2145
DIAPHRAGM-CELL METHOD FOR CONSTAKT MASSDIFFUSIONMEASUREMENTS
frequency of NMA is not appreciably affected by the presence of thiols. The effects of paramagnetic and diamagnetic metal ions indicate that the carbonyl oxygen, rather than the nitrogen, in S M A is the coordination site to these metal ions. This is the first experimental evidence of the binding site in NATA toward Cu(I1) and zinc ions. It is of interest to note that n.m.r. studies have shown’4that the added proton in dimethylformainide is also preferentially attached to the oxygen rather than the nitro-
gen, so that the binding site toward Cu(I1) and zinc ions in NMA is analogous to the binding site toward proton in dimethylformaniide. Aclcno*wledgment. The authors are indebted to Dr. Edwin D. Becker, of the Xational Institutes of Health, for reading the manuscript. (14) J. D. Roberts, “Nuclear Magnetic Resonance,” McGraw-Hill Book Co., New York, N. Y., 1959, pp. 70, 71.
Diaphragm-Cell Method for Constant Mass Diffusion Measurements. Interionic Diffusion and Friction Coefficients in Molten Silver Nitrate-Sodium Nitrate Mixtures1
by Richard W. Laity and Melvin P. Miller FriGk Chemical Laboratory, Princeton University, Princeton, New Jersey
(Received Januaru 23,1964)
A diffusivity method is described for systems in which constant volume cannot be niaintained. Results are presented for dilute solutions of AgX03 in NaS05 a t 310’: the massfixed diffusion coefficient of Ag+ is independent of concentration, the mean of eight determinations being (1.96 0.09) X cm.2sec.-l; the ordinary (volume-fixed) and “thermodynamic” diffusion coefficients increase with increasing concentration of Ag +; the silver-sodium friction coefficient is smaller than either of the cation-anion friction coefficients and apparently somewhat smaller than the sodium-sodium friction coefficient in pure n‘aN03 at the same temperature.
*
In attempting to account for the observed characteristics of equivalent conductivity (A) isotherms in binary fused salt mixtures, two additional transport parameters are of particular importance.2 One is a type of transference number ( P , or + as originally designated) which Aziz and Wetmore3 first used to describe results of Hittorf-type experiments on the system AgN03YaNO3. The other is the ordinary diffusion coefficient (D12)which characterizes the rate at which Ijke-charged ions interdiffuse. Although Aziz and Wetmore’s method for P apparently gave inaccurate results,
procedures subsequently developed have yielded satisfactory values of this quantity in a number of s y s t e n ~ s . ~ On the other hand, the only values of D12 we have found in the literature5 were obtained by a inethod of (1) (a) Supported in part by U. 8. Atomic Energy Commission Contract No. AT(30-1)-2644; (b) based on the Ph.D. Thesis of Melvin P. Miller, Princeton University, 1962.
R. W. Laity, A n n . N. Y . Acad. Sci., 79, 997 (1960). (3) P. M.Aziz and F. E. W.Wetmore, Can. J . Chem., 30, 779 (1952). (4) See chapkr by A. Klemm in “Molten Salt Chemistry,” M . Blander, Ed., Interscience Publishers, New York, N. Y., 1964. (2)
Volume 68, Number 8 August, I S 6 4
2 146
RICHARD W. LAITYAND MELVINP. MILLER
questionable validity.6 In the present work an application of the diaphragm-cell technique is described which has yielded iiew diffusion data for the system AgN03-NaN03 a t 310” in the range 2-8 mole % hgNOa. This is the only simple mixture of fused salts for which both thermodynamic activity coefficients and reliable values of A and P are currently available. Combined with experimental values of D12,such information makes it possible to calculate the “thermodynamic iiiutual diffusion coefficient’’ and the interionic friction coefficients.2
Experimental Method. A modification of the diaphragm-cell technique developed by Xorthrup and Anson7 was devised for this work. Due to slight but continuous gas evolution resulting from thermal decomposition of the melt, constant electrolyte volume could not be maintained in each conipartnient by sealing or stoppering. The simplest alternative was to keep both coinpartnients open to atmospheric pressure, providing a cell arrangeiiieiit that closely approximated a condition of constant mass. The drift in the relative concentrations of the mixtures on opposite sides of the diaphragm could be iiioiiitored continuously by following the e.m.f. between silver electrodes dipping into each compartment. Materauls. Baker and Adaiiison reagent grade silver nitrate and sodium nitrate were found to be adequate for use without further purification. Apparatus. The cell consisted of two concentric cylindrical Pyrex compartments, 25 and 50 m n . in diameter, respectively. The former, about 30 mi. in length, had a “iiiediuiii” porosity Pyrex fritted disk sealed into oiie end. Figure 1 shows the experimental arraiigenieiit, with both compartnients supported vertically in a larger vessel containing the constant temperature bath (eutectic of sodium and potassium nitrates) set into the cavity of an electric tube furnace. The magnetic stirring bars located in the bottom of each coiiipartiiieiit could both be rotated froin below by the powerful horseshoe magnet which was operated by a iiiotor underiieath the furnace. The bath itself mas stirred froni above as indicated in Fig. 1. Coiistant temperature (*0.5”) was maintained in the bath by a mercury-to-wire thernioregulator which controlled the input to a small auxiliary ininiersion heater (neither shown in Fig. l), while a constant voltage was fed to the furnace windings. The electrodes consisted of coils of 8-nim. silver wire attached to long platinuiii leads which were sealed through Pyrex glass tubing, The stoppers supporting the electrodes from above had slits to permit rapid pressure cquilibration with atmosphere. ,411 e.m.f. The Journal of Physical Chemistry
Figure 1. Constant-mass diaphragm cell arranged in furnace cavity: A, electrodes; B, thermocouple; C and I), stoppers with slits; E, stirrer; F, magnetic stirring bars; G, alnico magnet; H, ball bearing; J, firebrick; K, transite covers.
ineasureiiients were made with a Leeds and Northrup Type K potentiometer. Procedure. The cell was filled as follows. First, a mixture of AgN03 and NaN03 was melted in the outer compartment. Most of this (about 30 g.) was drawn into the inner compartment by applying suction. Additional salt (120 g.) of the approximate composition desired in the outer compartment (1-10 mole % richer in N a S 0 3 than that in the inner) was added until the outer liquid level was slightly above the inner. Stirring in both compartments was initiated and the cell was left standing a t least 12 hr. to establish hydrostatic eq uilibriuiii between compartments. (5) L. H. Harrison, Thesis, University of Munich, 1911, and A. Hoechberg, Thesis, University of Frankfort, 1915, both given in W. Jost, “Diffusion in Solids, Liquids and Gases,” Academic Press, New York, N. Y., 1952, p. 63 6. (6) M. P. IMiller, Ph.D. Thesis, Princeton University, 1962. (7) J. H. Northrup and M. L. Anson, J . Gen. Physiol., 12, 543 (1929).
DIAPHRAGM-CELL METHODFOR CONSTANT R l A s s DIFFCSIOK MEASUREMEISTS
A diffusion run consisted of taking e.m.f. readings a t frequent iiltervals over a period of 24-72 hr. and removing the contents of each compartment for analysis immediately after the last reading. The salt mixtures were then dissolved in water and aliquots were titrated for total Ag+ (Volhard method) and for total cations measured by H + displaced from Dowex 50 cation-exchange resin. Cell Constant. The effective length-to-area ratio of the diffusion path had to be determined in a separate experiment. Several methods were tried. Diffusion coefficients reported here are based on the cell constant obtained by measuring the resistance across the diaphragm of an aqueous 0.1 M KCl solution of known specific conductivity. The electrodes were mercury pools that effectively sealed the electrolyte inside the diaphragm by complete contact with the two faces. Although this determination was performed at 25”, calculation indicated that the cell constant at the 310” temperature of the diffusion experiments should differ by less than O.lyo. Therefore, no correction factor was applied. Measurements carried out before and after each run were generally in good agreement. Other approaches to determination of the cell constant included measurements of (1) diffusion in the same cell at 25” of an aqueous KC1 solution of kiiowa diffusion constant, ( 2 ) conductance across the diaphragm of molten K a y o 3 , (3) tracer-diffusion of pure niolten NaKOi using labeled sodium ions. Although the reproducibility of each of these methods was poorer than that of the aqueous conductance method, all results obtained showed substantial agreement. The best value was 0.735 cm.-’.
Analysis of Diffusion Data Boundary Conditions. The condition of hydrostatic equilibrium requires that there be virtually no pressure drop across the diaphragm. Instead of maintaining constant voluine, therefore, the levels of the two soluitions initially at diff ereit densities must approach one another as their compositions are equalized by diffusion. To see what restriction is imposed on the fluxes of AgNOi and YaSOa by this boundary condition, it is useful to divide the cell contents conceptually into three parts: V A ,the voluiiie of liquid in the inner compartment; V g , that in the outer compartment) above the level of the diaphragm; and Vc, the voluine below the diaphragm. If the inner compartment was positioiied so that the magnitude of Vc was comparable with V B , a significant increase in the mass of liquid below the diaphragm mould occur as the density of the outer compartment was increased by diffusion. An equal decrease would
2147
+
develop in the total mass of liquid in VA VB. Since it is the distribution of this constantly changing mass between VA and V B that is responsible for maintaining hydrostatic equilibrium across the diaphragm, it is apparent that the boundary conditions for such an arrangement would be rather complicated. However, if Vc is diminished until it becomes negligible compared to V B (by lowering the inner compartment), a very simple boundary condition is approached in m-hich the mass of liquid in each compartment remains constant. For the values of V A , VB, and lTcused in the present work the error introduced in the calculation of D by assuming this latter condition was shown6 to be less than 1%. Rate of Change of Concentration. To evaluate the diffusion coefficient (see next section) it is necessary to know the “initial” composition of each compartment, i e . , the composition at a known time interval before the end of the run, but after steady-state diffusion conditions have been established. This is obtained froin e.1n.f. readings as follows. The e.1n.f. measured between the silver electrodes is that of a concentration cell with transference. For AgS03-SaNOs mixtures it is related to composition by8
where XIA and X1B represent the mole fractions of AgN03, in the inner and outer compartments, respectively, and the y’s are the corresponding activity coefficients. (The absence of a term iiivolving a transference number results from the characteristic transport behavior ( P = X,)of this ~ y s t e m . ~ ) From the measured e.1n.f. and the analytical results a t the end of a diffusion run it is possible to evaluate the activitj coefficient term in eq. 1. The concentrations XI*’ and X I B ’ for any previously measured e.m.f., E’, can then be evaluated by a nicthod of successive approximations: first, assume that the activity coefficient term is constant for the small concentration changes occurring during diffusion
Now since the mass of salt in each coinpartineiit remains constant during diffusion, we can make use of the formula weights i1f1 and J f Z of the two salts to derive
XIA’-
X~B’
(%A (n1B
4- A n i ) [ n f * nf~ (Afi
- nf,)An~] (3) - An,)[,!!IznA- (1111 - L142)An,]
where An, is the number of moles of Ag?SOa that dif~
(8) R. W. Laity, J . AWL.Chem. Soe., 79, 1849 (1957).
Volume 68, iVumber 8
August, 1.964
2148
RICHARD W. LAITYAND
fused out of compartment A after its concentration was X ~ A ’n ;A = n l A n 2 A and n B = nlB n 2 B are the total nuinbers of moles in compartments A and B, respectively, a t the end of the run. Eniploying the approxiinate value of XIA’/XlB’ obtained from eq. 2 , eq. 3 can be solved for An1. This is used to calculate approximate values of X,A’and XIB’. The activity coefficient ratio associated with X,A’ and X1B is obtained from the known thermodynamic behavior of the system. In AgN03-NaS03 the terminal analyses of diffusion cells a t a number of different coi~ipositionswere consistent with a previous report thats
+
+
RT 1x1 E
=
A ( X ~ A’ XZB’)
YIB
where A is about 800 cal./mole. Froin the preceding calculation a new value of the activity coefficient term can be used in eq. 2. Repeating the calculation by putting the resulting value for X1A’)’XlB’ into eq. 3, better approximations are now obtained for An,, XI*’, and XI^'. The cycle is repeated (three or four times) until values of XI*’ and X I B f obtained froin successive calculations show no significant difference. Solution of the DifSusion Equation. When the cell has compartments of fixed volume, VA and V B ,the diffusion coefficient D can be calculated from experimental data using an integrated form of Fick’s second law
where AClo and AC1 are the initial and final differences in concentration (moles per unit volume) of difiusant between conipartnients A and B, x is the cell constant, and t is the time of the diffusion process. For the constant mass boundary condition the volunies of liquid in each compartment vary slightly during diffusion. As a result, the relation of D to experimental variables beconies much more complicated. For the conditions employed in the present work it was found that eq. 4 could be substituted for the more rigorous relation by using the mean values of VA and VB. These quantities are obtained froin the initial and final quantities of salt in each compartment and the known densities of the ~nixtures.~The error introduced by this simplification was less than 1%.
Results and Discussion Results of the eight runs carried out a t 310” are listed in Table I. (A few runs a t higher temperatures were attempted; these showed poorer reproducibility, apparently due to the increased rate of silver-catalyzed decomposition of the melt a t the electrodes.) The The Journal of Physical Chemistry
~ ~ E L P. ~ IMILLER N
column headed rfl gives the mean coniposition during each run, obtained by averaging the mean compositions of the two compartments a t the beginning and end of the run. At the highest value of R1 (8 mole % ’ AgK03) the initial concentration in the inner conipartment was 13 mole %. Concentrations higher than this were not attempted due to the difficulty of obtaining accurate e.1n.f. measurements without having too great a concentration span between compartments for the results to be meaningful (see eq. 1). The column headed DIM gives the mass-fixed diffusion coefficient of Ag+ obtained froin experimental data using eq. 4. DIzv is the volume-fixed or “ordinary” diffusion coefficient of either ion. The latter is calculated from D I Mand the known molar volumesg and masses of the salts by standard methods. lo Dlz’, the thermodynamic mutual diffusion coefficient,l 1 is obtained from the relation yi + dd-)1In11 Xi
Dlnf = D l a V / ( ~
where the subscript i refers to either salt. The last column of Table I gives values of the interionic friction CoefficientrIPcalculated from the relation12
~--
012’
RT
r12
+
1 X2h3
+
(5) xlr23
The cation-anion ffiction coefficients ?”13 and rZ3were taken to be equal in accord with the results of transference experiments, the values being based on the conductance ineasurenients of Wetmore, et al.g The principal source of error in the present work was in the deterniinatioi~of e.1n.f. Readings tended to fluctuate over several hundredths of a mv., but the accuracy was apparently worse than this, as indicated by comparison of each final e.ni.f. reading with that calculated from analysis of the cell contents. Discrepancies were as great as 0.70 inv. and averaged *0.27 inv. This was considerably poorer precision than had been obtained previously in this laboratory,s but the error was apparently a random function of electrode “stability” which could not be eliminated. It leads to an average uncertainty of =t3.5y0in the calculated values of DIM. From Table I it is seen that there is no systematic trend in the variation of DIM with concentration, fluctuations about the mean value of 1.97 X low5 (9) J. Byrne, H. Fleming, and F. E. W. Wetmore, Can. J . Chem., 30, 922 (1952). (10) R. P. Wendt and L. J. Gosting. J . Phys. Chem., 63, 1287 (1959) (11) R. W. Laity, ibid., 63, 80 (1959). (12) The general expression is correctly given first in footnote 7 of R. W. Laity, ibid., 67, 671 (1963).
DIAPHRAGM-CELL MIETHOD
FOR CONSTAXT AgASS
DIFFTJSION MEASUREMEK'TS
Table I: Results of Diffusion Measurements in AgNOs-NaNOa at 310" Run no. XI D1" x 106, Onv X lOS, 1 2 3 4
5 6
7 8
0 0239 ,0292 " 0319 ,0378 0442 0540 .0625 .0770
Averages ,0451
DlZ'
x
106,
2149
r12
x
10-0,
cm.2 sea.-l
cm.2 sec.-1
om.%sec.-l
joules sec. cm.-2 mole-1
1.98 1.95 1.89 1.74 2.10 1.98 1.90 2.17
2.03 2.01 1.95 1.80 2.201 2.09 2.02 2.33
2.10 2.09 2.04 1.90 2.34 2.25 2.20 2.59
0.41 0.42 0.56 0.90 -0.05 0.11 0.22 -0.44
1.96 i 0.09
2.05 =k 0.11
2.19 f 0.16
sec.-l averaging about =k4.5%. We conclude that
DIM is nearly independent of concentration over the range studied. The other two diffusion coefficients, DlZvand D12',show a tendency to increase with concentration that is confirmed by the correspondingly greater average deviations. This behavior is to be expected from the physical properties of the system (mass, molar volume, and thermodynamic behavior) if the value of DIMis constant. Since all three diffusion coefficients must extrapolate to the same value a t infinite dilution, the best figure for this limiting value is given by the average of DIM. The only diffusion results previously reported for this system are the 1911 figures of Harrison6 on mixtures of about the same composition. Although he worked a t temperatures 20-70" higher, extrapolation to the temperature of this work gives a Dlzvvalue about twice the average of these found here. This is not surprising, since the Harrison method is expected to suffer from convective mixing of the solutions.6 On the other hand, a chronopoteiitiometric study of Ag-i. in Nay03 carried out in this 1aboratoryl3 appears to confirm the validity of the present results. Extrapolation of values obtained a t 315, 340, and 360" gives Doh = (1.96 =t: 0.05) X lou5 cm.2 sec.-l for solutions a t 310" containing 0.04-0.4 mole yo AgN03. (At infinite dilution the chronopotentionietric diffusion coefficient Doh becomes identical with the other three. l 4 ) The large fluctuations in the figures listed for r12 illustrate the extreme sensitivity of this friction coefficient to the precision of the diffusion data from which it is calculated. From the mean of DIM,the infinite dilution value of r12is estimated to be (0.72 f 0.23) X lo8 joules sec. cm.-2 molecl. The increase in D12'with concentration implies a downward trend in r12' but it appears unlikely that the latter actually become8 negative in this range. NIoreover, a systematic uncertainty that results from the possible error in the values of r I 3used in eq. 5 makes negative values of r12
0.27 f 0.31
even more unlikely. Experimental uncertainty in the transference results on which these quantities are based is such that setting ~ 1 3equal to ~ 2 3gives a maximum value for the former. rI3 may be as much as 13% lower than r23 and it is only the latter quantity that is known accurately from conductance measurenienks in this region. It follows from eq. 5 that figures as much as 0.5 x lo8 joules sec. c i r r 2mole-' greater than those listed for rlz in Table I would still be consistent with experimental data. In view of such uncertainties it is difficult to draw reliable conclusions about r12 from the results of our measurements. However, one or two general conclusions appear to be warranted. It is apparent that in dilute solutions of AgIYOs in XaK03 the value of this cation-cation friction coefficient increases as infinite dilution is approached, but remains considerably sinaller than either of the cation-anion fraction coefficients. The sodium nitrate coefficient r 2 3 is 4.23 X lo8joules sec. cm.-2 mole-lat infinite dilution, while the silver nitrate coefficient ~ 1 may 3 lie anywhere between 3.68 and 4.23 x 108. Perhaps even more significant is the observation that it now appears probable that the silver-sodium friction coefficient a t infinite dilution in NaN03 is smaller than the sodium-sodium coefficient rZ2 in the pure salt. The latter is calculated from self-diffusion resultsl5 to be 1.25 X lo8at 310". It had been expectedz that r12 and r22might be about equal in view of the apparent equality of ~ 1 3and ~ 2 3 . The present results seem to warrant the speculation that r13 does not equal r23 after all, but instead lies nearer the low end of the range permitted by the transference results. The correspondingly higher value that is (13) R. W. Laity, K. Kawamura, and J. D. McIntyre, to be published. (14) R. W. Laity and J. D. McIntyre, theoretical results t o be published. (15) A. S. Dworkin, R. B. Escue, and E. R. Van Artsdalen, J . Phys. Chem., 64, 872 (1960).
Volume 68, Number 8 Au,gust I 1964
LOUISWATTS
2150
then calculated for r12 (between 1.0 and 1.2 X lo8 at infinite dilution) prompts us to replace our former anticipation of equal values for the two cation-cation coefficients with an alternative suggestion: at infinite dilution the ratios r12/r22and r13/r23may be found nearly the same when more accurate data are available for this system. The interionic friction coefficients in-
CLARK
volviiig Ag+ called for by this conjecture have the following values at 310": rI2 = 1.1 X lo8, r13 = 3.8 X lo8 joules see. cm. --2 mole-
Acknowledgment. The authors are indebted to Rfr. L. Chen, who performed some of the calculations on the IBRf-7090 computer.
The Kinetics of the Decarboxylation of Malonanilic Acid in Polar Solvents
by Louis Watts Clark Department of Chemistry, Western Carolina College, Cullowhee, North Carolina (Meceined January 30, 1964)
Kinetic data are reported for the decarboxylation of nialonaiiilic acid in 11 polar solvents, namely, 772-cresol, p-cresol, o-cresol, 1,4butanediol, 2,3-butanediol, 1,3-butanediol, acetanilide, aniline, N-ethylaniliiie, quinoline, and 8-methylquinoline. The activation parameters for the reaction are calculated and compared with those for malonic acid and other related acids. The results indicate that the mechanism of the decarboxylation of inalonaiiilic acid is not the same as that for nialonic acid, but that the malonanilic acid apparently functions as a nucleophilic agent.
Kinetic studies have been carried out on the decarboxylation of several P-keto acids, including acetoacetic acid and a , a-dimethylacetoacetic acid.' Results of these studies suggest that the mechanism probably involvcs a chelated six-membered ring, which loses C02 to form an enol, the enol then reverting to the iiiore stable tautomeric form
H
H
\/ C
R-C
/ \
I
I'
0
0 ,..
/
H
The J o u r o d of Phcjsical Chemistry
.1
0
11
R-C-CHs
Because of the iniportaiice of P-keto acids in enzymic reactions detailed information on the effect of solvents and other factors on the reactioii would be highly desirable. However, these compounds are generally so unstable that their preparation, separation, and purification are unfeasible. On the basis of rcsults obtained in studies on the decarboxylation of malonic acid in quinoline and other solvents Fraenkcl and eo-workers proposed a cyclic iiiechanisni for the reaction yielding the enol of acetic acid which then tautomerized.2
(1) (a) E. M. P. Widmark, Acta med. Scand., 53, 393 (1920); Chem. Abstr., 15, 2763 (1931); (b) K. J. Pedersen, J . Am. Chem. SOC.,51, 2098 (1929); (c) i b i d . , 60, 595 (1938). (2) G. Fraenkel, R. L. Eelford, and P. E. Yankwich, i b i d . , 76, 1 5 (1954).
