ROGER G. BATESAND DOKALD ROSESTHAL
1058
Vol. 87
STAKDARD POTE3TIAL OF THE SILVER-SILVER CHLORIDE ELECTRODE AhTD ACTIVITY COEFFICIENTS OF HYDROCHLORIC ACID 1K AQUEOUS METHAP\'OL (33.4 TT'T. %) WITH ASD WITHOCT ADDED SODIUM CHLORIDE A T 25' BY ROGERG.
BATES AND
DONALD ROSENTHAL
Solictzon Chemistry Seetzon, Nuttonal Bureau 0.f Standards, Washzngton, D. C Received Sonember 15, I966 From measurements of the e.1n.f. of hydrogen-silver chloride cells at 2 j 0 , the standard potential of the silversilver chloride electrode has been found to be 0.2010 v. in aqueous methanol (33.4 mt. %). The activity coefficient of hydrochloric acid has been determined for molalities from 0.016 to 1.3 in 33.4% methanol and has been found to fit the extended Debye-Huckel equation with an ion size of 4.3 A. The variation of the activity coefficient of hydrochloric acid ( T I ) in HC1-NaC1 mixtures of constant total ionic strengths 0.16 to 1.3 in 33.4% methanol was found to be linear with the molality of salt, nz2. The coefficient (YIZ in the equation log y1 = log y1(0) al~rnz (where is the activity coefficient of hydrochloric acid in a salt-free solution of the same totalionic strength) has the values 0.040 and 0.034 a t ionic strengths of 0.16 and 1.3, respectively.
-
Introduction Electromotive force measurements of the cell
Experimental
P t ; Hz (g,, 1 atm.), HCl(m) in CH,OH ( X mt. %),
HD,
Ag
with pure methanol as the solvent have been made by Nonhebel and Hartleyl and by Austin, Hunt, Johnson, and Parton. Aqueous methanol solvents were studied by Harned and Thomas3 ( X = 10 and 20), by Parton. et uZ.,* ( X = 43.3, 64.0, 54.2, and 94.2) and by Oiwa4 ( X = 20,40,60, 50, and 90). It appears that the molality (m) of hydrochloric acid did not exceed 0.1 in any of the media with methanol content greater than 20%. The behavior of the activity coefficient of hydrochloric acid in mixtures of the acid and sodium chloride of constant total molality of unity in aqueous methanolic solvents (X = 10, 20, 30, 40, 50, and 60) has been investigated, however, by Akerlof, Teare, and Turck.j For a study of salt effects and medium effects on indicator equilibria, the activity coefficient of hydrochloric acid at molalities between 0.01 and 1.0 iii aqueous methanol (X = 33 4) was needed, as well as the influence of added sodium chloride on the activity coefficient in this range of total ionic strengths. An interpolation of the standard potential for the cell did not seem to be feasible, inasmuch as the results of Harned and Thomas3 and of Oiwa4 differ by 0.6 mv. a t X = 20. Measurements of the e.ni.f. a t 25' of the cell were therefore made in the medium X = 33.4 for solutions in which m varied from 0.016 to 1.3 and for selected mixtures of hydrochloric acid and sodium chloride of constant total ionic strength. The mixtures were studied a t five ionic strengths between 0.16 and 1.3. The standard electromotive force of the cell at 25" was determined, activity coefficients were calculated, and the "Harned rule" coefficient alZwas determined for the acid-salt mixtures in aqueous methanol ( X = 33.4). (1) G Konhebel and H Haitley Phzl V a g 161, 60, 729 (1925) ( 2 ) J M Austin A H H u n t F 4 Johnson, and H ;"; Parton unpublished u o r k cited by R A. Robinson and R H. Stokes ' Electrolyte SoluY T 1959, Appendix tions ' 2nd E d , Academic Press, I n c , N e a York, i 82
(3) H 6 Harned and H C Thoinas, J A m Chem Soc
57, 1666 (19361,
88 781 (1936)
(4) I T Oina, Sa. R p t s Tohoku Unav , I 41, 47 (1957) ( 5 ) G kkerlof, J W Teare, and H. Turck, J . A m Chem. Soc
(1937)
59, 1916
The cells used were of the same geneml, design as those long in use in this Iaboratory,B modified in the following ways to enhance their suitability for measurements with non-aqueous and mixed solvents: The size of the celI was considerably reduced, and the top portion of each electrode compartment was construct,ed entirely of glass. The compartments were joined at the bottom by a short length of capillary tubing, and each accommodated only one electrode, instead of a pair of identical electrodes as in the larger cells. A dual saturator for the entering hydrogen gas was a part of each cell. The saturator contained about 12 ml. of solution, whereas the electrode compartments themselves required about. 20 ml. The electrodes were prepared by methods already described elsewhere.7 The solutions were prepared in 100-nil. amounts froin 40 ml. of Spectm Grade methanol and aqueous solutions of hydrochloric acid and sodium chloride of knoT1-n concentration. Polarographic examination of the methanols showed that the concentration of formaldehyde was less than 3 X 10-6 X. The weight of methanol and the total weight of solution were determined, making possible the calculat'ion of the molalities of the solutes and the weight composition of the solvent. The lat,ter varied from 33.4 wt. % for the most dilute solution to 34.3 wt. % for the most concentrated. All of the observed e.m.i. data were adjusted to correspond to a solvent composition of 33.4 wt. %. For the most concentrated solutions studied, this adjustment, added 0.57 mv. to the measured e.m.f. Corrections to 1 atm. partial pressure of hydrogen were made with the use of known vapor pressure data for methanol-water mixtures.9
Results Standard Potentials.-The corrected values of t,he e.m.f. ( E ) for solutions of hydrochloric acid are summarized in Table I. In order to det'erniine the standard electroniot'ive force sEO of the celllo (by definition" also the standard electrode potent'ial of t'he silver-silver chloride electrode) the mean ionic activity coefficient of hydrochloric acid in 33.4 wt. yo m.ethanol was expressed by the extended Debye-Huckel equation, modified as necessary for concentrations on t'he molal scale. The density of the solvent was taken as 0.944 a t 2 5 O , the dielectric constant 64.0,12 and the mean molecular weight 2 1.1. By trial it was found that a value of 4.3 A. for the ion-size parameter a" gave a good fit of the experi(6) R . G. Bates and R. F. Acree, J . Res. NatE. Bur. Std., 30, 129 (1948). (7) R. G. Bates, "Electrometric pH Determinations," John Wiley and Sons, Inc., New York, N. Y., 1954, pp. 16G and 2 0 5 . (8) T h e authors are indebted t o J. K. Taylor and G. Marinenko for the polarographic examination of the methanol. (9) J. A. 1'. Butler, D. W. Thomson, and W. H. Maclennan, J . Chem. Soc., 674 (1933). (10) The subscript s signifies t h a t the standard state is aqueous methanolic solvent rather than pure water. (11) J. A. Christinnsen, J. Am. Chem. SOC.,82, 5517 (1960). (12) P. S. AIbriSht and L. J. Gosting, ibid.. 68, l O G l (1946); T. Shedlovsky and R,. L.R a y , J . Piius. Chem.. 60, 151 (1956).
STXND-~RD POTEXTIAL OF SILVER-SILVER CHLORIDE ELECTRODE
May, 1963
TABLE I CLECTROVOTIVE FORCE ( E ) OF THE CELLPt, H 2 ( g , 1 ~ T M), HCl(m) [SOLVEVT: 33.4 WT. qo CHIOH, 66.6 WT. 70HzO], AgC1, Ag AT 25" ( I N v.) Standard Electromotive Force (*Eo)a t 25' m E SEO 0 20127 0 01590 0 42240 40855 20104 02113 38911 20126 03178 35622 20080 063% 20093 09560 33717 32374 20108 1276 31323 20113 1595 27955 20096 3198 24365 20085 6436 22070 20105 9741 20284 20101 1 307 Mean: 0 20103 i 0 00011 Std dev of the mean: 0 00005 v.
mental data, This is the same value found for hydrochloric acid in water,l 3 l 4 suggesting that ion association is negligible in 33.4 wt. % methanol. thus becomes The complete formula for
where
TABLE I1 MEAKIOSIC ACTIVITICOEFFICIENT, s y i , OF HYDROCHLORIC ACID IN THE SOLVENT CH,OH (33.4 WT. Yo), HzO (66.6 WT. yo)AT 25" m [Ext 1 SY* 0 005 -0 0006 0 906 01 0009 875 02 0012 837 05 0014 780 07 0015 758 1 0015 735 2 0013 696 5 0009 671 7 0007 678 1 0 0005 703 1 2 0003 725
It is customarily expressed as an activity coefficient, my+. From the standard potentials of the cell in the two solveiits, log my4 = (0.22234 - 0.20103)/0.11831 = 0.1801 a t 25' and m y 4 = 1.514. This expresses the well known fact that the escaping tendency of hydrochloric acid is greater in methanol-water solvents than in the pure aqueous solutions. Mixtures of Hydrochloric Acid and Sodium Chloride. -The linear variation (with composition) of log y3 for hydrochloric acid and alkali chlorides in their mixtures of constant total ionic strength has been established not only for aqueous solution^'^ but also for methanol-mater solvents up to X = 6OS5 This relationship is often called the "Harned rule." In the notation of Harned
log YI = log
[Ext.] -lOg(l $- 0.0422 W Z ) ( 2 ) The slope 4.6052RTlF has the value 0.11831 v. a t 25'. The extended terms [Ext.] were obtained with the aid of the tables given by Groiiwall, La Xer, and Sandved.l5 The coefficient (0.132) of the m term in equation 2 was determined graphically by plotting, as a function of m, the apparent sEo values (computed without the second term on the right of eq. 2 ) . derived from each e.m.f. measureThe values of ment are listed in the last column of Table 1. The average value is 0.20103 v., the mean departure from the average value is 0.00011 v., and the standard deviation of the mean is 0.00005 v. By application of the standard formulas interrelating the concentration scales, the standard potential on the molar scale, &,O. is found to be 0.1980 v., whereas that on the inole fraction scale, These values appear to agree with s E ~ ois, 0.0027 the (interpolated) results of Oiwa4within 0.1 mv. Activity CoeEcients.---The activity coefficient of hydrochloric acid, sy&,related to unity a t infinite dilution in 33.4 wt. % methanol, was calculated by equation 2 a t round molalities from 0.005 to 1.2 and is given in Table 11. The corresponding values of [Ext.] (eq. 2) are listed in the second column. The primary medium effect is a measure of the change of free energy which accompanies the transfer of one mole of HCl from infinite dilution in water to infinite dilution in 33.4YGmethanol
1089
YUO)
-
wmz
(3)
Iyhere y1 is the activity coefficient of hydrochloric acid in the mixture of HCl(m1) and NaCl(mn)and yl(o) is the activity coefficient of the acid in a salt-free solution of the same ionic strength as the mixture. Electromotive force data were obtained a t 25' for nine mixtures of hydrochloric acid(ml)-sodium chloride(mz) at five different ionic strengths ( I ) in 33.4 wt. "/o methanol. The values of log .yi for hydrochloric acid in each solution were computed by the equation
wherea,s those for the salt-free solutions were calculated by eq. 2. These two quantities are, respectivel;y, the log y1 and log yl(0) of eq. 3. The slope cyl2 was computed from the measurements
TT.
TABLE I11 COEFFICIENTS I N MIXTCRESO F HYDROCHLORIC ACID *4ND SODIVM CHLORIDE, SOLVENT: 33.4 WT. % >IETHANOL, AT CONSTANT TOTAL IOSIC STRESGTH ( I ) ;VALCESO F cyl2 hTlV1TY
I 0.15g.5
0.3200
0.8435
HCl(in HzO) = HCl(jn 33.4% RleOH) (13) H S Harned and B B Owen, "The Physical Chemistry of Electio-
lytic Solutions," 3rd E d , Reinhold Pub1 G o r p , Ken- York, N. Y , 1968, ChapteIs I 1 a n d 14. (14) R G Bates and V E Bower, J Res .VatZ Bur. Std ,63,283 (1954). (15) T. H Gronxall, V K. La Mer, and K. S a n d l e d , Phuszk 2 , 29, 358 (1928).
0.9712
1,306
For
Molality of -loa HC1 SaCl E a ( v ~ ) Obsd. 0.1595 , , . 0,1502 ,1520 ,1277 0.03191 0.31904 ,09575 ,33701 ,06366 ,1525 0.3200 ... O.lG9l ,1280 0.1920 0.30411 ,1774 ,06385 ,2560 ,32204 ,1779 0.6435 , , . 0.1706 0.3217 0.26300 ,1817 ,3217 ,5150 ,28753 ,1903 ,1287 0.9712 ... 0.1550 ,3238 0.6473 0.25180 ,1779 ,1295 .8418 ,27620 ,1852 1.306 ... 0.1318 0.3261 0 . 9 7 9 9 0.24252 .1653 cy12
=
0.035 a t each ionic strength.
sYf
Calcd.a
Mean
a
2
... 0.1613 ,1536 0.040 3~ 0.016
... 0.1758
0 . 1 7 8 1 0.039 f 0.0135 ,.. 0.1819 ,1886 0 . 0 3 6 i0 . 0 0 2 ,,
.
0.1777 ,1846
0 . 0 3 d f 0.901
... 0.1661
0.034
N. A. DAUGHERTY AND T. w.KEWTON
1090
on each mixture, aiid the mean value is given in the last column of Table 111. The result a t I = 1 is iii good agreement with 0.034 interpolated for X = 33.4 and t = 25’ iii the values found by dkerlof, Teare, and Turckj for a total ionic strength of unity. It has already been noted5 l3 that addition of methanol to the aqueous solvent is almost without effect on the value of aI2(the value is 0.033 for aqueous mixtures of hydrochloric acid aiid sodium chloride of I
Vol. 67
= 19. The results given in Table I11 suggest that 0 1 1 ~ decreases slightly with increasing I , but the reduced accuracy with which 0112 can be determined a t ionic strengths below 1 probably makes such a conclusion unwarranted. Thus, the values of -log s y in~ the sixth column of Table 111 (calculated with a constant value of a12 = 0.035 a t each ionic strength) differ from the “observed” values on the average by hardly more than the experimental error.
THE KINETICS OF THE REACTIOS BETWEEN YAKADIUM (V) AND I R O S (11) BY X.A. DAL-GHERTY~ AND T. W. NEWTON Cnzversaty of Cal?fornia, Lo8 Alamos Scientific Laboratory, Los Alanzos, New Mexico Received iYovember 16, 196d
+
+
The kinetics of the reaction ]‘(IT)Fe(I1) = V(1V) Fe(II1) have been studied in acid perchlorate solutions from 0.047 to 1.0 M in HC104 over a temperature range from 0 to 55.6” at fi = 1.0. The rate law found is -d[V(V)]dt = k’[V(V)I[Fe(II)I,where k‘ may be given by: k‘ = a[H+]-’ b c[H+]. The e[“] term strongly predominates the others; values of AH* and A S * for this path were found t o be 1.52 i 0.16 kcal./mole and -37.3 f 0.6 e.u.
+ +
Introduction It has been found that the rapid reaction between V(V) and Fe(I1) can be studied by an extension of ordinary spectrophotometric techniques. This reaction is of interest to us for two reasons. First, V(T’) in acid solution is probably Toe+ and is structurally similar to the +5 actinide i 0 q 3 and a comparison of the kinetics of its reduction reactions with the analogous ones of the actinide ions should help elucidate some of the factors which determine such rates. One of these factors is the formal ionic entropy of the activated complex which for reactions involving actinide ions appears to be predominantly determined by the charge on the complex.4 The second reason for interest is to see whether this correlation extends to reactions between transition metal ions. Previous kinetic work on the reduction of V(V) by inorganic ions in non-complexing solutioiis is that of Ramsey, et al., who studied the reduction by iodide iom5 Experimental Reagents.-Two stock solutions of T7(T’) perchlorate were prepared. For the first, Fisher Scientific Co. “purified” ammonium meta vanadate was recrystallized from hot water and heated to about 900” in an electric muffle to convert the ammonium salt to the oxide. This was dissolved in 3.34 M HClO4 and treated with ozone to oxidize traces of V(1V) to V(T7). Excess ozone was removed by passing oxygen through the solution for 16 hr. The second solution was prepared by dissolving vanadium metal in 5 HNO, and fuming with HC104 to remove nitrate and to oxidize the vanadium to V(V). The V(V) content of these solutions was determined by titration of aliquots with standard FeS04 solution, according to the method of Hammett.6 The titrations were done in 6 X HzS04 to the ferrous phenanthroline end point. The two stock solutions were found to be 0.16 and 0.02 M in V(T7). The free acid in the first stock solution was estimated (1) Talk done under the auspices of the U. S.Atomic Energy Commission. (2) Los Alamos Scientific Laboratory, Summer Staff Member. (3) hi. J. LaSalle and J. W.Cobble, J. Phlls. Chem., 59, 519 (1955). 44) T. W.Newton and S. W. Rabideau, %bid., 68, 365 (1959). (5) J. B. Ramsey, E. L. Colichman, and L. C. Pack, J . Am. Chem. Soc., 168,1695 (1946). d6) C. H. Walden and L. P. Hammatt, ibid., 66, 57 (1934)
to be 3 . 2 .Tf based on the initial acid concentration and the final I-(V) concentration. The second stock solution contained far less vanadium and the acid wa9 found to be 4.2 J f by titration with S a O H to the brom phenol blue end point. For the kinetic runs, only a small fraction of the total acid came from that present in the vanadium stock solutions; so errors in the estimation of the acid concentration in these stock solutions were completely negligible. Most of the kinetic runs were made using the first stock solution but several were made with the second. Within the experimental error the same concentrations of the two solutions gave the same results; so it is unlikely that significant concentrations of catalytic impurities were present in either stock solution. A stock solution of Fe(I1) was prepared by dissolving a weighed amount of Mallinckrodt analytical grade iron wire in 0.5 M HClOd and then adding sufficient 3 M HC10( to give a solution 0.10 .lit in Fe and 0.50 M in HC104 upon dilution to the final M volume. The solution was found to contain about c1-. Solutions of He104 were prepared by diluting analytical reagent grade concentrated acid. The concentrations of the solutions were determined from density measurements.? The concentrated acid had been freed of reducing impurities by boiling at atmospheric pressure and cooling in a stream of scrubbed argon. Solutions of LiClOr were prepared by neutralizing analytical reagent grade Li2C03with HClO,, boiling out the COZ,and crystallizing from water at least three times. The salt solutions were analyzed by density determinations; the concentration vs. density functions were determined from previously analyzed solutions.8 The water used in the preparation of all solutions was doubly distilled; the second distillation was from alkaline KRIn04 in an all Pyrex still. Apparatus.-Rate runs were made in specially shaped Pyrex cells which were positioned in a small water-filled thermostat in the light beam of a Cary recording spectrophotometer, Model 14. The cells were similar to small erlenmeyer flasks to which two 25 mm 0.d. tubes were sealed coaxially to provide a light path of about 10 cm. The ends of these tubes were left rounded since the water in the small thermostat eliminated most of the focussing effect which otherwise would have been present. The contents of the cells m-ere stirred from below by means of Teflon covered magnetic stirring bars. The spectrophotometer was operated in the ultraviolet range using the hydrogen lamp. Since the cover of the sample-containing cell compartment was removed during kinetic runs, measurements were made with the room darkened. The reaction was started by injec(7) I,. H. Briokwedde, J . Res. IVaatl. Bur. Std., 42, 309 (1949). ( 8 ) T . R’. Xerrton, J . Phus. Chern., 62, 943 (1958).
