DIFFUSION IN DILUTE HYDROCHLORIC ACID-WATERSOLUTIONS
2333
Diffusion in Dilute Hydrochloric Acid-Water Solutions
by J. A. Harpst, E. Holt, and P. A. Lyons Department of Chemistry, Yale University, New Haven, Connecticut
(Received January 88, 1565)
Diffusion coefficients for dilute aqueous HC1 solutions have been measured a t 25” using a conductometric technique. The applicability of the Onsager-Fuoss transport theory has been confirmed for the case of a negative electrophoretic correction. Limitations of the method used are reviewed. The diffusion data can be used to predict precisely the activity coefficient of HCl in dilute aqueous solutions.
Introduction There have been extensive studies of diffusion in dilute electrolyte solutions, in particular 1-1 electrolyte solutions. For this latter class, there is abundant evidence that diffusive flow is correctly predicted by the theory of Onsager and Fuoss. This work is reviewed in standard treatises.’ In very dilute solutions the definitive work was performed by Harned and associates using a conductometric technique. The Lucite cells used in these studies were not suitable for use with acids. It has been shown by one of the authors that these cells appear to adsorb protons. However, it was possible to devise a satisfactory all-glass cell for weak electrolyte studies.2 Modifications of this design were used for the present work on strong acids. Prior to this study there had been no accurate diffusion data reported for strong acids which were of value for a comparison with theory. The most reliable measurements have used the stirred diaphragm cell procedure. The nature of these experiments precludes the possibility of obtaining data in very dilute solutions. For example, the excellent diaphragm cell data of Stokes for HCl-HZO extend only to 0.05 M . 3 A major point of interest in the comparison of diffusion results with theory is the validity of the “electrophoretic effect” which, for the 1-1 salts which have been studied, is quite small and positive. Since many possible experimental errors in the conductometric procedure (due to such random factors as vibration, poor temperature control, etc.) tend to give high values for the diffusion coefficient, it might be argued that the agreement of experiment with theory was fortuitous. Because of the great difference in the ionic mobilities of H + and C1-, it develops that the over-all electro-
phoretic effect is somewhat larger than for 1-1 salts and, more importantly, it is negative. This means that diffusion data for dilute aqueous HCl solutions should provide a cleaner, single test for the theory than any system yet studied. In addition, this work was an obvious and necessary prelude to studies on multicomponent systems, such as ;\‘ICl-HC1-H20 and HClmixed solvent, which were being considered in this laboratory.
Experimental Materials. Baker’s Analyzed reagent grade HCl was diluted with distilled water and used without further purification. The conductance of the water used was monitored to ensure that solvent corrections a t all times were negligible. Baker’s Analyzed reagent grade KC1, used in the calibration of auxiliary cells, was recrystallized twice from water, dried in a vacuum oven a t 145”, and stored in a desiccator. Equipment and Procedure. The cells used for this work consisted of three thin-walled pieces of glass tubing bonded to rectangular plate-glass end plates. One end plate was provided with three holes into which the tubes just fit. Slits to accommodate 1 X 4 mm. platinum electrodes were cut into opposite sides of the tubing in pairs a t precisely one-sixth of the distance from the top and bottom of the cylindrical compartment in which the restricted diffusion would take place. (1) See, for example, H . S. Harned and B. B. Owen, “The Physical Chemistry of Electxolytic Solutions,” 3rd Ed., Reinhold Publishing Corp., New York, N. Y., 1958, pp. 245-252; R. A . Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworth and Co. Ltd., London, 1955, pp. 293-308. (2) E . Holt, Ph.D. Thesis, Yale University, 1961. . (3) R. H. Stokes, J . Am. Chem. SOC.,72, 2243 (1950).
Volume 69, Number 7 J u l y 1965
2334
The apparatus was assembled with Bondmaster No. M-648-T air-drying epoxy cement, using No. CH-23 curing agent. After several days of cure, the sliding surface of the bored end plate was ground flat (and to the proper final height) by the use of a diamond wheel in a milling machine head and then lapped. Cell 1 had tubes which provided a diffusion compartment 7 2 mm. high, 13 mm. in inside diameter, and 1 mm. in wall thickness. This cell was fragile and after several months hairline cracks appeared near the electrode inserts. Neither the use of soft glass tubing to match the coefficient of thermal expansion of Pt nor considerable care to keep the cell always a t 25 f 3” prevented this from occurring. In cell 2 the corresponding dimensions were 7 2 , 13, and 2 mm. The heavier wall tubing used in the latter cell delayed the onset of disintegration for just over 6 months. This type of unit, though simple, is not recommended as a permanent laboratory accessory and, in fact, has since been supplanted here by an inevitably more elaborate, rugged, all-glass device. With only minor differences, the procedure followed ~ is the same as outlined by Harned and N ~ t t a l l . Their paper should be consulted to get a detailed account of the introduction of samples, measurement of conductances a t the upper and lower electrode pairs, and the computation of the diffusion coefficient. Successful results in this work required very light platinizatiori (-5 ma. current for about 1 min. was satisfactory). After the measurements were complete -about 5 days-the cell was removed from the bath, shaken, invcrted for a few hours, and returned to the bath for overnight equilibration. The cell constants of the electrode pairs were then determined. Following this, the concentrations in the cells were determined by removing measured amounts of the cell contents, diluting appropriately, and measuring the resistance of the latter solutions in auxiliary conductance cells which had bcen ~ a l i b r a t e d . ~ To verify the conductometric results a t higher concentrations, the Gouy interferometric procedure was used. The general procedure for this method has been well described,6 and slight modifications employed in this laboratory have been noted before.’ A specially designed Tiselius cell with a 5O-mm. channel length along the optic axis was employed since the refractive increment across the boundary was so small.
Results and Discussion Calculations of differential diffusion coefficients were made from the equation u A In (KB - KT - AK) D = -(1) 8 2 At The Journal of Physical Chemistry
J. A. HARPST,E. HOLT,AND P. A. LYONS
where a is the length of the closed cell compartment, K B and KT are the conductances a t the bottom and top electrode pairs a t time t , and AK = Kgm- KT- corrects for the difference between the cell constants. Because of the possibility of a slight drift in cell constants, AK is usually treated as a parameter which may be precisely evaluated by an iterative procedure.s The calculated results are listed in Table I together with quantities pertinent to the comparison with theory. Despite the fact that a precision of 0.1% has been obtained by this method for KC1 solutions, in the present work on HCI the results appear to have an uncertainty of about 0.2-0.3%. The criterion for acceptability of the reported conductometric results was that values of D, computed in a given experiment from various pairings of the K and At values, should have an average deviation from the mean of =t0.2y0 or less.
Table I D’ X
C,
mole/l. 0.0 0.0063 0.0113 0.0144 0.0154 0.0188 0.0199 0.0216 0.0247 0.0286 0.034h 0.05i
pa
1.0 0.9643 0.9563 0.9529 0,9520 0.9492 0.9485 0.9473 0.9456 0.9438 0.8419
105b
3.337 3.218 3.191 3.180 3.176 3.167 3.165 3.161 3.155 3.149 3.143
A’C
A I ! ~
-0.0236 0.0068 -0,0306
0.0098
-0.0338 -0.0349 -0,0379 -0.0388 -0.0402 -0.0426 -0 0451 -0 0483
0.0113 0.0117 0.0132 0.0136 0 0143 0.0154 0.0166 0.0181
DOFX 10s*
D X loaf
A X
3.337 3.202 3.171 3.158 3.154 3.144 3.141 3 136 3.130 3.122 3.114 3 10
3.217 3.173 3.160 3.147 3.133 3.149 3.136 3.129 3.122 3.11 3.07
-0.001 -0.018 -0.020 -0.029 -0.034 -0.016 -0.025 -0.026 -0 027 -0.033
1050
‘ q = (l+c(blny,/dc)). *D‘=DO(l+c(blnyJbc)); A’ = 2000RT(A~l!f’/~). A ” = 2000 x DO = 3.337 X RT(A.M”/c). e DOF is the value predicted by eq. 2. D is the experimental value. A = D - D’. Gouy result. ‘ Stirred diaphragm result of Stokes.3
’
With this criterion it was not possible to extend the range of measurement in either direction beyond the concentration range listed. Thus this method would appear to be unsatisfactory for studying diffusion in multicomponent systems of HX-lIX-H20 a t high concentrations a t constant total molality. JIany of (4) H. S. Harned and R. L. Nuttall, J . A m . Chem. SOC.,69, 736 (1947). (5) J. E. Lind, Jr.. J. J. Zwolenik, and R. >I. Fuoss, ibid., 81, 1557 (1959). (6) L. G . Longsworth, ibid.. 69, 2510 (1947); L. J. Gosting, E. Hanson, G . Kegeles, and M.s. Morris, Rev. Sci. Instr., 20, 209 (1949).
(7) P. A. Lyons and C. L. Sandquist. J . A m . Chem. Soc., 75, 3896 (1953). (8) H . S. Harned and D. M.French, Ann. N. Y . Acad. Sci., 46, 267 (1945).
DIFFUSIONIN DILUTEHYDROCHLORIC ACID-WATERSOLUTIONS
3.30
2335
In eq. 3, the first- and second-order electrophoretic terms are given by
D.
2
--AH’ =
3.20
(Izz/XIO - IzI~XZO)’ 3.132 X 10-19
2(A0)
9
‘1 212~1
rlo(€T>”z (1
C ~ F
+ Ka)
and 3.10
J
I 0.01
0.02
0.03
0.04
c , mole/l.
Figure 1. Comparison of diffusion coefficients for HCl-H,O with Onsager-Fuoss theory: , complete OnsagerFuoss theory; -. . .-, theory without electrophoretic terms; I, Gouy method; 0,cell 1; 0, cell 2.
the difficulties encountered in this diffusion study are much the same as those which Stokes has described in his elegant study of conductance in HC1 solution^.^ Fortunately, the conductometric data appear to be internally self-consistent. A short theoretical extrapolation indicates agreement with the optical value. It is interesting that a continued extrapolation agrees with Stokes’ lowest value within the accuracy of his experiment. I n Figure 1, the data are compared with the Onsager-Fuoss theory; the agreement is very good. For convenience, the values of electrophoretic contribution have been tabulated in Table I. They are obtained by subtracting from the measured value of D the quanc(d In y,/dc)) as suggested by tity D’ = Do(l Guggenheim.’o This quantity A (column 8, Table I) may be compared with the sum of columns 4 and 5 (after multiplication tiy q ) . The Onsager-Fuoss equation for strong electrolytes is often written
+
C
where
+
r#~(Ka)= [eZKK“Ei(2Ka)/(l K u ) ~has ] been tabulated conveniently in Table 5-3-2 of the Harned and Owen treatise. Since the ionic mobilities of H + and C1- differ so much, the negative electrophoretic term, AdV’, is larger than A B ” ; a t 0.01 M it is three timesasgreat. Thus, in contrast to the case for 1-1 salts, for this system the theory predicts a negative electrophoretic contribution, a direction opposite to that which might occur due to errors of the type mentioned earlier. As has been pointed out by Harriedll and associates, precise activity coefficients may be evaluated from electrolyte diffusion data in dilute solutions. These HC1 data can be treated in the same way, giving a t c = 0.01, as an example, yk = 0.903 as compared with 0.9048 obtained from e.m.f. studies. The fit is of course better a t lower concentrations. The agreement of theory and experiment for this system, coupled with substantial confirmation for salt systems in which the pertinent effect has a different sign, suggests that either the complete theory is valid or we are dealing with interesting and repeated coincidence. Acknowledgment. This work was supported in part by an Atomic Energy Commission Grant, AT(30-1)1375. For helpful discussions we are grateful to H. S. Harned. (9) R. H . Stokes, J . Phys. Chem.. 6 5 , 1242 (1961). (10) E. D. Guggenheim, Trans. Faraday Soc., 5 0 , 1048 (1954). (11) H. S. Harned, Proc. Natl. Acad. Sci. U . S . , 40, 551 (1954).
Volume 69, r u m b e r 7
July 1964
