J . Phys. Chem. 1986, 90, 2441-2445
2441
Diffusion of Protonic Species in Aqueous NaOH as a Function of Concentration, Temperature, and Pressure, and Diffusion of Water in Aqueous NaF, NaBr, NaCIO,, NaBF,, NaNO,, NaNO,, and NaBrO, at 298 K and 0.1 MPa Allan J. Easteal* and Lawrence A. Woolf Research School of Physical Sciences, The Australian National University, Canberra, A.C. T., Australia (Received: October 31, 1985; In Final Form: January 8, 1986)
The diffusion coefficient of protonic species in 2 and 19.5 mol dm-3 aqueous sodium hydroxide is reported for temperatures in the range 267 to 313 K and pressures up to 294 MPa. The anomalous pressure dependence at constant temperature (below about 313 K) of the self-diffusion coefficient of water is eliminated by the addition of 2 mol dm-3 sodium hydroxide. The diffusion coefficient of HTO or H 2 0 has been determined for 2 mol dm-3 solutions of sodium bromide, perchlorate, fluoroborate, nitrate, nitrite, and bromate, and for 0.15-0.90 mol dm-3 sodium fluoride, at 298 K and 0.1 MPa. For the hydroxide and halide (except for sodium fluoride) solutionsthe tracer diffusion coefficient of water (D(HT0)) varies linearly with the reciprocal of the cube of the crystal radius of the anion. Both D(HT0) and the relative viscosities ( q / q o ) of these solutions vary in a simple fashion with the limiting partial molal volumes of the anions (p(X-)), and the values of D(HT0) and q / q o for sodium fluoride solution are consistent with those for hydroxide and the other halides. Significant departures from the graphs of D(HT0) and q / q o vs. p ( X - ) are shown by solutions of sodium salts with nonspherically symmetric anions.
Introduction Intra- (tracer) diffusion coefficients of solute species in aqueous electrolyte solutions are available for numerous electrolytes over a range of concentrations and temperatures, but for the most part these measurements have been restricted to normal atmospheric pressure. In many cases the solvent intradiffusion coefficient has also been determined for these solutions as either a tracer (e.g., H D O or HTO) or a self-diffusion coefficient (e.g., by the N M R spin-echo technique). The electrolytes which have received most attention have been halides (particularly chtorides) of alkali, alkaline earth, and some transition metals. Though there is some published work on various other salts, diffusion data for hydroxides are sparse. The principal reason for the lack of data for hydroxides undoubtedly stems from the experimental difficulties which are associated with diffusion coefficient measurements on corrosive solutions, since the conventional glass diaphragm cell method is clearly not applicable to alkali metal hydroxide solutions of high concentration. The experimental difficulties are severe also for measurements of diffusion coefficients in such solutions under pressure, because the thin-walled metal bellows which have been utilized for containment of and transmissidn of pressure to relatively inert solutions in high-pressure diaphragm cells may be subject to chemical attack. These problems have been overcome by the recent development of a cell for N M R spin-echo measurements on corrosive solutions. The design of the cell has been discussed in detail previously.' In the present context the important point is that the sample solution is in contact only with PTFE (Teflon). The cell has the additional feature that it can be used for high-pressure measurements. One of the objectives of the present investigation was to test the PTFE sample cell with a highly reactive sample, and to that end we have determined the diffusion coefficient of water in an almost saturated (19.5 mol dm-3) aqueous solution of sodium hydroxide. An additional aim was to establish whether the anomalous pressure dependence of the self-diffusion coefficient of water at temperatures below about 308 K is eliminated by addition of a moderate concentration of electrolyte. For that purpose we have measured D ( H 2 0 ) for 2 mol dm-3 sodium hydroxide over a wide temperature and pressure range. A comparison of D(H20) for 2 mol dm-3 NaOH at 298 K and 0.1 MPa with D(H,O) data for alkali metal halide solutions under the same conditions has been extended to sodium bromide, per-
* On leave from the Department of Chemistry, University of Auckland, Auckland. New Zealand. 0022-3654/86/2090-2441$01.50/0
chlorate, fluoroborate, nitrate, nitrite, and bromate by measurements of the water diffusion coefficient for these solutions. The water diffusion coefficients in 2 mol dm-3 NaOH, NaCl, NaBr, and NaI solutions suggested that, in relation to its effect on D(H,O), OH- acts as if it were a small halide ion. For this reason, the diffusion coefficient of water in aqueous sodium fluoride has been determined also, although the highest concentration of N a F which can be attained at 298 K is considerably smaller than 2 mol dm-). Experimental Section A saturated solution of NaOH was made up at 293 f 1 K by adding an excess of N a O H to water in a PTFE vessel. The supernatant liquid was filtered rapidly through a stainless steel sinter and analyzed by quantitative dilution and titration against standardized hydrochloric acid; 2 mol dmW3NaOH was made up by dilution of the 19.5 mol dm-3 solution. The N M R spin-echo measurements were made using the technique and procedures which have been reported previously,2 except that the PTFE sample cell was used instead of a metal bellows cell. The water diffusion coefficients were determined with an accuracy of the order f1.5-2%. Temperatures were maintained constant to within f0.02 K and were measured with an accuracy of f0.05 K by using a calibrated platinum resistance element. Pressures were measured to f0.4 MPa with a calibrated Heise-Bourdon tube gauge. The water diffusion coefficient at 298 K and 0.1 MPa, in electrolyte solutions other than NaOH, was determined where it was convenient to do so as D ( H T 0 ) by using the glass diaphragm cell technique and associated liquid scintillation counting procedure^.^ Those data should be accurate to within f l % . In some cases (sodium fluoride, fluoroborate, nitrite, and bromate) D ( H 2 0 ) was measured by the N M R spin-echo technique with a probable accuracy of f 1.5-2%. The solubility of sodium fluoride in water is such that a saturated solution at 298 K has a concentration less than 1 mol dm-3. Consequently, the water diffusion coefficient was measured for six solutions with N a F concentrations from 0.15 to 0.90 mol dm-3 in 0.15 mol dm-3 increments to establish the concentration dependence of D(H20) and by extrapolation the value of D ( H 2 0 ) ( I ) Easteal, A. J.; Woolf, L. A,; Wilson, F. L. J . Magn. Reson. 1983,54, 158. (2) Harris, K. R.; Mills, R.; Back, P. .I.Webster, ; D. S. J. Mogn. Reson. 1978,29, 473. (3) Mills, R.; Woolf, L. A. The Diaphragm Cell; The Australian National University Press: Canberra, 1968.
0 1986 American Chemical Society
2442 The Journal of Physical Chemistry, Vol. 90, No. I I, 1986
Easteal and Woolf
TABLE I: “Proton” Diffusion Coefficient in 2 mol dm-3 Aqueous Sodium Hydroxide
109D(H) /
T/K 313.15
298.1,
1090(~)/ m2s-I
p/MPa
m2d
T/K
D/MPa
0.1 50.2 99.2 150.5 200.3 250.2 294.0
2.30 2.21 2.22 2.16 2.12 2.07 2.00
288.15
0.1 49.4 99.5 152.3 201.0 250.5 290.5
1.25 1.24 1.23 1.21 1.18 1.14 1.12
0.1 50.6 99.9 147.9 199.5 250.3 293.0
1.65 1.63 1.60 1.57 1.52 1.49 1.46
278.15
0.1 25.8 49.3 99.7 150.2 183.3 220.4
0.92 0.93 0.92 0.90 0.90 0.88 0.86
267.88
0.1 52.3 99.1
0.65 0.65 0.65
1.8
:I-, 0. 6
TABLE 11: “Proton” Diffusion Coefficient in 19.5 mol dm-3 Aqueous Sodium Hydroxide
T/K
p/MPa
313.15
0.1 26.3 51.0 75.0 98.8 126.0 151.2 193.0
305.1,
0.1 25.7 50.1 75.6 98.5 120.4 150.7 193.3
1090(~)/ mzs-l T/K 0.147 298.15 0.138 0.134 0.132 0.127 0.121 0.119 0.110
p/MPa 0.1 25.0 47.8 77.4 101.1 123.8 149.8
t
1090(~)/ m2s& 0.0628 0.0614 0.0589 0.0562 0.0547 0.0520 0.0504
, ,
)----c--.
50
0
150
100
200
250
1 300
p/MPa
Figure 1. Pressure and temperaturedependence of the “proton”diffusion coefficient in 2 mol dm-’ NaOH: m, 268.08 K; 0 , 278.15 K; A, 288.15 K; 0,298.15 K; 0 , 313.15 K.
0.0993 0.0967 0.0918 0.088 1 0.0847 0.0814 0.0790 0.0749
for a hypothetical 2 mol dm-3 solution. The viscosities of 2 mol dm“ fluoroborate, nitrate, nitrite, and bromate solutions were determined by using a flared capillary viscometer, with an estimated accuracy of f l % .
Results and Discussion The measured diffusion coefficients for the sodium hydroxide solutions are listed in Tables I and 11. For both solutions, the temperature and pressure dependence of D(H) can be expressed by In D(H) =
0.041, 0
,
, 40
,
, 80
,
, 120
,
, 160
,
,
,
200
p/MPa
Figure 2. Pressure and temperature dependence of the “proton”diffusion coefficient in 19.5 mol dm-’ NaOH: 0,298.15 K; 0, 303.15 K; 0 , 313.15 K.
The coefficients of eq 1 are listed in Table 111. Since rapid proton exchange between OH- and H 2 0 occurs in aqueous hydroxide solutions, the measured diffusion coefficient should be a weighted mean of the diffusion coefficients of OHand H 2 0 and can be expressed by
limiting (C(Na0H) = 0) values at 0.1 MPa. For OH- the limiting m2 s-’, was obtained value of its diffusion coefficient, 5.2* X from the limiting conductance4 and for water the value adopted, 2.29, X m2 s-I, was that given by Mills;s these provide D(OH-)/D(H20) = 2.297. Use of this equality in eq 2 provides
D(H) = [1/(2c(H,O) + c(OH-))] X (2c(H,O)D(H,O)
D(H2O) = 0.97,D(H)
[C(H,O) = 5 5 , C(OH-) = 21
D(HZ0) = 0.80,D(H)
[C(H,O) = 42.3, C(0H-) = 19.51
+ c(OH-)D(OH-))
(2)
where c denotes molar concentration. An estimate can be made of the relative magnitudes of D(H20) and D(0H-) and thereby the contributions of the hydroxyl ion and water to D(H). Because D(0H-) and D(H,O) cannot be measured separately at finite concentrations of NaOH it is necessary to assume that the ratio D(H,O)/D(OH-) does not depend on the concentration or pressure and can be obtained from the
(3) (4)
This estimate shows that the contribution of OH- to the overall (4) Robinson, R. A,; Stokes, R. H. EIecfrolyfeSolufions; Butterworths: London, 1968; p 465. (5) Mills, R. J . Phys. Chem. 1973,77, 685.
The Journal of Physical Chemistry, Vol. 90, No. 11, 1986 2443
Diffusion of Protonic Species in Aqueous N a O H
TABLE 111: Coefficients of Eq 1” for 2 and 19.5 mol dm-3 Aqueous Sodium Hydroxide 2 mol dm-’ NaOH A = -15.4164975 E , = 16.0993047 103CI= 8.79722537 1OSC2 = -4.40021594 E2 = -4.68930574 E3 = 0.38879567 109C3= 17.3066943
103Ell= -6.12762613 105E,2= 2.75908043 103Ezl= 1,02296712 106E22 = -4.37462464
a = 1.03’
E , = 269.408073 E2 = -75.4326931 Bs = 6.81945926
A = -315.087935
19.5 mol dm-I NaOH C1 = 0.28544323 103C2= -1.04001727 109C3= 6.0027315
= -0.17476152 lO4EI2= 6.34757285 102Ezl= 2.66014244 105E22= -9.69188264
Ell
a = 0.29’
“For D(H) expressed in lo9 m2 s-’, T in K, and p in MPa. bMean deviation (%) of experimental points from values calculated from eq 3. 55L’
WL
0
50
100
150
200
250
p/MPa
48
-
35
c
’
’
’
I
’
’
”
‘ ‘ 1
-I
0
48
88
128
160
280
p/MPa
Figure 3. Pressure and temperature dependence of E, (eq 5) for 2 mol dm” NaOH. Symbols as in Figure 1.
Figure 4. Pressure and temperature dependence of E, for 19.5 mol dm-’ NaOH. Symbols as in Figure 2.
measured proton diffusion coefficient D(H) increases from 2% in 2 M sodium hydroxide to 20% in the 19.5 M solution. The pressure dependence of D(H) at constant temperature is shown in Figures 1 and 2. It is apparent that for the less-concentrated solution (Figure 1) the anomalous variation of the tracer or self-diffusion coefficient of water with pressure6-* is absent, although the curvature of the graphs is opposite to that which is typical of (nonaqueous) liquids. As the temperature decreases D( H ) becomes less pressure dependent and the behavior becomes more like that of pure water. For the more-concentrated solution D(H) decreases almost linearly with pressure and the slope decreases to a lesser extent with decreasing temperature than for the 2 mol dm-3 solution. The value of D(H,O) at 298 K and 0.1M Pa, estimated from eq 4, is about 2.5% of the self-diffusioncoefficient of pure water under these conditions. However, that value of D(H,O) is roughly twice as large as would be expected on the basis of the viscosity of the solution (estimated from the concentration dependence of the viscosity at 293 K9) compared with the viscosity of water. The implication may be that some kind of cooperative mechanism is involved in diffusive motion of water in the solution but that
process does not contribute as significantly to viscous flow. The temperature and pressure dependence of the coefficient defined by E , = -R[a In D / 8 ( l / T ) l V (5)
(6) Angell, C.A.; Finch, E. D.; Woolf, L. A,; Back, P. J . Chem. Phys. 1976, 65, 3063.
(7) Woolf, L. A. J. Chem. SOC.,Faraday Trans. 1 1975, 71, 784. (8) Harris, K . R.; Woolf, L. A. J. Chem. SOC.,Faraday Trans. 1 1980, 76, 377. (9) Handbook of Chemistry and Physics, Weast, R.C.,Ed.; CRC Press: Boca Raton, 1982; 63rd ed.
is shown in Figures 3 and 4. For the 2 mol dm-3 solution, the pressure dependence of E, is slightly temperature dependent, the temperature dependence of E , is slightly pressure dependent, and the values of E , are very similar, at corresponding values of T and p , to those which have been reported’ for diffusion of H T O in ordinary water. By contrast, for the 19.5 mol dm-3 solution E , varies in a complex manner with pressure and temperature. Moreover, although E , increases with decreasing temperature for both solutions, for a temperature change from 3 13 to 298 K at 0.1 MPa E, increases by about 70% for the 19.5 mol dm-3 solution compared with 14% for the 2 mol dm-3 solution. The “activation volume” defined by AVD = -RT(a In D / ~ P ) ~ (6) and shown in Figures 5 and 6 is fairly close to zero for the 2 mol dmw3NaOH solution (as it is for diffusion of HTO in water) and increases in a fairly simple manner with both pressure and temperature. For the 19.5 mol dm-3 solution the values of AVDare much larger; AV, decreases with increasing pressure only at low pressure and varies in a complex manner with temperature at constant pressure. The diffusion behavior of water in 19.5 mol dm-3 NaOH is, overall, unlike that of water in either pure water or 2 mol dm-3 NaOH. The reason for the diffusion behavior is that in the 19.5
2444 The Journal of Physical Chemistry, Vol. 90, No. 11, 1986
Easteal and Woolf TABLE I V Water Diffusion Coefficients and Relative Viscosities for 2 mol dm-3 Sodium Salt Solutions at 298.15 K and 0.1 MPa
anion F-
1.
109D(HTO)/m2SKI (1.62)' 1.95 2.049
c1Br1-
c
0.
Id
E
m
E
1.56 2.055 2.05 2.010 1.98
Br0,-
1.85
>
Q 0.
1.1538 1.090
2.155
OHC104B F4NO,NO,-
0 '
4/V0
(1.44)b 1.2186
(1.55)' 1.150 1.171
1.179 1.204 1.346
By linear extrapolation of D(H20)data at lower concentrations
and conversion to D(HT0) using eq 9. For 0.15, 0.30, 0.45, 0.60, 0.75, and 0.90 mol dm-3 NaF, the measured values of D(H20)were 2.26, mz s-l, respectively. bBy linear 2.23, 2.17, 2.1 1, 2.07, and 2.02 X extrapolation of data at lower concentrations from ref 8. 'By interpolation of data at 293 K from ref 7.
-0.
p/MPa
Figure 5. Pressure and temperature dependence of AVD (eq 6) for 2 mol dm-3 NaOH. Symbols as in Figure I .
{ 2.11 C 7
f*
P A 0
eo
3.
?.. 0
L
l
40
l
l
80
l
I
100
1
1
I
120
I
140
l
,
140
.
.
,
180
,
250
220
riM*l/pm
Figure 7. The tracer diffusion coefficient of water in 2 mol dm-3 alkali metal salt and nonelectrolyte solutions at 298 K and 0.1 MPa: m, NaOH; 0, NaBrO,; 0, NaCI; A, NaNO,; A, NaBr; V, NaBF,; $, NaI; a, LiC1; b, KCI; c, RbCI; D, CsCl; e, CH30H;f, CH,CN; g, acetone. the dashed line represents the diffusion coefficient of HTO in pure water. Inset: Correlation of D(HT0) and l / r ( X - ) 3 : B, NaOH; 0, NaC1; A, NaBr;
3.
3.
2. 9
\qI
t 0
40
80
120
160
280
p/M?a
Figure 6. Pressure and temperature dependence of AVD for 19.5 mol dm-3 NaOH. Symbols as in Figure 2.
mol dm-3 solution the H,O/NaOH mole ratio is only about 2.2 so that there is no "bulk" water present. The solution is more akin to a fused salt hydrate where the constituent particles are anions and hydrated cations than to a conventional solution in which the solvent is present in large excess. The present water diffusion coefficient data for 2 mol dm-3 sodium salt solutions at 298 K and 0.1 MPa are given in Table IV, together with relative viscosities for the solutions. The table includes, for purposes of comparison diffusion and viscosity data from the literature for NaCl,*,'O NaI,'1.12and NaBr.'O The values of D(H20) for the sodium fluoride solutions up to the maximum (IO) Stokes, R. H.; Mills, R. In The International Encyclopedia of Physical Chemistry und Chemical Physics, Guggenheim, E. A,, Mayer, J. E., Tompkins, F. C., Eds.; Pergamon: Oxford, 1965. ( 1 1) Hertz, H. G.; Mills, R. J . Chim. Phys. 1976, 73, 499. (12) Dunlop, P. J.; Stokes, R. H. J . Am. Chem. Sot. 1951, 73, 5456.
$, NaI;
a, NaCIO,;
0 , NaN03.
concentration of 0.9 mol dm-3 can be represented with a rms by the equation deviation of 8.6 X 109D(H20)/m2s-' = 2.309 - 0.319[c(NaF)/mol dm-3]
(7)
and the relative viscosity datai3for N a F solutions with c I0.96 mol dm-3 are well represented by the relationship v/qo
= 0.9999
+ 0.2l8O[c(NaF)/mol
dm-3]
(8)
A comparison of the diffusion coefficient of water in 2 mol dm-3 N a O H at 298 K and 0.1 MPa with D for water in 2 mol dm-3 solutions of other alkali metal salts is shown in Figure 7, in which the value for NaOH has been estimated from the measured diffusion coefficient by using eq 3. Also, since some of the water diffusion coefficient data in the literature refer to H T O rather than H 2 0 , D(H,O) values were converted to D ( H T 0 ) by using the factor5
D(H20) = 1.03D(HTO)
(9)
(assuming that the ratio D(HZo)/D(HTo) has the Same in the electrolyte solutions as in pure water). Values of D(HT0) ( 1 3 ) Nightingale, E. R.; Benck, R. F. J . Phys. Chem. 1959. 63, 1777.
Diffusion of Protonic Species in Aqueous N a O H for 2 mol dm-3 solutions of acetonitrile,14methan01,'~and acetone16 have also been plotted in Figure 7 against equivalent hard-sphere radii for these solutes1' to provide a comparison of the effects of Coulombic and non-Coulombic forces on the water diffusion coefficient. (The value of D ( H T 0 ) in 2 mol dm-3 aqueous methanol was obtained from the experimental value for H2I80 in that solution.) Figure 7 provides a diffusion coefficient-based classification of solutes as either structure-making (D(HT0) < D,(HTO), where D,(HTO) is the tracer diffusion coefficient of HTO in water in the absence of solute) or structure-breaking (D(HT0) > D,(HTO)). This aspect has been discussed at length elsewhere."
