J. Phys. Chem. 1987, 91, 985-987
and Da$ representations have been found we have used in this paper the fab notation in accordance with the previous work on electrolyte solution^.^"^^ Acknowledgment. Part of the measurements were performed during H.W.’s visiting fellowship at the Research School of
985
Physical Sciences, Australian National University, Canberra, Australia. Dr. R. Mills and his colleagues are thanked for their kind hospitality. Financial support of this project by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. Registry No. LaC13, 10099-58-8.
Diffusion of Cations and Solvent Molecules in the Concentrated LiN0,-NH,
System
Ryuji Kusaka, Kazuhiro Ban, Yoshio Nakamura,* and Shigezo Shimokawat Department of Chemistry, Faculty of Science, and N M R Laboratory, Faculty of Engineering, Hokkaido University, Sapporo 060, Japan (Received: July 25, 1986; In Final Form: October 9, 1986)
The diffusion coefficients of both the cation and the proton have been determined in concentrated LiN03-NH3 solutions by means of the NMR spin-echo technique. The observed diffusion coefficients and their activation energies for the Li’ ions and NH3 molecules become nearly equal at compositions greater than 20 mol % LiNO,. The effect of solvation of the Li’ ions on the diffusion coefficients is discussed.
Introduction In solutions of strong electrolytes in a highly polar liquid such as water, the dissolved ions produce a major perturbation in the local structure of the solvent liquid. This perturbation is so marked as to produce “solvated” ions. In aqueous solutions the presence of the hydrogen bonds adds a further difficulty for understanding of its structure and dynamical properties.’ Liquid ammonia is also a strongly polar liquid with the dipole moment of 1.48 D (water 1.84 D), but the hydrogen-bonding ability of an ammonia molecule is less remarkable than that of a water molecule, since an ammonia molecule donates three protons but only one electron pair. It is thus expected that ammonia solutions will be more suitable than aqueous solutions for the investigation of the solvation phenomena. For this purpose we have measured the diffusion coefficients of both lithium ions and ammonia molecules up to a very concentrated solution range of the LiN03-NH3 system. The diffusion coefficients were measured as a function of composition and temperature by means of the spin-echo technique using 7Li and proton as N M R probes. It has already been shown by Garroway and Cotts2 that the dissolved lithium metal in liquid ammonia have substantially the same diffusion coefficients as ammonia molecules at the composition of 20 mol % metal. This strongly suggests that the dissolved alkali metals cations are solvated by four ammonia molecules. Our investigation was thus focused on this composition. Experimental Section Reagent grade LiN03 (Wako Pure Chem. Ind. Ltd.) was dried at 110 OC under vacuum for 24 h. Liquid ammonia was purified by distilling from sodium metal solutions and stored in a container with a Teflon stop cock. Liquid ammonia was introduced into a N M R measuring tube which contained a known amount of LiN03. The amount of ammonia introduced was determined by weighing the ammonia container. N M R tubes were made of Pyrex glass and were 8 mm in inner diameter. A pulsed N M R spectrometer (Bruker CXP type) was used. A stabilized direct current was supplied to a gradient coil attached to the N M R probe head. In the steady gradient method the diffusion coefficient D is given by3
where A ( G , h ) and A(0,27) are the magnitudes of the echo height NMR Laboratory.
at 27 with and without the field gradient G, respectively. y is the gyromagnetic ratio of the nucleus under study (proton or 7Li). Values of G were determined from the shape of echo^,^,^ which were proportional to the coil current and usually from 0.3 to 5 G cm-’. The resonance frequencies were 38.25 MHz for proton and 14.865 M H z for ’Li. The diffusion coefficients were determined by varying 7 at a fixed G. Between successive measurements of spin-echos, we had a sufficient waiting time, taking account of T , values of each samples5 Measurements were made at three temperatures, 273, 283, and 294 K, using a temperature control unit (Bruker VT-1000) within f l K.
Results and Discussion It has been estimated* from the inequality between the longitudinal and transverse relaxation rates of the protons in pure ammonia that the lifetime of the intermolecular proton exchange is longer than IO4 s, which is many orders of magnitude greater than molecular ammonia jump times. Thus, we can safely regard the self-diffusion coefficients measured for the protons as the diffusion coefficients for the ammonia molecules. The results for the diffusion coefficients of the ammonia molecules are presented in Figure 1 as a function of temperature. The results for pure ammonia are in reasonable agreement with values in the literat ~ r e . ~The . ~ results of the diffusion coefficients for the lithium ions are given in Figure 2 . In Figure 3 the diffusion coefficients for the ammonia molecules and for the lithium ions at 273 K are plotted against the concentration of lithium nitrate in solutions. The estimated errors in the diffusion coefficients are f5% for the ammonia molecules and &lo%for the lithium ions. It is seen that the diffusion coefficients for both the constituents are essentially the same above the composition of 20 mol 7% lithium nitrate. The activation energies for the diffusion processes, ED fitted to the Arrhenius equation D = Do exp(-ED/RT) are given in Figure 4. Again, the values of ED for the ammonia molecules and the lithium ions become practically equal at the composition of 20 mol % of the salt. These facts strongly suggest that each lithium ion is solvated by four ammonia molecules and conserves this structure during a diffusion step. It can be assumed then that solutions with less than 20 mol % lithium nitrate are homogeneous mixtures (1) Enderby, J. E.; Neilson, G. W. Rep. Prog. Phys. 1981, 44, 593. (2) Garroway, A. N.; Cotts, R. M. Phys. Rev. A 1973, 7, 635. (3) Carr, H.Y.;Purcell, E. M. Phys. Rev. 1954, 94, 630. (4) Douglass, D. C.; McCall, D. W. J . Phys. Chem. 1958, 62, 1102. (5) Uchibayashi, K.;Niibe, M., Nakamura, Y. J . Chem. Eng. Data 1985, 30, 214. ( 6 ) Haul, Von R.; Dorfmuller, Th. Z . Naturforsch. 1964, 19a, 100. (7) O’Reilly, D. E.; Peterson, E. M.; Scheie, C. E. J . Chem. Phys. 1973,
58. 4072.
0022-3654/87/2091-0985$01.50/0
0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91, No. 4 , 1987 -3:
Kusaka et al.
1
25 5
-7 33
10
0
37
35 lGOO/T
Figure 1. Diffusion coefficients of ammonia molecules in the LiN0,NH, system. Numbers in the figures denote the concentration of LiNO, in mol %. - - -, pure N H , (ref 7).
20 LINO, mol%
30
Figure 4. Composition dependence of the activation energies of the diffusion coefficients of NH, and Li' in the LiN0,-NH, system. E , is the activation energy of the viscosity (ref 5).
I
I 294K
28.5
-6
-7
3.3
3.5
0
37
lGOO/T
Figure 2. Diffusion coefficients of lithiam ions in the LiN0,-NH3 system. Numbers in the figure denote the concentration of LiN0, in mol %. -4
1
'H
I * ' A
A
. A
'Li
0
A
i
A
273 K e~
-7
'
1
10
0
20 LINO, m o l %
30
Figure 3. Composition dependence of the diffusion coefficients of N H 3 and Li' in the LiN0,-NH, system at 273 K.
of lithium ions solvated by four ammonia molecules, unbound ammonia, and nitrate ions. Although t h e lifetime for solvation is long (>lo-" s) compared to the time for a diffusion step (s), it is evidently shorter than the time for diffusion measurements, s. The exchange of unbound which was usually of the order of and bound (solvated) ammonia is so rapid that only one average proton N M R signal was observed. Thus, the observed diffusion coefficients for ammonia molecules DNHlare averaged ones for the unbound (subscript u) and the bound ammonia (subscript b) 'TU
D N H=~
lb
D, + -Db + lb + lb
where 7, and 7 b are respectively the lifetimes of the unbound and bound states. A t equilibrium, each fraction can be given by the mole fraction of the respective species
(3)
where C i s the mole percent of lithium nitrate in solutions. We assume further that the diffusion coefficient for the bound am-
5
10 15 LiNO, m o l %
_1
20
Figure 5. Composition dependence of the diffusion coefficients of the bound ammonia ( D b ) and unbound ammonia (D,)at 294 K.
monia, Db, is equal to that for the lithium ion, DL,+. Then we can deduce the values of the diffusion coefficient for the unbound ammonia, D,, using eq 2 and 3. The results are shown in Figure 5 as a function of composition. The values of D, in solutions are evidently smaller than the diffusion coefficient of the pure ammonia. This shows that the ammonia molecules not bounded directly to the lithium ions are also impeded in their translational motion by the presence of the lithium ions. The solvation effect of nitrate ions may be ignored in view of the results in aqueous solutions.8 We may then regard the observed diffusion coefficient of unbound ammonia D, as a sum of the contributions from the ammonia molecules in the second solvation shell (second zone) and the bulk ammonia. Recently, Hewish et aL9 gave a direct evidence for the existence of the second solvation shell from a quasi-elastic neutron scattering experiment for aqueous solutions of NiClz and MgC12. They also gave a value of 15 f 2 for the number of water molecules in the second ~ o n e . ~They J ~ showed that the diffusion coefficient of water molecules in the second zone (Ds,) approaches that of the central ion in the infinitely dilute ~ o l u t i o n .Thus, ~ if we take D,, = 1.o X 10-j cm2 s-l from the extrapolation of Db to the dilution limit in the present system and neglect its composition dependence, we can estimate the number of ammonia molecules in the second zone. We obtain a value of 20 from the value of the D, for the 3.58 mol % solution. The change of the slope of the curve for D, at about 5 mol % suggests a depletion of the bulk ammonia around this composition. In the concentration range between 5 and 20 mol % salt ( 5 < C C 20), the values of D, are nearly constant and still larger than those of Db or DL,+. In this region, all the unbound ammonia molecules are in the second zone which overlaps with each other. The presence of nitrate ions in this zone may destroy the stability of the zone and moderate the overlapping effect, resulting in nearly constant values of Du in this region. The structure-breaking effect of nitrate ions is known in aqueous solutions.s (8) Marcus, Y . Introduction to Liquid State Chemistry; Wiley: London, 1977. (9) Hewish, N. A,; Enderby, J. E.; Howells, W. S. Phys. Reu. Lett. 1982, 48, 756. (IO) Neilson, G. W.; Enderby, J. E. J . Phys. C 1978, 11, L625.
Diffusion in the Concentrated LiN03-NH3 System At the composition of 20 mol % ' lithium nitrate, we can regard the solution as consisting of solvated lithium ions, Li(NH3)4+,and nitrate ions as in a pure fused salt. It is known that the repulsive part of the intermolecular potentials plays an essential role in the transport properties of dense fluids. Therefore, the hard-sphere description is very helpful for the interpretation of such properties. van Loef" has applied a hard-sphere approach to the transport properties of fused salts, regarding them as single-component systems with an average hard-sphere diameter for cations and anions. Here we try to use such a hard-sphere description for the present 20 mol % solution. The essential parameters of the hard-sphere description are the hard-sphere diameter, u, and the particle number density, p . The former is usually best determined experimentally from the compressibility data, but they are not available for the present system. We have therefore determined the value of u from the present data of the diffusion coefficient. For this purpose, we employed the rough hard-sphere (RHS) model of Chandler,12 which has successfully been applied to polyatomic molecules such as CCl,. In this model, the observed self-diffusion coefficient D is given by D e DRHs = ADsHs (4) where DsHsis a self-diffusion coefficient of the smooth hard-sphere (SHS) systems. The constant A is less than unity and has been found to be 0.54 for CCl,. An expression for DsHs is given by Chandler12 from the computer simulation results by Alder et a l l 3 as a function of u and p Dsns =
(3/8)(kBT/mr)1/2a(3.7043 - 6 . 3 3 5 5 ~ 0+~2 . 6 7 1 8 ( ~ p ~( )5~) )
The number density of the present system has been determined in the previous work.5 With the same value of A as for CCl, we obtained a value of E = 4.81 X cm from the experimental result of D at 294 K. According to Chandler12, the viscosity coefficient, q, of CC14 has the form = 0.149(kBT/aD) (6) Using this relation, we obtain q = 6.6 CPwith the present values for u and D. This value is in good agreement with the experimental value of q = 6.4 cPs at 294 K. From the present value of u, the packing fraction is obtained as 0.53 by use of the relation y = ( r / 6 ) p u 3 . This value is con(11) van Loef, J. J. Z . Naturforsch. 1976, 31a, 967. (12) Chandler, D. J . Chem. Phys. 1975, 62, 1358. (13) Alder, B. J.; Gass, D. M.; Wainwright, T. E. J . Chem. Phys. 1970, 53, 3813.
The Journal of Physical Chemistry, Vol. 91, No. 4, 1987 987
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siderably larger than those found for monatomic liquids at their 0.45. However, it is interesting to note that melting point, y such a high packing fraction has also been found in the lithiumammonia system,2J4in which 20 mol % metal solution can be regarded as a single-component liquid metal, consisting of Li(NH3)4+ions and free electrons. We also note that in the analysis of van Loef" a larger packing fraction was obtained for molten alkali nitrates 0, 0.52) than for molten alkali halides 0,N 0.48) near the respective melting point. From the average hard-sphere diameter of the salt solution, we can deduce the diameter of the cm. This value is smaller Li(NH3),+ ion, which is u = 5.5 X cm,14 prethan the value in the metal solution, u = 6.3 X sumably due to the electrostriction effect. Although the hardsphere description may be very approximate for the present system, we think that the high packing is one of essential characteristics of the system. Such a high packing may be achieved by the knobby structure of the solvated cation, Li(NH3)4+,as well as that of the nitrate ion. For knobby species apparent packing fractions may increase considerably over the value expected for perfectly spherical species.2 In more concentrated solutions (C > 20), the anions may be directly coordinated to the cations. Such a situation was demonstrated for concentrated aqueous salt solutions from diffraction s t u d i e ~ . ' ~ JIn~ this concentration range, the diffusion coefficients and their activation energies for lithium ions and the ammonia molecules are nearly constant, as shown in Figures 3 and 4. At the highest concentration of the present study ( C = 28.5), the number of ammonia molecules per lithium ion is 2.5. Thus, the first solvation shell contains some anions among solvated ammonia molecules. The experimental results show that the diffusional motion of the solvated lithium ions is not much affected by such a decrease of ammonia molecules. It is noted that the viscosity and its activation energy still increase in this r e g i ~ n which ,~ indicates a simple Stokes-Einstein relation does not hold there. It will be very helpful to study the diffusion coefficient of nitrate ions in the highly concentrated region in order to investigate the correlation of the diffusive motion of the cations, anions, and solvent molecules. Registry No. NH3, 7664-41-7; LiN03, 7790-69-4; Li, 7439-93-2. (14) Thompson, J. C. Electrons in Liquid Ammonia; Clarendon: Oxford, U.K., 1976. (15) Ichikawa, K.; Kameda, Y.; Matsumoto, T.; Misawa, M. J . Phys. C 1984, 17, L725. (16) Copestate, A. P.; Neilson, C. W.; Enderby, J. E. J . Phys. C 1985, 18, 4211.
