Journal of Structural Chemistry, Vol. 45, No. 5, pp. 825-831, 2004 Original Russian Text Copyright © 2004 by L. Ɍ. Vlaev and S. D. Genieva
ELECTRON TRANSPORT PROPERTIES OF IONS IN AQUEOUS SOLUTIONS OF SODIUM SELENITE L. Ɍ. Vlaev and S. D. Genieva
UDC 541.8
Ion diffusion kinetics has been studied using the data of conductivity measurements for aqueous solutions of sodium selenite with different concentrations and at different temperatures. Molecular and ionic selfdiffusion coefficients have been determined for infinitely dilute solutions in the temperature range 288 K313 K. The limiting values of ion mobility and changes in the energies of translation of water molecules from ions’ hydration shell have been found. At elevated temperatures, 'E 0tr increases for both ions in direct proportion to the crystallographic radius of the latter. Ion hydration numbers at 298 K have been calculated. The results of this study are interpreted in the light of Samoilov’s theory on positive and negative hydration of ions. Keywords: sodium selenite, aqueous solutions, ion diffusion kinetics, Samoilov’s theory.
INTRODUCTION In physical chemistry of solutions, conductivity studies have become a traditional tool for investigating solvation and transport properties of electrolytes. These properties depend on both the radius and the degree of hydration of ions [1-8]. Within the framework of Samoilov’s theory [1] ion hydration may be negative or positive depending on the mobility of water molecules in the hydration sphere of ions, which may be higher or lower than the mobility of water molecules in bulk water. Therefore, it is interesting to study the temperature dependence of short-range hydration of ions in aqueous solutions of electrolytes. Short-range hydration of ions is characterized by the energy difference between the potential barriers separating two adjacent equilibrium positions of water molecules in water and defining water translation from the hydration shell of ions, 'E 0tr [9-16]. This information is derived from the temperature dependence of equivalent conductivity of aqueous solutions of sodium selenite. As is known, sodium ions are characterized by minor positive hydration compared with that of the selenite ion [17], but no data are available in the literature concerning the temperature dependence of 'E 0tr for the selenite ion. On the other hand, aqueous sodium selenite is the starting compound for obtaining selenites possessing low solubility [18] and serving as precursors for the preparation of the appropriate selenides [19]. Compounds from both classes are known [20] to be good semiconductors and ferroelectrics and are of interest from the viewpoint of microelectronic applications. Therefore, the aim of the present work is to investigate the electron transport properties of sodium selenite ions in aqueous solutions in the temperature range 288 K - 313 K.
A. Zlatarov University, Burgas, Bulgaria;
[email protected]. Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 870-876, September-October, 2004. Original article submitted July 3, 2003.
0022-4766/04/4505-0825 © 2004 Springer Science+Business Media, Inc.
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EXPERIMENTAL The starting solution of sodium selenite was prepared by dissolving Na2SeO35H2O (Fluka, analytical grade) in bidistilled water (̃ = 8.9u10–7 Scm–1 at 298 K). Dilution of the aliquot parts of this solution gave a series of 17 solutions with concentrations in the range 0.0010 g-equivl–1 - 0.1000 g-equivl–1. Exact concentration of each solution was measured by means of iodometric titration of sodium thiosulfate using the procedure of [21]. Conductivity measurements for the solutions were carried out on an Inolab-WTW digital conductometer (Germany). The conductometric cell constant (k = 0.4752 cm–1) was determined by the classical procedure [22] using the standard solutions of potassium chloride. The temperature range was 288 K - 313 K (one degree step). The temperature was maintained to an accuracy of r0.05 K using a U-1 thermostat (Germany). The solution was placed in a 100 cm3 glass vessel equipped with a water jacket and was stirred with an electromagnetic stirrer. To avoid solution of CO2 and other atmospheric gases affecting the conductivity of the solution, the vessel was closed with a rubber stopper with a conductometric cell passed through it. The conductivity measurement error was up to r0.2%. All experimental data were processed by the least-squares method.
RESULTS AND DISCUSSION Figure 1 presents the temperature dependence of the limiting equivalent conductivity of sodium selenite and its ions obtained by processing the original results of [23] using the Fuoss–Onsager method. It can be seen that the limiting equivalent conductivity of the selenite ion exceeds that of the sodium ion and increases with temperature. Based on the values of O 0r one can find the activation energy of equivalent conductivity EAr , which is determined from the dependences of ln O 0r on 1/Ɍ linearized by the least-squares method (Fig. 2). The values of EAr were averaged over temperature in the range 288 K - 313 K, the mean value being 15.9 kJmol–1 for sodium ions and 17.1 kJmol–1 for the selenite anion. For inorganic acids, it equals 9.6 kJmol–1 [24]; for some inorganic salts, however, it was found in the range 12 kJmol–1 - 36 kJmol–1 [25]. The higher value of EAr for the selenite ion compared with the sodium ion is explained by the larger size and larger value of positive hydration of the former [17].
Fig. 1. Temperature dependence of the limit equivalent electric conductivity of sodium selenite: 1) O0Na , 2) O0SeO 2 – , 3) O 0Na 2SeO3 . 3
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Fig. 2. Dependence of ln O0r on 1/T for ions: 1) Na+, 2) SeO 32 .
Fig. 3. Temperature dependence of self-diffusion coefficients for ions: 1) Na+, 2) SeO 32 ; 3) Na2SeO3. To calculate the ion self-diffusion coefficients for infinite dilution Dr0 , we employed the following equation [2-8]: Dr0
RT O 0r , | zr| F 2
(1)
where zr is the charge on the ion, F is Faraday’s constant, and all other parameters have the conventional sense. The molecular self-diffusion coefficient Dm0 for infinite dilution was calculated using the NernstHaskell formula [2-8, 26, 27]: Dm0
D0 D0 ( z | z |) z D0 | z | D0
RT O 0 O 0 (v v ) , z | z | F 2 (O 0 O 0 )
(2)
where D0 and D0 are the ion self-diffusion coefficients for infinite dilution; v+ and v– are the stoichiometric numbers of the cations and anions. Figure 3 presents the temperature dependences of the corresponding self-diffusion coefficients, which show that the molecular and ion self-diffusion coefficients for infinite dilution increase with temperature as nonlinear functions. The 0
different slopes of the curves dD /dT is explained by the different dimensions of ions, degrees of hydration, and mobility of water molecules in the vicinity of cations or anions [26,27]. Then we calculated the limiting mobility of the selenite ion 0 uSeO 2 and compared it with the analogous quantity for the sodium ion using the equation [27]: 3
ur0
O 0r . | zr | F
(3)
Transport of hydrated ions in solution is accompanied by sustained exchange of the neighboring water molecules. Different ions are characterized by different activation energies of water translation from the hydration shell of the ion between the equilibrium positions. In a first approximation, the apparent activation energy of ion conductivity in water El0 may be represented as the sum of the activation energy of the viscous water current Ez0 and a certain correction 'Etr0 ; the latter term defines the difference between water molecules in the hydration shell and in bulk water in effects of bond cleavage with the environment and formation of an appropriate vacant “hole” [13]: El0
Ez0 'Etr0 .
(4)
From the equations of simplified kinetic theory for the temperature dependence of viscosity it follows that [28] K0
A exp( Ez0 / RT ).
(5)
Ac exp( El0 / RT ).
(6)
For the limiting equivalent conductivity of ions [1, 29], O 0r
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Fig. 4. Dependence of ln(u r0 K) on 1/Ɍ for ions: 1) Na+, 2) SeO 32 . In view of Eqs. (5) and (6), we record O 0r K0
AAc exp('Etr0 / RT ),
(7)
where 'Etr0 is the energy difference between the activated transitions of water molecules from the hydration shell of ions El0 in solution and in bulk water Ez0 'Etr0
El0 Ez0 .
(8)
According to Samoilov’s theory [1], 'Etr0 may appear to be positive or negative. When 'Etr0 is negative, it is said that the ions are negatively hydrated; when 'Etr0 is positive, they are positively hydrated. For the latter, the mobility of the water molecule near the ion typically decreases compared to that in bulk water [9-16]. Since the limit mobility of ions ur0 is directly proportional to the equivalent conductivity of ions in the case of infinite dilution [Eq. (3)], instead of O 0r in Eq. (7) we can record ur0 . Then 'Etr0 for the given ion may be calculated from the equation [8, 26, 27]: 'Etr0
R
d ln(ur0 K) d (1/ T )
RT 2
d ln(ur0 K) . dT
(9)
Figure 4 presents the curves of ln(ur0 K) vs 1/Ɍ for the selenite and sodium ions, which can be approximated by the following polynomials of the second degree: ln(ur0 K) 0 ln(uSeO 2 K) 3
11.29 6.86 102 / T 1.16 105 / T 2 , 4.03 4.67 103 / T 6.94 105 / T 2 .
(10) (11)
Differentiating Eqs. (10) and (11) with respect to temperature, by virtue of Eq. (9) one can calculate 'Etr0 for any temperature in the stated range. Table 1 lists several kinetic parameters for both ions. It can be seen that 'Etr0 increases with temperature for both ions. For the sodium ion, 'Etr0 is only negative, while for the selenite ion, it increases to positive values at elevated temperatures. In the light of Samoilov’s theory of positive and negative hydration of ions [1] and taking into account the high value of the coefficient ȼcr of the selenite ion [17] and our results, one can say that at elevated temperatures the selenite ion is transformed from negatively to positively hydrated ion. With this approach, hydration is not regarded as the binding of ions with
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TABLE 1. Kinetic Parameters of Conductivity for SeO 32 and Na+ Ions at Different Temperatures
288
293
Temperature, K 298 303
D0 105, cm2s–1
1.02
1.73
1.34
1.51
1.69
1.89
D –0 105,
0.75
0.86
0.98
1.12
1.27
1.44
4.12
4.64
5.20
5.77
6.38
7.00
6.04
6.81
7.66
8.58
9.59
10.66
–1.00
–0.88
–0.77
–0.67
–0.56
–0.46
–1.19
–0.50
0.16
0.79
1.41
2.01
Parameter
2 –1
cm s
u 0 104, SC–1cm2 u0 104, SC–1cm2 0 'Etr( ) , 0 'Etr( ) ,
–1
kJmol
–1
kJmol
308
313
a particular number of water molecules; rather, this is the action of ions on the translational motions of the nearest water molecules. Since the values of the second term in Eq. (8) are the same for the two ions (and faintly decrease as the temperature increases), the increasing value of 'Etr0 is determined by the increasing value of El0 . The temperature coefficient 'Etr0 is larger for the selenite ion (smaller for the sodium ion). As a result, at 297 K, 'Etr0 for the selenite ion becomes zero and then takes positive values at elevated temperatures. This tendency of variation in 'Etr0 is also observed for a series of other ions [11, 14-16, 26, 27, 30]. While for alkaline metal ions 'Etr0 is low positive or negative below 323 K, for larger ions it rapidly increases, taking rather high positive values at higher temperatures [26, 27]. The observed dependences of the transport characteristics of ions are explained by differences in the dimensions and hydration numbers of the ions. From the equation derived from the Stokes law [8, 31, 32] rs
| zr | F 2 6SN A KO 0r
(12)
one can calculate the Stokes radius of the traveling solvated ion. For effective radii of ions, Gill [33, 34] suggested using the following empirical equation: reff
rs 0.0103H ry ,
(13)
where H is dielectric permeability of water [2]; ry is a parameter whose value is 0.085 nm for nonassociated solvents and 0.113 nm for associated solvents having high values of H (water). Using the estimated effective radii of the ions and the equation [8, 31, 32] ns
4S 3 (reff rcr3 ), 3VL
(14)
we calculated the solvation numbers of the ions ns. In Eq. (14), VL is the volume occupied by one water molecule (0.0022 nm3 [8]), and rcr is the crystallographic radius of the ion [35-37]. The transport number of ions tr0 is calculated from the equation [6-8] t
O 0 , accordingly, t– = 1 – t+. O 0 O 0
(15)
The values of the above-mentioned parameters of the ions at 298 K are listed in Table 2. From Table 2 it follows that the selenite ion is characterized by a larger effective radius, as well as by the higher hydration and transport numbers compared with the sodium ion. Taking into account the values of the coefficient ȼcr for the two ions [17], one can say that the selenite ion is more positively hydrated by Samoilov’s theory than the sodium ion. This is
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TABLE 2. Conductivity, Radii, Hydration Numbers, and Transport Numbers (limiting values) for the Selenite and Sodium Ions at 298 K Parameter
Na+
SeO32
O0r , Scm2g-equiv–1
50.14 0.06 0.098 0.184 0.377 18.10
73.92 0.26 0.276 0.249 0.443 22.60
0.41
0.59
±
Bc rcr, nm rs, nm reff, nm ns tr0
supported by the high value of ns for the two ions. A comparison of the values of ns for different ions [32, 37] shows that the lithium, sodium, and SeO32 ions, characterized by greater positive hydration, have the highest values. In our opinion, the maximal value of ns may be as high as 20. This assumption is based on the tetrahedral structure of the water molecule [38] and on the fact that an icosahedron composed of 20 close-packed tetrahedra is a thermodynamically most stable spatial configuration of tetrahedra [39]. Therefore, small and positively hydrated ions will obviously tend to adopt this configuration. The lower the extent of positive hydration, the lower the hydration number, which is just observed for alkali metal ions [32, 37]. The higher values of ns for the selenite ion (22.6 at 298 K) may be explained by “overfilling” of the icosahedron because of the larger size of the ion and the higher value of its coefficient Bcr. Among 50 ions listed in [17] only the Mg2+ and TeO32 ions have higher values of Bcr compared with the selenite ion. Therefore, for these two ions, the hydration number is expected to be higher than 22. To conclude, the electron transport characteristics of ions dissolved in water are correlated in a complex manner with the hydration radius and hydration number of ions and with the activation energy of translation of water molecules from the hydration shells of ions. That is why some general tendencies are not readily evident for any type of ion, and can only be suggested for some individual groups of ions, namely, for alkaline, alkali earth, or halide ions. Acknowledgment is due to the Scientific Research Fund of the University for financial support (project NIH 25/02).
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