KINETICSALT EFFECTI N BROMATE-BROMIDE REACTION
Jan., 1935
degree in the values of ( F " - E;)/T, which is ample accuracy for most practical thermodynamic purposes.
Summary The following form of expression is proposed for the approximate representation of heat capacities of solids and gases a t high temperatures
[CONTRIBUTION FROM THE CHEMICAL
C, = a
51
+ bT + cT-I/a
It is shown that for several typical substances for which accurate data are available, the heat capacity, heat content, and free energy may be represented with sufficient accuracy for thermodynamic computations by this expression and its integrated forms. ANN ARBOR,MICH.
LABORATORY OF THE
RECEIVED OCTOBER34, 1934
UNIVERSITY OF CALIFORNIA]
The Kinetic Salt Effect in the Fourth Order Reaction Br0,Ionization Quotients for HS0,- at 25'
+ Br- + 2H+-+.
BY WILLIAMC. BRAYAND HERMAN A. LIEBHAFSKY The volume of each mixture was usually 250 cc. and was smaller only when the concentrations of the reacting substances were rather high. The BrOa- i-5Br6Hf= 3Bra 3Hz0 (I) flasks used had closely fitting glass stoppers, have been measured a t 25", and in the presence which were sealed with paraffin in the long-time of added perchlorate, in order to obtain values of experiments with very dilute solutions. The gas k that may be compared directly with those ob- space above the solution was not large. The tained by Young and Bray' in their study of the stock solutions of sodium bromate, hydrobromic acid, sodium bromide and magnesium perchlorate reaction BrOa3H202 = 302 Br3Hz0 (11) and the distilled water were brought to the temin perchloric acid solutions. One of the reasons perature of 25' before mixing. The perchlorate for undertaking this work was to determine solution was prepared by neutralizing a measured whether, a t low ionic strength, the specific rate, quantity of very concentrated perchloric acid k , increases rapidly in the manner required by the solution with magnesium oxide, diluting to a conclusions of Young and Bray. It also seemed definite volume, and adjusting the concentration desirable to re-examine the earlier results in sul- of hydrogen ion to a value equal to or slightly fate solutions of Skrabal and Weberitsch2 (Re- greater than lo-' molal. With the above procedure it was possible to action I) and of Bray and Davis3 (Reaction 11), and to analyze them by a method which distin- determine accurately the quantity of bromine guishes between the change of k due to the pres- liberated before the concentration of any reactant ence of HS04- and that due to variation in ionic had decreased by a large percentage amount, and, therefore, to calculate k by means of the fourth strength. In each experiment all the bromine liberated order differential equation. Average rather than in the time allowed was determined iodimetrically initial concentrations were used, and all concenin the reaction flask by means of an accurately trations were expressed as moles per liter. This standardized 0.02 M sodium thiosulfate solution. "method of constant rates" has been discussed The reaction, I, was stopped by adding a solution by a number of investigator^,^ and methods of which contained the necessary amount of phos- obtainingexact values of k have been described y ~ by~ Skrabal and Weberitsch.2 phate buffer and a large excess of potassium iodide, by De L ~ r and Since in our experiments the product of the initial This method of determining bromine in the presconcentrations never exceeded the product of the ence of bromate is not new, and the precautions average concentrations by more than 10.5%, the necessary for accurate iodimetric analysis need error in k due to our method of calculation never not be described in detail.
In the present investigation of the rate law, -d(BrOa-)/dt = k(Br03-) (Br-) (Hf)2, initial rates of the reaction
+
+
+
+
+
( I ) Young and Briry. TAISJOURNAL, 64,4284(1932). (2) Skrabal and Weberitsch, Monalsh., 96, 211 (1915). (3) Bray and Davis, THIS JOURNAL, SS, 1427 (1930).
(4) See, for example, (a) Lash Miller and Bray, J . Phys. Chcm., 7, 92 (1903); (b) De Lury, ibid., 7, 239 (1903); ( c ) 10,423 (1906): (d) Skrabal and Weberitsch, Ref. 2.
WILLIAM C . BRAYAND HERMAN A. LIEBHAFSKY
52
VOl. 57
one experiment was carried out. Near yl/' = 0.35, and also near p1ln= 0.85, there are given in Fig. 1 the results of a group of three experiments, in which the concentrations of hydrobromic acid were near 0.00735, 0.0111 and 0.0184 M . An average of the spreads for these two groups probably gives a fair estimate of the accuracy of our measurements. In the group a t the lower (higher) ionic strength, the intermediate value of K was obtained at the lowest (highest) acid concentration : the addition of magnesium perchlorate even in moderate amounts thus does not alter the manner in which hydrobromic acid enters into the rate law. There is in Fig. 1 little if any evidence of a difference in the kinetic salt effects of the t h e e electrolytes up to ,ul" = 0.5. The points in the diagram are represented fairly well by a single curve, which corresponds closely to the (l/2) log yBacI2curve in a i'' diagram. Extrapolation to p"* = 0 by means of this curve yields the value ko = 506, which is only 6.37, less than the value, 540, selected by Young and Bray. = p'/zoO. The results of Young and Bray' a t 25" (ReFig. 1.-Variation of k with ionic strength. Reaction I: action 11) are plotted in Fig. 2. I n the range of BrOs- + 5Br6Hf = 3Br2 3Hz0. The electrolyte the measurements, fil" = 0.23 to 0.9, all the is mainly HBr, 0 ; NaBr, V; Mg(ClO&, 0. Cf.Table I. points are close to a single, rather flat curve. corresponds to the exponent, 4, in the equation, k/y4 = a true constant, given by Young and Bray.' (They concluded that the activity coefficient, y, is equal to Y H B ~when the ionic 0.60 strength is less than 0.5.) This method of plot- i ting was adopted because it furnishes an excel- 3 lent representation of the actual experimental 0.50 data, and enables K O , the value of k a t = 0, to be estimated accurately by comparison with a family of log y curves. The method is closely 0.2 0.4 0.6 0.8 related to that used by Randall6 in interpreting PI/'. equilibrium and electromotive force data. Fig. 2.-Variation of k with ionic strength. Data of Three sets of experiments are shown, in which 3HzOa = 302 the ionic strength was due mainly to hydrobromic Young and Bray. Reaction 11: BrOl+ B T + 3Ha0. The electrolyte is mainly HC104, 0 ; acid, sodium bromide and magnesium perchlo- HCIO, with some NaBr added initially, V ; NaClO, and rate, respectively. In the first two series the HClO,, 0; NaC104, HClOd and some NaBr, A. V 9 bromate concentration was varied from 3.74 to represents the average of 9 experiments. Cf.Table I. M , and the lowest concentration of 9.58 M. Extrapolation by means of the log y curve for hydrogen ion or bromide ion was 2.16 In the perchlorate series the concentration of HC1 or HBr confirms the value ko = 540. As bromate was always in the neighborhood of 3.80 the log y curves for these acids are the highest in M , and that of hydrobromic acid was near the family of log y curves referred t o above, a 7.35 (lo+) Mfor all ionic strengths a t which only distinctly lower value of ko can be obtained from these data only by using another method of (5) (a) Randall and Vietti, TRISJOURNAL, 60, 1528 (1928); (b) extrapolation. Examination of the data shows Randall, J . Chcm. Educ., 8, 1082 (1931).
exceeded a few tenths of a per cent. It was clearly not worth while to estimate and add this small correction. The results of Skrabal and Weberitsch2 in sulfate solution, obtained by means of the method of constant rates, prove that there are no appreciable initial disturbances in Reaction I, and therefore justify the calculation of k from a single rate measurement. The experimental data at ionic strengths less than p = 1 are presented in Fig. 1: values of log k are plotted against pl/'. The factor,
+
+
+
Jan., 1935
KINETICSALTEFFECTIN BROMATE-BROMIDE REACTION
53
A discrepancy of this kind would signify that that the kinetic salt effects are nearly identical €or perchloric acid and sodium perchlorate up to there is a retarding effect in Reaction I which is / p 2 = 0.7. This is a striking result, for these absent (or a t least smaller) in Reaction 11. In electrolytes, when added to 0.1 M hydrochloric the latter reaction, hydrogen peroxide (as well acid, have widely different effects6 on YHCI. as bromide ion) is available for the removal of the I t therefore seems probable that in this range of various reactive compounds intermediate between ionic strength the y-function that measures the bromate and bromine, so that these compounds decrease in the specific rate of this reaction would probably accumulate to a greater extent in I not be altered if other uni-univalent electrolytes than in 11. The discrepancy in question may were added, or even magnesium perchlorate up to be explained by assuming that the rate-determining step of the fourth order reaction is reversible, p = 0.3. Data corresponding to the curves of Figs. 1 and since the maximum rate could then be obtained 2 are summarized in Table I. The ionic strength only when the intermediate product in this step is calculated from concentrations in moles per is removed with sufficient rapidity. It may be liter. Values of log y may be obtained by sub- noted that chlorine has a marked retarding effect in the complicated reaction' between chlorate tracting (Ijg) log ko from (1/4) log k. and chloride ions in acid solution, and that in TABLEI this case the simple fourth order reaction has been OF REACVALUESOF k BAEEDON RATEMEASUREMENTS demonstrated only in the presence of a "chemical TIONS 1 AND 11 (cf. FIGURES 1 AND 2) depolarizer,"* like iodide.4a k(I) is less ('/d log R ~,~~ ReacReacthan k U I ) It would seem, therefore, that hydrogen pertion I tion I1 k(I) k(I1) by, % oxide is a better depolarizer for the bromate0 0 (01.676) (0.687) (506) (540) 6.3 0.0025 0.05 ,652 (.659) 406 (433) 6.3 bromide reaction than is hydrobromic acid a t .01 .10 .632 (.639) 337 (360) 6.4low concentration, and that this fact necessitates .04 :20 ,600 .607 2514- 2586.3 the use of two types of log y curves in extrapolat.585, 201 219 .30 .576 .09 8.2 ing the two sets of results in Fig. 2. We are 12.8 .40 .554 .569 165 189 .16 consequently assuming that Curve I would extra17.5 .50 ,537 ,558 141 171 .25 23.2 .60 .522 ,550 122 159 .36 polate to the origin of Curve 11, as indicated by 29.1 ,545 107 151 .70 '507 .49 the broken line in Fig. 2, if the retarding effect 93 146 .80 ,492 ,541 .64 36.3 gradually disappeared in the region of very low .90 .478 .538+ 82 142f 42.2 .81 concentrations, and that ko = 540 a t 2.5'. 1.00 1.00 ,463 ,536 71 139 48.9 The analogous iodate-iodide reaction is ordiThe values of the specific rate based on Re- narily of the fifth order, but becomes fourth order action I are always less than those based on Re- at very low concentrations of i ~ d i d e . ~Bray and action 11. The difference is large at high ionic LiebhafskylO concluded that the fourth and fifth strength, decreases rapidly to about G% a t f i l l 2 order reactions have independent rate-determin= 0.2, and therefore probably approaches zero ing steps, and discussed possible intermediate at low ionic strength. The constant percentage compounds. Recently Skrabal" has published = 0.2 shown in the table is a comprehensive discussion of these and related difference below due to the method of extrapolation, and is not reactions, and has considered the possibility that to be regarded as an experimental result. a fifth order bromate-bromide reaction might The very large divergence a t high ionic strength occur at high concentrations of bromide ion. may be due in part to a difference in the kinetic We have found no evidence of such a reaction at salt effects of sodium and magnesium perchlo- ionic strengths below 0.7 (and concentrations of rates; but, as we have seen above, such specific hydrobromic acid not greater than 0.1 but differences seem in this case to be very small be- its existence is indicated by the results of some low pl/' = 0.5 to 0.7. There remains in the range experiments a t very high ionic strengths. p"' = 0.2 to 0.6 a discrepancy of 6 to 20% in the (7) Luther and MacDougall, 2.physik. Chem., 62, 199 (1908). (8) Skrabal, 2. Elektrochcm., 80, 124 (1924). values of k, which we believe to be too large to be (9) Abel and Hilferding, 2. physik. Chem., 136, 186 (1928); cf. accounted for by a systematic error of measure- Skrabal. Ref. 8. (IO) (a) Bray, THISJOURNAL, 62, 3582 (1930); (b) Liebbafsky, ment in the one or other set of measurements. ibid., 13, 2083 (1931). E
~
w,
(6) Murdock and Barton, Tars JOURNAL. 44, 4077 (1933).
(11) Skrabal, 2. Ekktrochcm., 40, 231 (1934).
WILLIAMC. BRAYAND €IERMAN A. LIEBHAFSKY
54
The magnesium perchlorate series of Fig. 1 was extended to ionic strengths near 3, and the sodium bromide series to ionic strengths above 4. In the iatter series, values of k as high as 800 were found at CxaBr = 4.2 -If and C,+ = 0.009 M ; the results furnish at least qualitative evidence for
0.2
0.4
0.6
0.8
p=/7.
Fig %-Variation of k with ionic strength in presence Reaction I : uncorrected, Table IIA, 0 ; corrected for HS04-, Table V, 0 . Reaction 11: uncorrected, Table IIIA, A ; corrected for HS04,Table V, A . Curves I and I1 are from Figures 1 and 2. of sulfate.
the existence of the fifth order reaction corresponding to the differential equation d(BrOo-)/dt = k’(BrOa-) (Br-)2(H+)2. In the magnesium perchlorate series, so long as the concentration of hydrobromic acid did not exceed 0.007 M , the values of h were not far removed from Curve I produced. However, at p = 3, k was found to increase with increasing concentrations of hydrobromic acid, even a t those concentrations for which no such effect had been observed a t low ionic strength; and the increase was more rapid than had been indicated by the sodium bromide experiments. Such results are difficult to understand, and show further investigation to be necessary. The results of the rate measurements in sulfate s o l ~ t i o n sand , ~ ~of~ our calculations, are presented in Fig. 3 and Tables I1 to VI. The original data, corresponding to complete ionization of sulfuric acid, are given in Tables I1 and 111, and are represented by the lowest points in the diagram. The effect of the presence of HS04- is illustrated by the slanting, nearly straight line drawn through one point, 4B : (l/4) log k increases and P’’’ decreases as smaller and smaller values are assumed for the equilibrium quotient KHS04-
= CH+CEO~--/CHEO~-
A point on a line may be determined as follows. Assume any value of the specific rate, k, greater
VOl. 57
than the uncorrected value k’, and calculate the concentration of hydrogen ion from the relation k(CHt)’ =
k’(2C)’
where C is the concentration of sulfuric acid in moles per liter. The values of p , pl’* and KHsOpmay then be determined, since Cso4-- = CH+- C and CHsO4- = 2C - CH+. It is evident that two sets of equilibrium quotients may be calculated from each set of kinetic data in sulfate solution, since each line cuts the two curves, I and 11. The values of KHs04-shown in Tables I1 and I11 are obtained in this way. All the kinetic res u l t ~ at ~ , 25’ ~ are included in IIA and IIIA. In Nos. 11, 12, 13 and 15, Table 11, the values of (k) tabulated by Skrabal and Weberitsch were used (and should not have been changed by Young and Bray). It is important to note that a small error in (k)may alter greatly the calculated value of KHS04-; thus in No. 12, if the observed specific rate had been 132 instead of 137, KHs04would have been 0.073 instead of 0.110. It is therefore remarkable that only one result, No. 9, must be rejected; and that the two sets of KHS04- values in Tables IIA and IIIA are in reasonably close agreement. This agreement, together with the diSergence of the ionization quotients in Tables IIB and IIIB, leads us to conclude that the kinetic results in sulfuric acid solution are consistent with those in perchloric 1
I
I
I
I
I
1
I
I
I
b.
Jan., 1935 VALUES OF
KINETICSALT EFFECT I N BROMATE-BROMIDE REACTION
TABLE I1 KHSO,,-CALCULATED FROM THE KINETIC DATAOF SKRABAL. AND WEBERITSCH AT 25 '. 5Br6H+ = 3Br2 3H20 A. By comparison with Curve I
+
+
CHSOr
15
0.02
6 9 11 14 10 8 2
.03
13 12
CKBdr
(k)
CKBr
0.001 0.005 .0005 .05 "003 .OOl .1 .005 ,001 .1 .005 .002 .1 0: .Ol .05 .10 .001 .005 .OEl .001 .1 ,0025 . O O l .2 ,005 ,001 .2
(l/aJ log k Uncorrected
130 0.257 95 .375 1202 ,332 151 ,341 162 ,342 103 .387 72 .553 80 .501 142 .457 137 .465
I
REACTION I : Br0,-
+
#'/a
Expt.
0.529 ,494 ,520 ,545 .552 ,503 ,464
.4iF ,538 ,534
pl/P
(1/4) log k Curve I
0.210 ,324 ,328 ,338 ,340 347 ,416 ,442 ,456 ,464
0.598
.S i 1
,569 ,567 ,566 ,565 ,582 ,547 .545 ,543
CH+ calcd.
35
P/4
KHSO~-
0.0291 ,0422 ,00478 ,00902 ,00939 ,04514 ,1336 ,0720 .00485 ,00960
0.0243 ,0290
0.0205 .0401 ,1229 ,0664 ,00880
0.0189 ,0202 ,0364 ,0323 ,0277
.OOGY? ,0370 ,0675 ,0443 ,0675 ,0566 ,0760 ,110
)log
KHSOF
i.596 i.n15 Reject 1.642 1,707 1 , 6F2 -
1,707 1.F88 i. - 720 1.7'60
B. By comparison with Curve I1 Curve I1
Expt.
15 6 8 2 12
0.606 .582 ,570 .565 ,562
0.205 .317 ,390 .429 ,462
TABLE I11 BRAYAND DAVIS. REACTION 11: BrOaBr3H20 A. By comparison with Curve I1
VALUES OF KHSO,-. CALCULATED FROM THE KINETIC DATAOF
+
C€Il804 Expt. moles/liter
1A 1B 3A 2A 2B 3B 4A
4R
0.05 .06 .06 .06 06 12 12 .18 I
CKBrOj
0.00587 .01174 ,00489 .00978 ,00978 .00489 .00493 ,00493
ke
98 98 97 100
('/4) log k Uncorrected
0.395 .402 .430 ,436 101 ,436 76 .604 76 ,604 65.6 .738
0.498 ,498 ,497 ,500 ,501 ,470 .470 ,454
a%
log k
('/4)
Curve I1
0.299 ,312 ,330 ,344 ,348 ,443 ,443 ,525
0.5855 0.06677 ,582 ,06785 ,579 ,08213 .577 ,08420 ,5765 ,08476 ,564 ,1558 ,564 ,1558 ,556 ,2253
+ 3Hz01 = 302 f P/d log
CH+ calcd.
1.569 1.576 1.640 -1.627 1.610
KHso4-
0.0336 ,0377 ,0480 ,0570 ,0595 ,0654 ,0654 ,0754
KH804-
1.632 -1.644 -1.670 I ,690 1.694 1.704 -1.704 1.719
B. By comparison with Curve I Expt.
IA 0.312 2A ,362 3B, 4A ,483 4B 593
Curve I
0.573 0.07072 ,5615 ,0904 ,540 ,1740 ,522 ,2635
0.0500 ,0926 ,1420 ,2240
-i . 6 7 5
1.742 -1.788 1.840
At low ionic strengths, the values of KHs0,- the curve in Fig. 4 to agree with the l , ' ~log Y N ~ S O ~ should increase rapidly with the ionic strength; curve. and (l/J log KHso,- when plotted in a diagram TABLE IV should yield a curve similar to one of the family of HS04- = H + + SO4-- EQUILIBRIUM QUOTIENTSAT 35" log y curves.6 In Fig. 4 are represented the results (Cf.FIG. 4) from Tables IIA and IIIA, and those of Sherrill KHSO4log and Noyes12 based on conductance measurements KLO41O2KH8040 1.15 0 of sulfuric acid and sodium acid sulfate. The 1.43 0.024 0.05 results are more concordant than was to be ex1.74 .I ,045 pected. We accepted the limiting value, K & s O 4 - = 2.43 ,0815 .2 0.0115,13adopted by Sherrill and Noyes, and drew 3.25 .3 .113 (12) Sherrill and Noyes, THIS JOURNAL., 48, 1861 (1926). (13) This is nearly the same as the value 0.0120 recently found by Hamer, THIS JOURNAL 66, 860 (1934), in an extensive series of electromotive force measurements in dilute solutions, and temperatures ranging from 0 to 60'.
.4 .5 .fl ?
. I
,1405 ,165 .I85 ,200
4.19 5.25 6.32 7.28
WILLIAMC. BRAYAND HERMAN A. LIEBHAFSKY
56
In Table IV are listed values of KHS04- which correspond to the smooth curve in Fig. 4. It is believed that these results, in spite of their uncertainty at the higher ionic strengths, will prove useful in interpreting experimental data in dilute sulfuric acid solutions. TABLE V VALUESOF k, CORRECTED FOR PRESENCE OF HS0,Kinetic Data of Skrabal and Weberitsch, Tahle II EXrJt.
15 ti
11 14 1(d
s
:3 13 13
p’/2
10’KHSOa-
108cHA
k
0.212 ,327 ,339 .339 ,342 ,395 ,437 ,456 ,463
2.51 3.50 3.60 3.60 3.63 4.13 4.58 4 78 4.84
29.4 43.3 9.0 9.0 43.6 124.9 69.8 4.77 9.2
241 182 186 700 191 185 164 156 162
Kinetic Data of Bray and Davis, Table I11 FXpt.
pi/’
1.4 0.298 1B ,305 3.4 ,319 2.4 ,327 2B ,327 3 B , 4 A ,425 4B .506
10*KHBOr-
10*CH+
k
3.25 3.31 3.42 3 48 3.48 4.45 5.32
66.4 66.6 78.3 78.4 78.4 147.8 215.6
222 221 228 234 23 6 210 183
By means of these values of KHS04-we have calculated values of the specific rate, k, from the kinetic data in sulfuric acid solutions. The process is the reverse of that outlined above, and involves successive approximations. The results are listed in Table V and plotted in Fig. 3. As was to be expected from the method of evaluating KHSO,-, the results of Skrabal and Weberitsch for Reaction I, are in general agreement with Curve I, and those of Bray and Davis for Reaction I1 with Curve 11. The agreement would have been better if somewhat higher values had been assumed for XHS04-above pi” = 0.3.
Summary Initial rates of formation of bromine in the reaction, I, between bromate arid bromide ions in
VOl. 57
acid solution were measured at 25’ between ionic strengths as low as 0.003 and as high as 4. Values of the specific rate, k, of this fourth order reaction were compared with those obtained by Young and Bray in their study of the reaction, 11, in which bromate ion is reduced by hydrogen peroxide at ionic strengths between 0.06 and 0.8. These results were also compared with published kinetic data for the two reactions, I and 11, in sulfuric acid solutions. The comparisons were made by plotting ‘/4 log k against p”’. At low ionic strengths, k increases rapidly with decreasing ionic strength and the extrapolated value is in satisfactory agreement with the value, 540, calculated by Young and Bray. There is no evidence of specific salt effects when p is below 0.3 to 0.5. At ionic strengths above 0.02 the values of k from Reaction I are distinctly smaller than those from Reaction 11, and the difference increases with increasing ionic strength. It is probable that the maximum rate of the fourth order reaction can be measured only when intermediate compounds are removed sufficiently rapidly by a chemical depolarizer, and that hydrogen peroxide is a better depolarizer than hydrobromic acid. The large values of k obtained at high concentrations of sodium bromide furnish qualitative evidence for the existence of a fifth order bromatebromide reaction. The results obtained in concentrated magnesium perchlorate solutions are difficult to understand, and indicate the need for further investigation. Analysis of the kinetic data for sulfuric acid solutions yielded values of the ionization quotients, KHSO~-, which are consistent with those calculated by Sherrill and Noyes from conductance measurements in more dilute solutions. It has been shown that the rapid increase to be expected in K H s O , - as the ionic strength is increased, which has been demonstrated by Sherrill and Noyes, continues into moderately concentrated solutions. RECEIVED OCTOBER26, 1934
