eq 3 and 4 into eq 2 giveis
I
I
I
0.4
06
0.8
1.0
0.6
0.8
1.0
(rn " I
1 L
-95
'0
E
(5)
4K*(3) =
When the concentration of electrolyte 3 is in moles per kilogram of medium (mi),the values of V and V2 are given by5 V = (1000 + m3'M3)/d (6)
V2 = 1000/d2 This gives the more common equation
g-It5 0 -125 0.0
0.2
0.4
(7)
for the apparent mold compressibility. The values of mi and m3 are related bly m3 =: mi(1 + 10-3m2M2) (9) For m2 = 0.725, the coefficient (1 + 10-3m2M2) = 1.04237. The adiabatic compressibilities (P) needed to calculate 4 K* were determined from the relative sound speeds (Au = u - u2)and densities (Ad = d - d,) by using
P = l/u2d
mg -105
(10) (where d2 = 1.025776) f 0.000023 g cmV3,u2 = 1540.82 f 0.03 m s-l, and P2 = 41.0622 X lo4 bar-' for the NaCl medium at 25 "c).The values of 4K*(3) calculated fram these compressibilitiesare given in Tables I-XXIX.14 The concentration dependency of rjK* (3) for some typical electrolytes (NaHCO:),Na2C03,and MgSO,) are shown in Figure 1. The values of 4K*(3) have been fit to the equation 4 ~ * ( 3= ) 4 ~ * ' ( 3 )+ A & 7 ~ 3 ' ) ~+/ ' (11)
Figure 1. The apparent molal adiabatic compressibilities of NaHCO, Na2C03,and MgS0, in 0.725 m NaCl at 25 "C plotted vs. the square root of m i .
The coefficients 4K*"(3), AK, and BK are given in Table XXX along with the standard error (a) of the fits. The infinite dilution partial molal adiabatic compressibility [-lis*o = (dC'*0/dP)93 of electrolyte 3 in the ionic medium is equivalent to the apparent molal adiabatic compressibility, 4 K*O. Although the values of 4 K* for electrolytes in 0.725 rn NaCl have been fit to eq 11 with standard errors cm3 mol-' bar1, the errors in R*O = less than 0.4 X 4 K*O are larger. To test the extrapolation procedure, we have made sound speed measurements on solutions formed by adding weighted amounts of NaCl to 0.725 m NaC1. cm3 The extrapolated value of 104dK*0= -39.67 X mol-l bar-l agrees very well with the value (-39.73 X lo-, cm3 mol-' bar-') calculated from the apparent molal adiabatic compressibility data of binary solutions.le The internal consistency of our values of can be determined by examining the additivity of the various salt pairs. For the differences between Na+ and K+ salts our results give I?*O(Na+)- I?*O(K+) = 6.4 f 1.4 X lo4 cm3molt1 bar-' (the maximum difference is 2.2 X cm3 mol-l bare1 for hydroxide salts). The difference between 104R*O(Cl-)and
2730
The Journal of Physlcal Chemlstty, Val, 84, No. 21, ig8Q
TABLE XXX: Coefficients of Eq 11 for Various Electrolytes in 0.725 m Nacl at 25 '@a:
- 104. electrolyte @IC*'@) 1 0 4 __~ K 1 0 4 __k 1 0 ~ ~ __ NaF 61.47 7.12 0.16 KF 56.46 8.81 0.16 1.63 HC1 0.63 0.18 31.17 LiCl 4.24 Q.23 NaCl 1.46 3.34 39.67 a.18 KC1 6.78 33.97 0.19 RbCl 30.72 6.99 0.40 CSCl 28.67 - 9.06 0.28 14.74 NH4C1 11.27 2.51 0.29 79.02 3.12 11.45 0.24 MgC4 CaC1, 75.97 8.13 8.26 0.11 SrC1, 88.52 13.16 3.84 0.13 BaC1, 88.87 8.60 10.02 0.09 NaBr 33.73 4.66 0.33 KBr 2 6.08 4.49 0.27 NH4Br 1.67 4.82 0.03 NaI 23.64 - 0.06 1.96 0.09 KI 0.11 16.61 1.64 0.07 NaOH 2.48 68.39 0-05 6.41 59.80 - 0.44 KOH 0.07 7.07 28.79 NaNO, -2.82 5.04 0.09 23.62 4.69 0.21 KNo3 52.24 NaHCO, 7.08 2.95 0.09 KHCO, 47.73 1.26 0.29 124.04 Na,C03 22.06 5.73 0.14 112.46 1.21 12.26 0.16 K2C0, 116.37 - 0.96 32.68 0.34 N4SO4 102.90 15.52 13.62 8.11 KZS04 119.73 31.04 0.28 Mgs04 The values of @ ~ * ' ( 3have ) units of cm3 mol'' bar-'. Since the values of @ ~ * ( 3at) 1 m are ten times more rdiable than at 0.1 m for a given error in sound velocity, the values of @ ~ * ( 3have ) been weighted by the factor 10 rn.
the various anions obtained from our results are 21.65 f 0.15 for F,-6.92 f 0.98 for Br-; -17.25 f 1.12 for I-; 27.28 f 1.45 for OH-; -10.62 a i 0.27 for NO3-; 13.17 f 0.60 far HC03-; 22.30 0.05 for 1/2C042-;and 17.75 f 0.27 for 1/2S042- (all in units of cm3 mol-' bar-'). From these comparisons our extrapolated values of R*O appear to be internally consistent to within 1.4 X 1Q4 cm3mol-l bar-'. Our best estimates for the conventional values of and R*O of ions in 0.725 rn NaCl are given in Table XXXI, At present no literature compressibility values are available to compare with our results. To the best of our knowledge this study represents the first measurements of adiabatic compressibilitiesin ternary electrolyte sdutions. The compressibility properties of ternary s y ~ ~ can e ~ s also be examined in terms of the mean apparent molal compressibility. The differentiation of the definition of the mean apparent molal volume [@v(2,3)]6with respect to pressure gives (12) @1&&33= [BV- BoVol/bz -t- ms) where Po and Vo are the adiabatic compressibility and volume of water. Substituting Vo= 1000/do and eq 3 into eq 12 gives
M"cl
et el.
TABLE XXJCI: Conventional Values @ the Partial Molal Volumes (V*O)and Compresssibilitiea (IC*") of Ions in 0.725 m Nacl at 25 'C VQp - 104Z*o,b ion cm3 mol-' em3 mol-' bar-' H' 0 0 Li+ - 0.42 29.64 Na+ - 0.63 38.14 K+ 9.73 32.44 Rb' 15.04 29.19 cs+ 22,13 27.04 NH, 18.30 9.74 MgZ' - 20.28 75.96 Ca2 -16.25 72.91 Sra' - 16.06 86.46 Ba2 - 10.30 85.81 F 0.86 23.18 C119.61 1.63 &26.34 - 4.67 137.67 -16.72 NO,81.11 - 9.09 OH- 1.86 28.81 HC0,27.39 14.70 (26:3.08 47.67 aslo: 21.82 38.56 Determined from the V*O of electrolytes in 0.726 m NaCl reported in ref 6. The cations were obtained from the C1 salts while the anions were obtained from the Na' and K+salts (with the exception of Br- which was obtained from Na+ and NH, ').
-
+
+
+
-45
I
*
where do is the density of water, MT = ( ~ ~ $ 4 f 2 rnf14)/(mz + rn3) is the mean molecular weight, and rnT = m2 + ma is the total molality of electrolytes in solution (la, =: 44.7736 X lo4 bar1 and do = 0.997045 g for water at 25 oC)?9J2 The values of aK(2,3)for the various electrolyte mixtures calculated from eq 13 are given in Tables IXXIX.14 Plots of (PK(2,3)vs. rn3 for some typical elec-
- 75
c
"---.-I
By differentiating eq 14 with respect to in3,it is possible to determine the partid molal adiabatic compressibility [K3* = ~ , ~ * ( +3 )m3(d4K*(3)/arn3)]of electrolyte 8: = @&3) + m ~ [ d @ ~ ( 2 , 3 ) / d m ~ l (16) Since @&3) = 4 4 2 ) and m~ = ne2 at m3 = 0, the infmite dilution K4*0 is given by &*O = 4 K(2) + mz[d~ ~ ( 2 , ~ ) / ~ m 4 (17) 1~~~o
x3*
Adiabatic Compressibllltles of Electrolytes
The Journal of Physlcal Chemlstry, Vol. 84, No. 21, 1980 2731
The derivative d aK(2,3)/dm3can be evaluated from the concentration depenclency of @~(2,3); however, the value a t rn3 = 0 is strongly dependent upon the degree used to fit the data. The values of K3*0 can also be determined by using Young’s rule17
TABLE XXXII: Coefficients for the Equationa 104AK, = A t Bm,
(18)
where the primes indicate that the apparent molal adiabatic compressibilities of electrolytes 2 and 3 are from binary solution data at the ionic strength (I)of the mixture ( I = wzm2 w3m3,where wi = 1/2CviZt is the valence factor equal to 1, 3, arnd 4, respectively, for 1:1, 2:1, and 2:2 electrolytes). The term AK, is the compressibility change that occurs when the two electrolytes are mixed a t the same ionic strength. By combining eq 15 and 18, we obtain
+
4K*(3) = (m2/m3)[4K1(2) - 4K(2)]
+ 4K’(3) + Mrn/m3 (19)
The differentiation of eq 19 with respect to m3 evaluated at m3 = 0 gives K3*0 =
[4K’(3)lms=O+ mdd4K(2)/dm31ms=o+ [a AKrn/dm3lm8=0 (20)
The values of 4 d(i) for various electrolytes in binary solution can be evaluated from16
4 K ( i ) = 4~;O(i) + A K ( ~ ) +V BK(i)I
(21)
where the parameteris 4 Ko(i),AK(i), and B K ( ~are ) given elsewhere.16 When eq21 is used the first two terms of eq 20 are given by
[4 K’(3)lms-0 e’ 4 K0(3) + A3m21/2+ B3m2 md64 ~(2)/dmd,,-0 := wdB~m2+ (A2/2)m21/21
(22) (23)
The value of 4 K’(3) a t m3 = 0 is the 4 K’ of electrolyte 3 in itself at the ionic strength of the medium (0.725 m). The term mz[d4K(2)/dm3]at m3 = 0 is equal to K2 - 4 K(2) = rnz[d4K(2)/dmz]for NaC1 at 0.725 rn times the valence factor w3 for the added solute. If AK, = 0, the value of R3*Ocan be estimated from
= 4Ko(3) + A3mz1/’ + B3m2 + w3[Bzm2 + (A2/2)rn~~/~l (24) To evaluate (dAK,/drn3) at m3 = 0, it is necessary to examine the concentration dependence of AK,. The values of AK, have been calculated for all the mixtures by using eq 18 in a rearranged form: K3*O
AK, (m2
=
+ m3)[@K(2,3)- (m2/mT)4 K’(2) - (m3/mT)+K’(3)] (25)
For most of the mixtures studied the values of AK, (given in Tables I-XXIX)14 are quite small. We have attempted to calculate d AK,/drn, by fitting the values of AK, to equations of the form AK, = A + Bm3 (26) The coefficients A’ and B are given in Table XXXII along with the standard error (a) of the fits. The values of (dAK,/dm3) a t m3 = 0 (B in eq 26) are given in Table XXXIII. For most of the electrolytes studied (8AK,/ dm3) at m3 = 0 is less than 2 X cm3 bar-l.
A B 0.128 -0.056 0.117 -1.962 0.167 -0.170 -0.306 -0.297 ‘0 0 0.100 0.235 -0.075 1.268 0.283 -1.058 0.096 -0.178 -1.634 0.015 0.097 -1.970 0.293 -1.734 0.193 -2.247 0.186 -0.248 0.188 -0.227 0.023 0.328 0.013 0.219 0.179 -0.363 0.397 -1.803 0.144 0.759 0.236 -0.162 0.056 -0.001 KNo, NaHCO, 0.027 5.028 - 0.104 0.456 KHCO, Na,CO, 0.372 -3.312 K2C03 1.188 0.694 Na,SO, 0.165 3.196 &SO, 0.887 -0.664 MgSO, -0.415 - 1.313 Units of AK, are in cm3 mol-’ bar-’. salt NaF KF HCl LiCl NaCl KC1 RbCl CSCl NH,Cl MgC1, CaCl, SrCl, BaCI, NaBr KBr NH,Br NaI KI NaOH KOH NaNO,
a
104~ 0.06 0.10 0.12 0.16 0 0.22 0.05 0.19 0.08 0.16 0.10 0.09 0.14 0.05 0.04 0.05 0.02 0.13 0.17 0.06 0.07 0.06 0.06 0.21 0.08 0.21 0.36 0.28 0.11
TABLE XXXIII: Values of (aAK,/am,) at m, = 0 for Mixing Various Electrolytes with NaCl at 25 “C and I = 0.725 m __
~-
10,.
( aAKm I
electrolyte am,), ,=o NaF -0.06 KF - 1.96 HCI -0.17 LiCl -0.30 NaCl 0.00 KC1 0.24 1.27 RbCl CSCl - 1.06 NH,CI - 0.18 - 1.63 MgCI, CaC1, -1.97 SrC1, -1.73 BaCI, -2.25 NaBr -0.25 KBr - 0.23
10,. ( aAT, /
electrolyte NH,Br Naf KI NaOH KOH NaNO,
KNo,
NaHCO, KHCO, Na,CO, K,CO, Na,SO, K2S04
MgSO,
am,), =,, 0.33 0.22 -0.36 - 1.80 0.76 -0.16 0.00 5.03 0.46 - 3.31 0.69 3.20 -0.66 - 1.31
The compressibility changes of mixing two electrolytes a t a constant ionic strength can be formulated by17
mrn = Y3(1 - .Y3)[k0 + kl(1 (27) where y3 = ~ 3 / ( m 2+ m3), 1 - y3 = yz, and ko and kl are
adjustable parameters related to ionic interactions. The differentiation of eq 27 with respect to m3, evaluated at rn3 = 0, yields (dAKm/dm3)ma=o= (ko + M / m 2
(28)
Thus, the values of (dAKm/dm3) at m3 = 0 determined from eq 26 are directly related to the AK, at an ionic strength of 0.725 m. Discussion The partial molal compressibilities of electrolytes in an ionic medium can be estimated by a number of methods.l+ Most of the methods are based on various models for ionic
2732
The Journal of Physicel Chemistty, Vol. 84. No. 21, 1980
TABLE XXXIV: Co_mparisons of the Measured and Calculated Values of K*O of Electrolytes in 0.725 m NaCl at 25 "C 1O4[z*'(rneas) - z*'(calcd)], cm3 mol-' bar-' ionic Young's specific electrolyte strength rule interaction HC1 LiCl NaCl KCl RbCl CSCl NH,Cl MgC4 CaC1, SrC1, BaC1, NaF NaCl NaBr NaI NaOH NaNO, NaHCO, Na,CO, Na,SO, NH,Br KF KBr KI KOH
KNo,
KHCO, K,CO, K,SO, MgSO,
4.1
- 0.9
- 1.1
3.5 0 1.8 1.2 3.3 0.2 2.5 3.7 0.8 - 2.9 k2.1 - 0.4 0 - 0.7 - 0.4 0.5 - 1.8 -4.6 0.4 - 5.5 il.8 0.2 4.3 0.6 - 0.9 2.0 0.7 -2.9 -4.6 - 2.2 19.9 i3.8
0
- 2.1 -1.5 -4.0 1.1 4.8 3.0 4.8 - 2.5 k2.9 -3.5 0 0.1
2.4 -4.4 2.5 0.4 - 0.3 5.1 22.3 2.2 - 6.0 - 0.1 2.4 -0.5 -0.1 - 6.9 5.4 2.2 - 3.4 i2.9
-
-
-
-
-
0.2
Millero et ai.
Overall, the values of R*O predicted by using Young's rule are slightly better than those obtained by using the ionic strength principle. In using the specific interaction m o d e P ~to~ estimate *~~ R*O,one assumes that specific short-range interactions in solution of constant ionic strength are limited only to ions of opposite charge.22 The partial molal compressibilities of electrolytes in water are represented b p
- 3.2 0
- 1.3
-0.8
- 3.4 0.2 - 2.0 - 3.4 -0.7 - 2.8 i 1.8 -0.2 0 - 1.3
where SKis the DebyeHuckel limiting law slope (= 4.22 X 10% at 25 0C),5vM is the number of cations and vxeis the number of anions formed when MX completely dissociates, [MX] is the molality of MX, and Bm is the specific interaction parameter which is a function of ionic strengths5 The R*O for an electrolyte is predicted from
0
- 0.4 1.4 6.5 - 1.4 4.2 il.9 0.5 -0.1 -1.2 -0.8 1.2 - 1.0 - 2.8 1.6 -2.4 -2.6 i1.4
-
-
interactions.lSu The simplest method is the use of the ionic strength principle.' This method assumes that the partial molal compressibility is equal to the value in water a t the ionic strength of the medium. The differentiation of eq 21 gives R,*O = (b~O(3)+ 1.5A,(3)I'I2 + 2 B ~ ( 3 ) 1 (29) A comparison of the measured values of R3*0with those calculated from eq 29 are given in Table XXXIV. For electrolytes with a common anion (Cl-) and cation (Na+) the ionic strength principle predicts values of R*O that agree to f2.7 X loa cm3mol-' bar-' (maximum difference of 5.1 X cm3 mol-' bar-') with the measured values. For electrolytes without a common cation or anion the predicted values agree to f2.9 X lo4 cm3mol-' bar-' with the measured values (maximum difference of 6.9 X cm3 mol-' bar-'). The use of Young's rule to estimate R*O was discussed earlier. This method assumes that the compressibility of mixing two electrolytes at constant ionic strength is zero. The values of R*O calculated from Young's rule (eq 24) are compared to the measured values in Table XXXIV. For electrolytes with a common anion, the differences are f2.1 X 10" cm3 mol-' bar-l, and for electrolytes with a common cation the differences are f1.8 X cm3mol-l bar-'. For electrolytes with uncommon ions, the differences are f3.8 X lo4 cm3 mol-' bar-'. This larger difference is due to the large error for MgS04 (the average is f2.0 X 10" cm3mol-' bar-' excluding MgS04). The large AK, for mixing NaCl and MgS04 is probably related to ion pairing effects.
where the values of BMXare at the ionic strength of the mixture. In a 0.725 m NaCl solution the value of R*O is estimated from
R*O ='?I
+ 1.94 X 1 0 - 4 +~ v ~ B ~ ~ l ( 0 . 7+2 5 ) ~ x B ~ d ( 0 . 7 2 5(32) )
The values of K*O calculated from eq 32 are compared to the measured values in Table XXXIV. For electrolytes with a common anion, the predicted values agree on the average to f1.8 X cm3 mol-' bar-'; with a common cation, the differences are f1.9 X 10" cm3mol-' bar-'; and for electrolytes without a common ion the dgferences are f1.4 X cm3 mol-' bar-'. The values of K*O predicted from the specific interaction model are better than those estimated by using the ionic strength principle and similar to the values predicted by using Young's rule. This finding is in agreement with our earlier work on partial molal volumes in 0.725 m NaC1.6 The failure of Young's rule and the specific interaction model to exactly predict R*O is due to the fact that the interactions between like charged ions are not considered. determined Although the values of ko = %(aAK,/amJ from our results have large errors, it is pcd%le to examine how the values of ko are related to other excess thermodynamic properties for the same system. Since the values of R*O are additive in a given ionic media, it is only necessary to consider the compressibilities of mixing electrolytes, with a common cation (Na+) and anion (Cl-). A comparison of the values of ko and uo for the mixings is shown in Figure 3. With the exception of HC03-, the values of ko appear to be linearly related to up The values of ko are the same sign as the appropriate value of uo. Thus, both ko and uo correlate with the enthalpy interaction term RTho and have the opposite sign. As found in enthalpy studies of othersa@ for common anion mixtures, the cations can be divided into two groups. The mixing of Na+ with the so-called "structure making" cations ( H', Li+,NH4+,Mg2+,Ca2+,Sr2+,and Ba2+)produces a decrease in volume and compressibility and an increase in enthalpy; while the mixing with "structure breaking" cations (K+, Rb+, and Cs') produces an increase in volume and compressibility and a decrease in enthalpy. Our compressibility and volume results support the general rule developed by Desnoyers et al.n for the structural interactions of ions in terms of the Gurney cospheres. The mixing of two electrolytes of the same
Adlabatlc Compresslbllltles of Electrolytes
The Journal of Physical Chemisfy, Vol. 84, No. 21, 1980 2733
-.c
/
I
2.0
-0.8 -0.6 -04 -0.2
0.2
0
( d AVm / d m 3 )
0.4
06
(a)
0.8
mS=o
0
1
2
3
4
5
6
7
2 2/r
--
-2
1
1
O /,
-0.6 -0.6 -0.4 -0.2
0
COMMON
I
CATION
MIXI'URES
0.2
0.4
0.6
0.8
( dAVm /dms Im 3: Flgue 3. Cwreiatbn of (dKddm,), 1o vs. (8 Vdam,), Do for mlxtng NaCl wRh electrolytes containing a [a) common anion [MCI) and (b) common cation (NaX) at 25 OC.
structural form causes a repulsion with a decrease in volume and compressibility and an increase in enthalpy. The mixing of two electrolytes of opposite structural forms causes an attraction with an increase in volume and compressibility and a decrease in enthalpy. Although the sign of uo, ko,and RTho can be predicted, it is not possible to predict the magnitude of the changes. There is also no unambiguous way of selecting the structural type of a given ion.29 We have, thus, attempted to correlate the excess thermodynamic roperties to various properties of the uncommon ion.s*i? The volume properties of ions in an ionic medium (e.g., NaCl) can also be examined by using a hydration mode1.2ps The partial molal volumes and compressibilities are separated into two major components Won) = V(int) + V(e1ect) (33) @on) = R(int) + R(e1ect) (34) where the intrinsic terms (int) are related to the size of the ion and packing effects, while the electrostriction terms (elect) are related to ion water interactions. The ionic medium is, thus, considered to be a relatively noninteracting solvent system. The intrinsic terms can be examined by using various semiempirical e q ~ a t i o n s ~based +*~~~ on the continuum model. The simplest forms being 0 = AT3 + B ( P / r ) (35)
R = A'?
+ B'(P/r)
(b)
(36) where r is the crystal radius. The values of A, B, A', and B'can be obtained from linear plots of V ( r / P )vs. (#/zZ). For simple monatomic ions such correlations have been successful in water and ionic media like s e a ~ a t e r . 2For ~~~ polyatomic ions one rum into the difficulty of estimating the ionic radius.
0
1
2
I 3
I 4
I 6
I 6
I 7
I 8
z'/r Fwre 4. Cwrelatlon of (a)volume of transfer (A V& and (b) com pesslblllty of transfer (AI?,,,,..) vs. Z2/rfor cations In 0.725 rn NaCl at 25 O C . AK- and AV- = 0 for H'.
In aqueous ionic media one can examine the transfer of ions from water to the ionic media, Apt, = ? - 90 and Alltrans= - IP (based on conventional values for the proton). Since the intrinsic contributions in water and the a ueous ionic medium should be similar,one would expect A$eans and A&,, to be related largely to changes in ion-water interactions (Le., electrostriction). From the continuum model one would expect AV- and hR- to be proportional to P/r. As shown in Figure 4, the values of AV- and AI?- for cations do not correlate very well with P/r. Cations of different charge fall on two separate lines. Similar plots for monovalent monatomic anions show little or no dependency on l/r. These findings are not surprising, since other factors, such as packing effects, are not the same in water and aqueous ionic media. The volume properties of ions can also be examined by using a simple hydration model.33 The electroatriction molal volume is given by V(e1ect) = n(?E - V B ) (37) where VE and VB are the molar volumes of water in the electrostricted (E) and bulk (B) solvent regions around an ion hydrated by n water molecules. If n and VE are assumed to be independent of pressure, R(e1ect) is given by R(e1ect) = -n@BVB (38) where BB = -(l/V B ) ( ~ V B / ~ is P )the bulk compressibility of water (44.773, X lo4 bar-' at 25 "C). This model predicts that V(e1ect) and R(e1ect) should be proportional V(e1ect) = kK(e1ect) (39) where k = - ( v E - VB)/@BVB. As shown in our previous work,*% the volume and compression properties of many
The Journal of Physical Chemlstty,
2734
Vol. 84, No. 21,
1980
I
104A&,
s
8
‘7
6
r
‘Y I1
: 4
..
1 2 V
= -0.5
+ 4.517AVt,,
(43) The success of the simple hydration model in 0.725 m NaCl indicates that simple ions are mostly hydrated to water molecules and that the interactions with Na+ and C1- ions are quite small. In more complex ionic medium like seawater stronger specific interactions may occur; however, since the A V and dK for ion pair formation have nearly the same slope as eq 41 and 42, the correlations of A&,, and AVtr, are probably the same. Further work in more complex ionic media and more concentrated NaCl solutions are needed to prove this postulation.
10 V
Mlllero et al.
2
-2
/-. eo-:
0
Acknowledgment. The authors acknowledge the support of the Office of Naval Research (N00014-75-(3-0173) and the Oceanographic Branch of the National Science Foundation (OCE73-00351-A01)for this study. Frank J. Millero thanks Dr. Giuseppe B. Macchi for his hospitality at the Institute di Ricerca Sulle Acque, Roma, Italy during the writing of this paper. Supplementary Material Available: Tables I-XXIX, listings of sound velocities, $K*(3), aK(2,3),and AKmfor the various electrolytes studied (15 pages). Ordering information is available on any current masthead page.
O
f
f
References and Notes
F-
0 0
IO
2.0
30
4.0
5.0
6.0
7.0
8.0
A Q ~: , 9-BO. ~ ~ ~c m 3 m 0 ~ - 1
Figure 5. Correlation of ARvs. A , V for cations (a) and anions (b) in 0.725 m NaCl at 25 OC. AR,,,, and AV,, = 0 for H+.
electrolytes correlated giving values of k = 3.6-3.9 X lo3 bar. Although K(int) can be taken as zero,32values of V(int) must be estimated by using semiempirical methods. This method, thus, has an unreliable feature similar to the continuum model. By examining the changes in volume and compressibility one can circumvent the problem of knowing V(int) and K(int). One has AV=kAl? (40) where AT and dK are the changes in volume and compressibility for a given process (e.g., ionization of acids or formation of ion pairs). As shown in Figure 5 the values of A&,, and AV, linearly correlate with each other. Similar correlatio_nsof ckangej in other thermodynamic properties (H- P,and C, - C,O) have been shown elsewheree5 The value of k = 2.2 X lo3 bar is lower than the values obtained for ions (k = 3.6 X 103bar),%the ionization acids ( k = 4.7 X lo3bar),36and the formation of ion pairs (k = 4.2 X lo3bar).% The linear correlations of vs. cm3 mol-’ bar-? Aut,,, for cations (a = 1.7 X 104A&r,, = -0.5 + 4.64Avtr(41) and anions (a = 2.0 X
cm3 mol-l bar-l)
104~~~= , , -0.9
+4
. 5 8 ~ ~ (42) ~ ~
can be used to estimate R of ions in 0.725 m NaCl from the values of IF’and AVtrm,. The correlations are quite good, being nearly within the experimental error of the measured values of R. Cations and anions can also be fitted to the same linear equatin (u = 1.8 X lo4 cm3mol-l bar1)
(1) Owen, B. B.; Brlnkley, Jr., R. S., Chem. Rev. 1941, 29, 461. (2) Millero, F. J. Limnol. Oceanogr. 1969, 14, 376; J . Phys. Chem. 1989, 73,2417; Chem. Rev. 1971, 71, 147; Geochfm. Cosmochm. Acta 1972, 36, 92. Ward, G. K.; Mlllero, F. J. 1975, 39, 1595. (3) Mlllero, F. J. Geochim. Cosmochlm. Acta 1977, 41, 215. (4) Leyendekkers, J. V. Mar. Chem. 1974, 2 , 89. (5) Mlllero, F. J. “ActMty Coeffldents In Electrolyte Solutions”; Pytkowicr, R. M., Ed.; CRC Press: Florida, 1979; Vol. 11, Chapter 2. (6) Millero, F. J.; Lafenlere, A. L.; Chetlrkin, P. V. J. Phys. Chem. 1977, 81, 1737. (7) Lee, J. Ph.D. Disertatlon, Yale Unhrerslty; Unhrerslty Mlcrofllm: Ann Arbor, Mlch:, No. 66-4606; Abstr. 8-27, 131 (1966). (8) Mlllero, F. J.; Kublnski, T. J . Acoust. SOC. Am. 1975, 57, 312. (9) Del Grosso, V. A.; Mader, C. V. J . Acoust. SOC. Am. 1972, 52, 961. (10) Plcker, P.; Tremblay, E.; Jolicoeur, C. J . Solutlon Chem. 1974, 3 , 377. (11) Mlllero, F. J.; Gonzalez, A.; Ward, 0. K. J. Mar. Res. 1976, 34, 61. (12) Kell, G. S. J . Chem. Eng. Data 1975, 20, 97. (13) Mlllero, F. J.; Lawson, D.; Gomler, A. J. cieophys. Res. 1976, 87, 1177. (14) See paragraph at end of text regardlng supplementary materlal. (15) The subscrlpt S Is omitted throughout the paper for slmpllclty. (16) Millero, F. J.; Ward, 0. K.; Chetlrkh, P. V. J. Acoust. Soc. Am. 1977, 61, 1492. (17) Young, T. F.; Smith, M. B. J. Phys. Chem. 1954, 58, 716. (18) Friedman, H. L. J . Chem. Phys. 1960, 32, 1134. (19) Scatchard, 0. J. Am. Chem. SOC. 1966, 90,3124; 1969, 91,2410. (20) Reilly, P. J.; Wood, R. H. J. Phys. Chem. 1969, 73, 4292. Rellly, P. J.; Wood, R. H.; Roblnson, R. A. lbld. 1971, 75, 1305. Robinson, R. A,; Wood, R. H. J. Solutbn Chem. 1972, 1 , 481. (21) Pitrer, K. S. J. Phys. Chem. 1973, 77, 268. (22) Guggenhelm, E. A. Phll. Mag. 1935, 79, 588. (23) Mlllero, F. J. “The Sea”, Goldberg, E. D., Ed.; Wlley-Intersclence: New York, 1974; Vol. 5. (24) WMtRekl, M. “Chemical Oceanogaphy”; 2nd ed.;Riley, P. G.; W o w , G., Ed.; Academic Press: New York, 1975; Vol. 1. (25) Young, T. F.; Wu, Y. C.; Krawetz, A. A. Dlscuss. Fara&ySoc. 1957, 24, 27, 77, 80. (26) Wu, Y. C.; Smith, M. 8.; Young, T. F. J . Phys. Chem. 1965, 69, 1868, 1873. (27) Desnoyers, J. E.; Arel, M.; Perron, 0.; Jollcoeur, C. J. phys. Chem. 1969, 73, 3346. (28) m y , R. W. “Ionlc Processes In Sdutlon”; Dover PubllcatiOn: New York, 1953. (29) Holtrer, A,; Emerson, M. F. J . Phys. Chem. 1969, 73, 26. (30) Hepler, L. G. J. Phys. Chem. 1957, 67, 1426. (31) Mukerjee, P. E. J . Phys. Chem. 1961, 65, 740. (32) Matheson, J. G.; Conway, 8. E. J . Solutbn Chem. 1974, 3, 455. (33) Millero, F. J.; Ward, G. K.; Lepple, F. K.; Hoff, E. V. J. Phys. Chem. 1974, 78, 1636. (34) Mlllero, F. J.; Lo Surdo, A.; Shin, C. J. phys. Chem. 1976, 82, 784. (35) Lo Surdo, A.; Mlllero, F. J. J . Solution Chem. 1980, 9 , 163. (36) Lown, D. A,; Thhsk, H. R.; Lord Wynne-Jones Trans. Faraday Soc. 1966, 64, 2073.
