J. Phys. Chem. 1982, 86, 4980-4987
4980
Investigation of Aqueous Calcium Nitrate, Zinc Nitrate, and Zinc Chloride Solutions Using Acoustic Velocity Measurements Ronald Carplo,'
Mehmed Mehlclc,' Frank Borsay,* Cedomlr Petrovic,' and Ernest Yeager
L7epartment of Chemistry, Case Western Reserve Univers&, Cleveland, Ohio 44106 (Recelved: January 19, 1981; In Final Form: July 13, 1982)
The concentration dependence of the sound velocity at ultrasonic and hypersonic frequencies has been measured for aqueous solutions of calcium nitrate, zinc nitrate, and zinc chloride over a concentration range extending from very dilute solutions to the hydrate melt stoichiometry. Substantial velocity dispersion has been observed throughout the composition range studied for the aqueous ZnC12system, but only at high solute concentration for the nitrate systems. Adiabatic compressibilities have been derived from the acoustic velocities and densities. A comparison of the compositional dependence of the 2-MHz adiabatic compressibilitiesof Ca(N0J2,Zn(NOJ2, and ZnClz solutions reveals fundamental structural differences. The magnitude of the adiabatic compressibility is shown to be a measure of the degree of complexation. Excess molar volumes and adiabatic compressibilities, derived by considering these systems to be binary mixtures of the tetrahydrate and water, are nonideal but show analogous behavior. The heat capacity ratios for several Ca(N03)2solutions were computed from the values of the adiabatic compressibility obtained in this study and the corresponding literature values of the isothermal compressibility.
Introduction Concentrated aqueous electrolyte solutions, and particularly those having the hydrate melt stoichiometry, have in recent years assumed more interest than previously from both theoretical and technological viewpoints. The theoretical interest can largely be attributed to the ease with which a number of such systems can be supercooled over readily accessible temperature ranges; thus, these systems can be used to study the previously neglected metastable region of the liquidus ~tate.~8 A number of hydrates such as Ca(N0J2.4HZ0, Zn(N03)z.6H20,Mg(N03)z.6H20,etc., form liquids which appear to be fused salt analogue^.^ Moreover, concentrated aqueous solutions have unique acid-base proper tie^.^^^ Technologically, these systems appear to be promising for use in thermal and electrochemical energy storage systems, fuel cells, and low-temperature protonic semiconductors as well as in treating metals for corrosion protection. The present work is part of a general study of the acoustic properties of aqueous solutions of zinc chloride, zinc nitrate, and calcium nitrate. An earlier paper dealt with the ultrasonic and hypersonic absorption of these electrolyte solutions.' The present paper is concerned primarily with the ultrasonic (u,) and hypersonic (uh) velocities of these three systems over a range of solute concentrations from very dilute solutions to hydrate melt stoichiometries. The acoustic velocity, u, is related to the adiabatic compressibility, PS, by the equation Ps = l / ( P U 2 )
(1)
where p is the density. The adiabatic compressibility, which is defined by the thermodynamic relation Ps = -(l/v)(av/aP)s (2) where V is volume, P is pressure, and S is entropy, is a very 'Present address: The Frank J. Seiler Research Laboratory, U S . Air Force Academy, CO 80840. *Present address: Standard Oil Company (Ohio) Research Laboratory, Cleveland, OH 44128. $Present address: Diamond Shamrock Corp., Painesville, OH 44077. k Present address: Department of Chemistry, University of Tennessee, Knoxville, T N 37916. 0022-3654/82/2086-4980$01.25/0
useful parameter in both the thermodynamic and kinetic molecular study of liquids. This usefulness arises from the sensitivity of P S to the electrostriction; i.e., Ps is directly related to the solvent shells around ions and thus local structure. For a system exhibiting structural and/or chemical relaxation, Ps in aqueous electrolyte solutions is usually less than that of pure water due to the electrostrictive force of the ions on the solvent. This loss of compressibility has been used by various investigators to study ion-solvent interactions and to determine solvation numbers in dilute solutions.* In the concentrated solutions involved in the present study, however, the competitive ion-ion and ion-solvent interactions are far too complex to permit the use of the oversimplified models of ion-solvent interactions underlying the solvation number computation for dilute solutions. Even though no quantitative interpretation of the data can be achieved at this time, such studies of electrolyte solutions over a wide range of concentration contribute to the development of models for aqueous electrolytes.
Experimental Section Details of the electrolyte preparation and analysis are given el~ewhere.~ The compositions of the solutions were established and monitored by means of refractive indexcomposition plots, using a Precision Abbe refractometer, to an accuracy of f0.3%. To prevent hydrolysis in the 0.10,0.52, and 1.04 m ZnClz solutions, it was necessary to add several drops of dilute perchloric acid to a 1-L volume of each solution. (1)Angell, C. A.; Sare, F. G. J. Chem. Phys. 1970, 52, 1058. (2) Angell, C. A. J. Phys. Chem. 1966, 70, 2793. (3) Angell, C. A. J. Chem. Educ. 1970, 47, 583. (4) Angell, C. A. J. Electrochem. Soc. 1965, 112, 1224. (5) Duffy, J. A.; Ingram, M . D. Inorg. Chem. 1977, 16, 2988. (6) Dyer, R. D.; Fronko, R. M.; Schlavell, M. D.;Ingram, M. D.J. Phys. Chem. 1980,84, 2338. (7) Carpio, R.; Borsay, F.; Petrovic,C.; Yeager, E. J. Chen. Phys. 1976, 65, 29. (8) Hall, C.; Yeager, E. In "Techniquesof Electrochemistry";Yeager, E., Salkind, A., Eds.; Wiley: New York, 1973; Vol. 2, pp 394-441. (9) Carpio, R. A. Ph.D. Thesis, Case Western Reserve University,
Cleveland, OH, 1974, University Microfilms No. 99372797.
0 1982 American Chemical Society
The Journal of Physical Chemistry, Vol. 86, No. 25, 1982 4901
Aqueous Ca(NO,),, Zn(NO,),, and ZnCI, Solutions
The ultrasonic velocities were obtained with a Steeg and Reuter 2-MHz acoustical interferometer (Type SI-1-2OOO). With this instrument the wavelengths of standing waves are measured between the parallel transducer and reflector disk. Movements of the reflector by half-wavelengths allow the determination of A, and then u, can be calculated from the relation u, = Av (3) when v = 2 MHz, the ultrasonic frequency. To determine the wavelength, we used 20 or more standing waves. The limiting factor controlling the accuracy of the results was the accuracy with which the solution composition was known and maintained constant. The temperature was controlled to h0.5 "C. The Brillouin measurements were made with a highintensity argon ion laser at 5145 A and at fixed scattering angles of 45", 90°, and 135". The scattered light was analyzed with a piezoelectrically driven Fabry-Perot interferometer. Optical quality samples were prepared by filtration through 0.1-pm Nuclepore polycarbonate filters. Additional details concerning the light-scattering spectrometer and experimental procedure can be found elsewhere.'~~The hypersonic velocity u h was computed from the Brillouin shift Av, the refractive index n, the laser wavelength Ao, and the scattering angle 0 by using the formula uh
= A,,(Av)/[2n sin (0/2)]
(4)
The values of n were measured with an Abbe refractometer which had been calibrated for the wavelength of the laser beam with distilled water. Two different scattering cells were employed during the course of these measurements. The majority of measurements were made with a Pyrex, semioctagonalcell (Smyth Precision Glass Manufacturing Co., Union City, NJ), which allows measurements to be made at scattering angles of 45", 90°, and 135". Some measuremets at the 90" scattering angle were made with a Hellma 101-0s quartz, fluorescence cell. Temperature control was maintained to fO.O1 "C by using a Lauda/ Brinkman circulator (Model K-2R). The error in hypersonic velocity increases with increases in concentration due to the accompanying increases in the Landau-Placzek intensity ratio and the broadening of the Brillouin peaks. Estimates based on the method of Fleury and Boon'O indicate that the error in the hypersonic velocity due to overlaps never exceeds 2% even in the most concentrated solutions studied. The indirect Archimedes method, described by Ewing and Mikovsky," was primarily used for the density measurements. For the dilute Ca(N03)2solutions a pycnometer was employed. The precision of the density measurements was at least 0.1 '%.
Results and Discussion In Figure 1 the hypersonic velocities obtained at 25 "C and a 90" scattering angle, as well as the correspondding 2-MHz ultrasonic velocites, are plotted as a function of the Ca(N03), concentration. For comparison the hypersonic velocity obtained by Ambrus at a 90' scattering angle for Ca(N03),-6H20at 23.3 OC1' is shown, as are the hypersonic velocities which were determined by Maret13 up to a concentration of 2.5 M. Of note is the small systematic dif(IO) Fleury, P.; Boon, J. P. Phys. Reo. 1969, 186,244. (11) Ewing, W. W.; Mikovsky,R. M. J.Am. Chem. SOC. 1950,72,1390. (12) Ambrus, J. H.Ph.D. Thesis, University of Maryland, College Park, MD, 1970. (13) Maret, A. R. Ph.D Thesis, Case Western Reserve University, Cleveland, OH, 1972.
TABLE I: Dependence of the Hypersonic Velocity and the Adiabatic Compressibility of Aqueous Ca(NO,), Solutions at 2 5 "C and a Scattering Angle of 90" AL
a
~O-JU,
p,
101*p,,
R
molality
GHz
m/s
g/cm3 cm2/dyn
128.0 46.8 24.0 14.7 13.1 9.89 8.01 7.58 7.13 6.0' 5.65 5.00 4.70 4.30 4.00
0.44 1.19 2.31 3.78 4.24 5.62 6.94 7.32 7.79 9.26 9.83 11.11 11.82 12.92 13.89
5.66 5.87 6.23 6.67 6.78 7.12 7.42 7.59 7.83 8.06 8.37 9.29 9.71 10.10 10.52
1.53 1.57 1.64 1.73 1.76 1.82 1.89 1.93 1.98 2.04 2.12 2.32 2.42 2.51 2.61
1.048 1.127 1.231 1.346 1.376 1.465 1.525 1.542 1.561 1.620 1.639 1.677 1.697 1.727 1.749
4.07 3.60 3.01 2.48 2.36 2.05 1.84 1.75 1.63 1.48 1.36 1.11 1.00 0.92 0.84
Reference 12.
TABLE 11: Composition Dependence of the 2-MHz Ultrasonic Velocity of Aqueous Ca(NO,), Solutions at 2 5 "C R
molality
Af, GHz
10-3u, m/s
g/cm3
50.13 30.34 15.22 12.21 10.18 9.17 8.17 7.15 6.14 5.15 4.13
1.11 1.83 3.65 4.55 5.46 6.06 6.80 7.77 9.05 10.79 13.45
1552.9 1590.6 1678.0 1717.8 1745.6 1770.0 1789.9 1810.7 1830.1 1856.3 1884.8
1.117 1.197 1.331 1.389 1.441 1.479 1.516 1.557 1.609 1.667 1.739
3.712 3.302 2.668 2.440 2.277 2.158 2.059 1.959 1.856 1.741 1.619
P,
TABLE I11 : Composition Dependence of the Hypersonic Velocity and the Adiabatic Compressibility of Aqueous Zn(NO,), Solutions at 5 0 "C and a Scattering Angle of 90"
~ f , 10-3u, R 50.1 30.1 15.1 18.1 10.1 9.06 8.15 8.00 7.10 7.10 6.17 6.00 5.12 5.00 3.80
molality GHz 1.11 1.85 3.69 4.62 5.53 6.13 6.84 6.94 7.95 7.95 9.03 9.26 10.89 11.11 14.62
5.96 6.12 6.58 6.76 6.93 7.00 7.12 7.16 7.22 7.22 7.34 7.35 7.42 7.36 7.51
p,
IO~~P,,
m/s
g/cm3 cm2/dyn
1.60 1.62 1.70 1.73 1.76 1.78 1.79 1.80 1.81 1.81 1.83 1.83 1.84 1.83 1.85
1.145 1.238 1.437 1.521 1,594 1.638 1.687 1.692 1.748 1.748 1.808 1.817 1.887 1.897 2.000
3.43 3.07 2.40 2.19 2.020 1.94 1.84 1.81 1.74 1.74 1.65 1.64 1.56 1.58 1.46
ference which was found by Maret13between his hypersonic velocities and the ultrasonic velocities of Subrahmanyam and Bhima~enachar.'~ Plots of the hypersonic velocity, obtained at 45O, 90°, and 135" scattering angles, and the 2-MHz ultrasonic velocity vs. solute concentration for the Zn(N03)' and ZnC1, solutions appear in Figures 2 and 3, respectively. The Zn(N03), measurements were conducted at 50 "C, since the more concentrated solutions could not be supercooled to 25 "C. The hypersonic velocities which were obtained at a fixed scattering angle correspond to sound waves at (14) Subrahmanyam, S. V.;Bhimasenacher, J. J. Acoust. SOC. Am. 1951, 23,219.
Carpio et ai.
The Journal of Physical Chemistty, Vol. 86,No. 25, 1982
4982
TABLE IV: Composition Dependence of the Hypersonic Velocity and the Adiabatic Compressibility of Aqueous Zn(NO,), Solutions at 50 "C and Scattering Angles of 45" and 135" -____ Af, lwu, p, 10"fis, R molality GHz m/s g/cm3 cm2/dyn
__
0
= 45"
50 30 15 12 10 9 8.00 6.00 5.00 3.80
1.11 1.85 3.70 4.63 5.55 6.17 6.94 9.26 11.11 14.62
3.16 3.26 3.54 3.59 3.70 3.14 3.82 3.85 3.87 3.90
50 30 15 10 8.00 6.00 6.00 5.00 3.80
1.11 1.85 3.70 5.55 6.94 9.26 9.26 11.11 14.62
7.72 7.98 8.60 9.13 9.37 9.53 9.53 9.90 I10.24
0 =
L
m
50 30
5
2
'0
6
6
i
35
4
R
1
-+-------
R 50.06 30.12 15.08 12.06 10.06 9.06 8.15 7.10 6.17 5.12 4.09 3.24
molality
53.41 20.00 15.00 12.01 10.01
15
12
10
6
6
5
4
35
135" 1.58 1.62 1.70 1.78 1.81 1.82 1.83 1.88 1.93
1.145 1.238 1.438 1.594 1.692 1.817 1.817 1.897 2.000
3.48 3.08 2.39 1.90 1.80 1.66 1.66 1.50 1.34
1.11 1.85 3.69 4.62 5.53 6.14 6.84 7.95 9.03
10.89 13.61 17.20
u, m / s
p,
1579.8 1610.0 1684.9 1710.7 1723.4 1723.8 1726.0 1722.4 1713.6 1699.6 1670.7 1630.1
Af,
50 30
3.58 3.16 2.43 2.28 2.07 1.99 1.86 1.76 1.68 1.59
lO"fiS, g/cm3 cm2/dyn
1.1449 1.2381 1.4367 1.5212 1.5943 1.6379 1.6867 1.7481 1.8084 1.8868 1.9788 2.0516
3.50 3.12 2.45 2.25 2.11 2.06 1.99 1.93 1.88 1.84 1.51 1.83
TABLE VI: Composition Dependence of the Hypersonic Velocity and the Adiabatic Compressibility of Aqueous ZnC1, Solutions at 25 "C and a Scattering Angle of 90"
'
R
m
1.145 1.238 1.437 1.521 1.594 1.638 1.692 1.817 1.897 2.000
TABLE V : Composition Dependence of the 2-MHz Ultrasonic Velocity and the Adiabatic Compressibility of Aqueous Zn(NO,), Solutions at 50 "C
Flgure 1. Hypersonic and ultrasonic velocities of Ca(N03)2.RH,O at 25 'C.
A
1.56 1.60 1.69 1.70 1.74 1.75 1.78 1.77 1.77 1.77
2
Flgure 2. Hypersonic and ultrasonic velocities of Zn(N03)2-RH20 at 50 O C .
different frequencies in contrast to the ultrasonic velocities which were obtained at a fixed frequency. The adiabatic compressibility vs. composition plots for the Ca(N03),, Zn(NOa),, and ZnC1, solutions are shown
8.94 7.88 6.90 5.97 5.01 5.01 4.48 4.00 3.56 3.26 3.0 2.83 2.30
molality
1.04 2.18 3.70 4.63 5.56 5.56 6.22 7.05 8.05 9.30
11.1 11.1 12.4 13.89 15.6 17.05 18.5 19.6 24.15
GHz 5.83 6.00 6.10 6.21 6.30 6.33 6.37 6.43 6.48 6.58 6.70 6.61 6.78 6.80 6.93 7.04 7.11 7.37 7.52
10-3v, m/s 1.56 1.58 1.59 1.60 1.62 1.62 1.63 1.63 1.64 1.65
1.66 1.64 1.67 1.67 1.69 1.71 1.70 1.78 1.79
p, 1o"P,, g / c m 3 cm'idyn
1.107 1.257 1.327 1.393 1.457 1.457 1.444 1.540 1.600 1.665 1.743 1.743 1.798 1.854 1.909 1.954 1.990 2.01 5 2.129
3.71 3.20 2.98 2.79 2.63 2.62 2.53 2.43 2.34 2.21
2.08 2.13 1.98 1.93 1.83 1.75 1.70 1.57 1..'17
in Figures 4-6,respectively. The data for Figures 1-6 are given in Tables I-VIII. The densities used in computing Ps for the ZnClz solutions were taken from the International Critical Tables15 and from the data reported by
Aqueous Ca(NO,),,
Zn(NO,),,
0 2 MHz Ultrasonic
1.93
1.81 -
45"
Scattering
A
90"
Scattei.ing
Scattering
0
135'
@
9O0ond 135' Overlap
Q
45'and
- *
1.75
The Journal of Physical Chemistry, Vol. 86, No. 25, 1982 4903
and ZnCI, Solutions
90'
Overlap
Water Velocity
-
-L g
1.69-
y1
m
'0 >
1.63-
1.57
-
*--
1.51
1.45 0
l
l
2
l
4
1
1
6
1
8
Flgure 3. Hypersonic and ultrasonic velocities of ZnCI,4?H,O
l
l
10
+ (u,'
- ~ O ~ ) [ w ~ ? / (-t l o~?)]
l
l
14
l
16
I
18
1
~
20
~
~
MOLALITY
22
at 25 "C.
Darbari et a1.16 The Zn(NO& densities at 50 O C were determined in this work. The 2-MHz ultrasonic velocities and adiabatic compressibilities were fitted to four-parameter equations by a nonlinear least-squares fitting routine. The parameters are listed in Table IX. Darbari et al.16 have determined ultrasonic velocities of ZnC1, solutions at 25 "C over the frequency range of 5-250 MHz. In cases where there was velocity dispersion, Darbari et al. fitted the velocity data to the following function for a single relaxation u2 = uO2
l
12
46
(5)
where uo and u, are respectively the values of u at frequencies low and high with respect to the relaxation frequency f,; w is the relaxation time (T-I = 27rfJ. The values of uo and u, were used to compute Po and om,respectively. These limiting values of the adiabatic compressibility are shown in Figure 6. The Pmvalue obtained by fitting the ultrasonic data yields a value which is substantially higher than the values obtained from hypersonic velocities. This illustrates the value of obtaining hypersonic velocities to complement ultrasonic data in such relaxational studies. The hypersonic and ultrasonic curves must meet at the R = value, i.e., the pure-water value, since water does not display any dispersion at the frequencies studied in this project ( R = moles of water/moles of salt). The relevant Greenspan and Tschiegg ultrasonic velocities for water are 1497.0 m/s at 25 "C and 1452.9 m/s at 50 OC.17 (15) International Critical Tables 1928, 3, 64. (16) Darbari, G. S.; Richelson, M. R.; Petrucci, S.J. Chem. Phys. 1970, 53,859. (17) Greenspan, M.; Tschiegg, C. J. Acoust. SOC.Am. 1959, 31, 75.
o
d
A
'
;
M Y)
'
'
: 15
12
~ 10
" 8
8"
" 6
"
10
" 5
'
12
14
6
MOLALITY
35
E
I
Figure 4. Hypersonic and ultrasonic adiabatic compressibilities of Ca(N03),d?H,0 at 25 OC.
The values of os are, therefore, 4.45 X lo-" cm2/dyn at 25 "C and 4.20 X cm2/dyn at 50 "C. The Ca(N0J2
~
4984
Carpio et al.
The Journal of Physical Chemistty, Vol. 86, No. 25, 1982
TABLE VII: Composition Dependence of the Hypersonic Velocity and the Adiabatic Compressibility of Aqueous ZnC1, at 25 "C and Scattering Angles of 45" and 135" p,
1O1'ps,
g/cm3
cm2/dyn
45" 1.52 1.57 1.57 1.58 1.58 1.58 1.59 1.60 1.61 1.62 1.62 1.64 1.62 1.64 1.64 1.65 1.76
1.107 1.257 1.327 1.393 1.457 1.457 1.494 1.540 1.600 1.665 1.743 1.745 1.798 1.854 1.909 1.954 2.129
3.91 3.31 3.10 2.92 2.79 2.75 2.71 2.60 2.46 2.33 2.22 2.13 2.16 2.01 2.00 1.92 1.52
0 = 135" 7.56 1.55 7.83 1.58 8.28 1.62 8.29 1.62 8.57 1.66 8.60 1.65 8.71 1.65 8.93 1.68 9.21 1.72 9.43 1.75 10.35 1.89
1.107 1.257 1.457 1.494 1.574 1.647 1.743 1.854 1.896 1.939 2.129
3.76 3.21 2.62 2.55 2.31 2.23 2.10 1.91 1.78 1.68 1.32
Af,
R
molality
53.41 20 15.00 12.01 10.01 9.99 8.94 7.88 6.10 5.97 5.01 5.01 4.48 4.00 3.56 3.26 2.30
1.04 2.78 3.70 4.62 5.50 5.56 6.22 7.05 8.05 9.30 11.1 11.1 12.40 13.89 15.60 17.04 24.15
53.41 20 9.99 8.94 6.90 5.97 5.00 4.00 3.56 3.26 2.30
1.04 2.78 5.56 6.21 8.05 9.30 11.11 13.89 15.60 17.04 24.15
GHz 0 =
3.07 3.19 3.24 3.29 3.31 3.36 3.33 3.37 3.42 3.47 3.51 3.57 3.52 3.61 3.59 3.64 3.99
lO-'V,
m/s
TABLE VIII: Composition Dependence of the 2-MHz Ultrasonic Velocity and the Adiabatic Compressibility of Aqueous ZnC1, Solutions at 2 5 "C
lO"P,,
R
molality
30 15.00 12.01 10.01 8.94 7.88 6.90 5.97 5.50 5.01 4.48 3.95 3.56 3.26 2.98 2.72
1.85 3.70 4.62 5.55 6.21 7.05 8.05 9.30 10.10 11.09 12.40 14.06 15.60 17.04 18.6 20.9
l O - % 4 m / s p , g/cm3 cm2/dyn
1.4945 1.5140 1.5260 1.5374 1.5438 1.5500 1.5576 1.5649 1.5663 1.5657 1.5657 1.5601 1.5567 1.5489 1.5455 1.5350
1.184 1.327 1.343 1.457 1.494 1.540 1.600 1.665 1.700 1.743 1.798 1.857 1.909 1.954
3.782 3.287 3.083 2.904 2.808 2.703 2.576 2.495 2.398 2.340 2.269 2.212 2.162 2.133
and ZII(NO,)~curves extrapolate to the water values, whereas, the ZnC1, curves display dispersion even at low solute concentration. The velocity dispersion, present for all three systems, was expected, based upon the dispersion in the acoustic absorption coefficient already reported.' When the velocity vs. composition plots of the three sytems are compared with the corresponding adiabatic compressibility plots, it becomes obvious that care must be exercised in attaching too much significance to changes in the velocity, for those changes are not mirrored in the adiabatic compressibility. Yet the velocity of sound has been utilized to study structural changes which occur in liquid mixtures. For example, maxima in the velocity have been found a t intermediate concentrations of mixtures formed by water with another component which may be
I
m
1
'
50 30
15
12
10
3
b
S
4
35
Hypersonic and ultrasonic adiabatic compressibilities of Zn(NO,),.RH,O at 50 O C . Figure 5.
acetone, a primary alcohol, acetic acid, some glycols, ether, etc.laZ0 Kinsinger et aLZ1have used the complex changes in the hypersonic velocity as evidence for a number of associated species in dimethyl sulfoxide-pyridine mixtures. The most useful information can be derived from the adiabatic compressibilities. A comparison of the 2-MHz adiabatic compressibilitiesof the Ca(N03),, Zn(N03),, and ZnC1, solutions at 50 "C is shown in Figure 7. To account for the differences in the magnitudes of the adiabatic compressibilities of these three systems, one must focus attention on the nature of the metal aquo complexes. These systems are indeed structurally different, as is reflected by their difference in viscosity, acidity, propensity for supercooling, and, in the case of the nitrate systems, differences in rotational relaxation times of the nitrate ions.22 For example, concentrated aqueous ZnCl, solutions are strongly acidic5 as are ZII(NO,)~solutions,23whereas Ca(N03)2.4HZ0is Previously, ultrasonic compressibilities of aqueous nitrates and chlorides have been reported over a much more restricted range of concent r a t i ~ n . ~It~was , ~ ~observed that at corresponding salt concentrations ps increased for salts of increasing ionic radius, and in the case of other salts the reverse was ob(18) Sette, D. In "Encyclopediaof Physics (Handbuch Der Physik)"; Flagge, S.,Ed.; Spring-Verlag: West Berlin, 1961; Val. II/I. (19) Negishi, N.; Yamazaki, M.; Torikai, Y. Jpn. J. Appl. Phys. 1967, 6, 1016. (20) Asenbaumand, A.; Sedlacek, M. Acoustica 1974, 30, 109. (21) Kinsinger, S.B.; Tannahill, M. S.;Greenberg, M. S.;Papov, A. I. J. Phys. Chem. 1973, 77, 2448. (22) Carpio, R. A,; Mehicic, M.; Yeager, E. J. Chem. Phys. 1981, 74, 2778. (23) Sare, E. J.; Moynihan, C. T.; Angell, C. A. J. Phys. Chem. 1973, 77. 1869. ---I
(24) Subrahmanyam, S. V.; Bhimasenacher, J. J. Acoust. S O ~Am. . 1960, 32, 835. (25) Murty, M.S . Indian J . Pure Appl. Phys. 1965, 3, 156.
Aqueous CB(NO~)~, Zn(N03),, and ZnCI, Solutions
The Journal of Physical Chemistry, Voi. 86, No. 25, 7982 4985
I
1
4.5s
4.1
0 2MHz Ultrosonic
o A
450 Scattering 900 Scattering 0 1 3 9 Scattering Q 9O0ond 135' Overlap Q 45'0nd 135' Overlap
6
Darbori et. 01, Bo et
01.
Pm
1.71
1.36
2 I
1
'
I
CklGQ50 30
6
4 I
15
8
1
I
I
12
10 9
1
8
12
10
14
16
18
20
22
1
I
1
I
I
I
7
6
5
4
3
2.5
Figure 6. Hypersonic and ultrasonic adiabatic compressibilities of ZnCi,.RH,O
MOLALITY R
at 25 OC.
TABLE IX u = a,
aqueous system
t, "C
10-4a0
Ca(N03)2 Zn(N03)2 ZnC1,
25 50 25
0.1478 0.1509 0.1461
aqueous system
t, "C
Ca(NO3),
25 50 25
Zn(N03)Z
ZnC1, a
u = 2-MHz velocity.
m = molality.
+ a,m + a,mz + a3m3m/sa 10-Za, - 10-'a, 0.7025 0.6966 0.1827
0.4342 0.6767 0.08192
P S = bo + b,m t b,m' t b3m3cm2/dynb 10lOb,, -10"b, 10"b, 0.4294 0.4023 0.4358
0.6115 0.5670 0.3602
0.5250 0.4765 0.2111
a3
SD in u
0.1014 0.1822 0.002656
3.04 5.48 2.20
-1013b,
10"(SD in 5 s )
0.1626 0.1298 0.04680
2.45 5.04 7.22
5s = 2-MHz adiabatic compressibility. m = molality.
served. The only conclusion that could be reached was that other than simple Coulombic forces have to be taken into account. If the compressibility data reported in this study are coupled with the results arrived at in previous studies of these systems, it can be concluded that for a fixed concentration less than 10 m the increase of &, i.e., Zn(NOd2 < Ca(N03)2< ZnC12,parallels the increased ion association present in these solutions. If we consider aqueous Zn(N03)zsolutions first, Bulmer et a1.26have shown by vibrational spectroscopy that, in dilute aqueous solutions, the hexaquozinc(I1) ion is a well-defined stable complex. In a recent study, Sze and Irish27have presented Raman data which have led to a (26) Bulmer, J. T.; Irish, D. E.; Odlberg, L. Can. J. Chem. 1975,53, 3806.
(27) Sze, Yu-Keung;Irish, D. E. J . Solution Chem. 1978, 7, 395.
number of important conclusions. Solutions of Zn(NO& less concentrated than 3.5 M consist primarily of Zn(HzO),2+and nitrate ions. Only a very low concentration of Zn[ON02(Hz0)5]+exists. Outer-sphere ion pairs [ Zn(HzO),J2+(NO3)-exist above 3.5 M. For concentrations of 6 L R > 2, both ion pairs and ion triplets are formed with the nitrato group acting as a unidentate ligand. Only when R < 4 does the coordination change of zinc from octahedral to tetrahedral become important. It is accompanied by an increased covalent character in the Zn2+-ON02bond. In contrast to the zinc nitrate solutions, vibrational spectral studies have led to the conclusion that contact ion pairs exist in calcium nitrate solutions even when R > 6. The bonding is believed to be completely electrostatic in the case of CaN03+.28 (28) Irish, D. E.; Davis, A. R.; Plane, R. A. J. Chem. Phys. 1969, 50,
2262.
4986
Carpio et al.
The Journal of Physical Chemistty, Vol. 86, No. 25, 1982
1
2
4
0
1
I
I
I
8
10
12
'4
MOL A L I T Y
Comparison of the 2-MHz adiabatic compressibilities of aqueous Ca(NO,),, Zn(NO,),, and ZnCI, solutions at 50 O C . Flgure 7.
Information on the local coordination geometry of zinc cations in ZnC1, aqueous solutions has been sought in a variety of studies. Strong Zn2+-C1 interactions are expected to compete with the Zn2+-H20interactions even in very dilute solutions. The velocity dispersion observed in this study at low concentrations is certainly evidence for the presence of complex ions. The studies of Darbari et and TamuraZ9show ultrasonic dispersion for dilute aqueous ZnCl, solutions. The transference numbers of Zn2+in aqueous ZnC1, solutions decrease with increasing concentration to near 0.5 M as do those of other 2:l electrolytes, then abruptly the transference number drops to large negative values at higher concentrations, suggesting the presence of anionic complexes of zinc.30 The most detailed evidence on the identity of the complex ions can be taken from the Raman study of Irish et al.31of aqueous zinc chloride over an extended concentration range and that of Shurvell and Dunham3, on aqueous solutions of ZnC1, containing various amounts of HC1. The main aquated species in the latter study, which is more recent, were shown to be ZnCld2-and ZnC1,. In the former study, four species were inferred to be present in the concentration range between 0.5 and 10.0 m namely, Zn(H20)2+,ZnCl+(aq),linear ZnClz(aq),and [ZnC14(H20),]-2.The above results are consistent with the presence of Z I I ( H ~ O ) ~ZnCP, ~ + , and possibly ZnClz species at low concentrations followed by an abrupt formation of higher chloro complexes. It may be that, at about 0.5 M, the octahedral ZII(H,O)~~+ complexes commence undergoing a transformation to tetrahedral ZnC142-species. These transitions could be largely responsible for the velocity dispersion observed here. An approach which has proved useful in dealing with molten-salt binary mixturese is now adopted; namely, we ~~
(29)Tamura, K.J. Phys. Chem. 1977,81,820. (30)Harris, A. C.; Parton, H. N. Trans. Faraday SOC. 1940,36,1139. (31)Irish, D. E.; McCarrol, B.; Young,T. F. J . Chem. Phys. 1963,39, 3436. (32) Shurvell, H. F.; Dunham, A. Can. J . Spectrosc. 1978,23, 160.
Mole Froction
of Tetrohydrote
Figure 8. Excess adiabatic compresslbllkies vs. mole fraction of tetrahydrate: Zn(N03),.4H20-H20 at 50 O C , Ca(N03),~4H,0-H,0at 25 O C , and ZnC12-4H,0-H,0 at 25 O C .
consider the variation with molar fraction of the magnitude of A&,,, computed by using the relation ABexc = Ps(expt1) - &(ideal) (6) where (7) PS(idea1) = Xtetrahydrate(PS)tetahydrate + XH20(PS)Hz0 In other words, we consider the systems here to be binary mixtures of the tetrahydrate and water. The tetrahydrate is selected since it is the most concentrated solution studied and in the past it has been popular to regard such melts as Ca(N03),.4Hz0 as fused salt analogues, consisting of strongly coordinated, centrosymmetric cation-water complexes. Excess molar volumes AVM are calculated in a similar fashion. These parameters are shown graphically as a mole fraction of the tetrahydrate in Figures 8 and 9. The behavior displayed by both parameters is nonideal. Notice, however, that there is a striking parallelism between the two plots. The initial rising portion of the curves is probably due to the fact that, as the salts are added to pure water, the hydrogen-bonded structure is destroyed and the ions become hydrated. The destruction of the hydrogen-bonded structure is probably complete by the time the maxima are reached, which corresponds to a water/salt ratio of approximately 8. In very dilute solutions the hydrated ions are well separated by bulk water. It might also be a reasonable assumption that, at the concentration corresponding to the maxima in the plots, all the free water has disappeared and that all the water molecules now reside in solution shells. Of note is the near linearity of the descending portion of the excess plots. This probably can be explained on the basis that the water molecules which now reside in the coordination spheres of the metal cations retain a modified but constant volume. Claes and Gilbert3 have found that
Aqueous Ca(N03),, Zn(N03),, and ZnCI, Solutions
The Journal of Physical Chemi$tty, Vol. 86, No. 25, 1982
4987
TABLE X : Heat Capacity Ratios for Ca(NO,),,RH,O ~-
1o"PT," cm2/dyn
3.63
1.40 1.73
1.60
1.14
1.65 1.95 2.05
0.95 1.06
4.85 5.95 7.02 a
Mote Fraction of Tetrahydrate
Figure 9. Excess molar volumes vs. mole fractions of tetrahydrate: Zn(N03),-4H20-H,0 at 50 OC, Ca(NO3),.4H,O-H2O at 25 OC, and ZnCI,.4H20-H20 at 25 OC.
this modified volume in the Ca(NO3),.4H,O-water system is 15.22 cm3at 50 "C. Using our density data and a similar approach, we found the molar volume of H 2 0 in the Zn(NO,),4H2O-water system at 50 "C in the same concentration range to be approximately 9 cm3, which is considerably lower than the molar volume of pure water at this same temperature as well as the bound water in the Ca(NO,), system. This is not unreasonable, considering that Zn2+ions have a radius of 0.83 A, while Ca2+ions possess a radius of 0.99 A; thus, the Zn2+ cations exert greater (33) Claes, P.; Gilbert, J. In "Ionic Liquids";Inman, D., Lovering, D. G., Eds.; Plenum Press: New York, 1981.
PT/PS =
R
1o"P,, cm2/dyn
1.84 1.94
Cp/C,
1.06
Values taken from ref 35.
electrostrictive forces. From X-ray investigations of 1M aqueous solutions, the cation-water distance for Ca2+is 2.330 A and it is 2.093 A for Zn2+.34 Also in this regard, low-frequency Raman vibrational modes in aqueous Zn(NO,), solutions which have been attributed to cationwater stretching of octahedral Zn(H20),2+complexes have been studied in detail by Bulmer et a1.26 The totally symmetric stretch of the hexaaquo(I1)ions is unperturbed at temperatures of less than 80 "C.The existence of such a mode implies a substantial degree of covalent character of the metal-oxygen bond. No such mode has been observed in the corresponding Ca(N03)2solutions, suggesting that the aquo species are more ion-dipole in nature. These differences in the polarization of water molecules coordinated to the cations probably account for the differences in acidity between the Ca(N03)2and ZII(NO,)~systems alluded to earlier. It is also possible to derive thermodynamic relationships from these compressibility data. When one uses the empirical equation for computation of of Ca(N03)2solutions at 2 MHz which is listed in Table IX and the corresponding values of the isothermal compressibilities & obtained by Peckston et ala, the ratios of the heat capacity at constant pressure to that at constant volume, Cp/Cv, at several compositions can be computed. These values are given in Table X.
os
Acknowledgment. We are pleased to acknowledge the support of the research by the Office of Naval Research, the US.Air Force Systems Command, and the Air Force Office of Scientific Research. We also thank Michael Kisselburgh and Mrs. Betty Darcy for typing the manuscript. (34) Bol, W.; Gerrits, G. J. A.; Van Panthaleonvan Eck, C. L. J . Appl. Crystallogr. 1970, 3, 486. (35) Peckston, L.; Smedley,S.I.; Woodall, G. J.Phys. Chem. 1977,81, 581.
