A THIRD ORDER IONIC REACTION WITHOUT APPRECIABLE SALT EFFECT HERMAN A. LIEBHAFSKY AWD ALI MOHAMMAD Department of Chemistry, University o j California, Berkeley, California Received November $4, 19%
9 kinetic investigation (7), under the simplest experimental conditions, of the reaction HZ02
+ 31- + 2H’
= 2H20
+ Is-
(1)
has confirmed the rate law d(L-)ldt = ki0 (Hz02) (1-1
+ ki(H20J (I-)
(E-)
(2)’
previously discovered, and usually explained by assuming thar the two rate-determining steps
+
H ~ O ? IHS02
+ I- +
k,0 4
H?O
+ IO+ HI0
kl H t + H20
(3) (4)
proceed simultaneously and independently. Within the ionic strength range investigated ( p C = 0.05 to 0.5), reaction 4 mas concluded to be without appreciable salt effect, a conclusion so unusual for reactions involving more than one ion that another investigation was undertaken to test it; confirmation thereof is, we believe, furnished by the results that are t o be presented here. If (H202)is so small that (H+) and (I-) remain sensibly unchanged as reaction 1 proceeds, equation 2 may be written d(Ia-)/dt = k’(H,O?) = [kiO(I-)
+ ki(I-)
(H+)l (H202)
Pa)
and k‘ may be evaluated as though it were the specific rate of a first-order reaction. Values obtained by measuring the rate at which 13- appears in reaction mixtures differing initially only in acid concentration may be plotted against (H+), as in figure 1;when divided by (I-), the slope of the resulting straight line gives directly the value of ICl, and the intercept similarly yields that of h0. From one such series of reaction mixtures to 1 A t 25”C., k10 = 0.69 a t low ionic strengths, and kl = 10.5. ( ) will be used t o denote “concentration of” in moles per liter. -+ will be restricted to reactions that may be rate-determining. Throughout, the minute constitutes unit time. 857
TEE JOORNAL OF PRPSICAL CHEMISTRY, VOL. XXXVIII, NO.
7
858
HERMAK A. LIEBHAFSKT AND ALI MOHAMMAD
another, the ionic strength may be altered by the addition of some salt, e.g., sodium perchlorate; k10and kl may thus be obtained at different ionic strengths. Such measurements have been made; the results thereof are given in tables 1 and 2, and plotted in figures 1 and 2. For sodium or barium perchlorate in moderate amount as added salt, these data show that the first term in equation 2, involving klO, varies linearly with the ionic strength, while the second, involving kl,is independ-
0
I
I
I
0.1
0.2
0.3
0.1
0.2 0.3
0.1
0.2 0.3
0.4
(H+) FIQ. 1. ABSEKCEO F SALT EFFECTON REACTION 4 Since the curves have been shifted vertically t o prevent superposition, numerical values for the ordinates have not been given. For every curve, any value of k’ may be found from table 1if the ionic strength, given above the curve, is used to identify the curve in question.
ent of it.2 (We shall not a t present be concerned with the curvature apparent in figure 2 a t the highest ionic strengths.) Granting the plausible kinetic interpretation that has been advanced for the rate law, equation 2, we must conclude that, although reaction 3 shows a “linear” salt effect Two factors insure that the salt effect on lciO will not appreciably alter the slopes of the lines in figure 1: at low (H+)the change in p caused by adding acid is so small that is not sensibly affected; a t high (H+) the contribution of reaction 3 t o the absolute rate is relatively small; in the region of intermediate (H+),both effects are operative.
859
THIRD ORDER IOXIC REACTION
TABLE 1 Detailed experimental results for jigure 1 Sodium iodide-perchloric acid solutions. Temperature, 25°C. Initially (H20z) =8X moles per liter. hverage (I-) = 5.72 X moles per liter. Values of (H +) are averages. SERIES
ADDED SALT
:ONCENTRATION OF l D D E D S A L T
k'
moles per liter
moles per /iter
0.054
0,02022 0,04130 0.0623 0.0834
0.0563 0.0706 0.0811 0.0964
0.108
0.02030 0.04130 0.0624 0,0834
0.0617 0.0715 0,0860 0.0990
0.162
0,02021 0,04130 0,0623 0.0834
0.0640 0.0773 0.0872 0.1010
5
0.305
0.02030 0,04130 0.0623 0,0834
0.0730 0.0850 0.098 0.110
6
0.540
0,02023 0.04130 0,0624 0,0834
0,0936 0.1040 0.1170 0.1290 0.1400 0.1490 0.1610 0,1740
2
3
4
1.677
(
7
1.004
0,00760 0,020u) 0.04130 0.0624
8
0.0985
0,00763 0.02027 0,04128 0,0624
0.0480 0.0550 0.0670 0.0794
9
0.0197
0.254
0.00767 0.02021 0.04130 0.0623
0.0510 0.0575 0.0698 0.0820
10
0.394
0.451
0.00761 0,02024 0.04130 0.0623
0.0530 0.0600 0.0730 0.0850
(
860
HERMAN A. L I E B H A F S P P AND ALI MOHAMMAD
TABLE 1-Concluded SERIES
ADDED SALT
:ONCENTRATIO> OF ADDED SALT
I;' ~~
moles per liter
11
12
13
14
NaClOr
NaClOc
NaC104
NaClOd
0.591
0.793
moles per liter
0'648
0'850
11
16
NaC104
Na2804t
3.643
1
0,02024
[
0.0832
0.0730 0.0850 0.0961 0.1085
(
0.02030 0.04130 0.0623 0.0834 0.2934 0.3871 0.4202
0.0880 0.1024 0.1152 0.1277 0.2600 0.2990 0.3400
0,00753 0.02O24 0,04130 0.0623
0,1330 0.1410 0.1540 0.1670
0.03048 0.04520 0.0621 0.0800 0.0987
0.0619 0,0684 0.0775 0,0890 0.0984
1
1.700
0.0644
3.70
0.25
0.0600 0.0680 0.0800 0.0940 0.1070 0.115
0,04126 0.0623 0.0832 0.0998
0.983
1.643
0.0580 0.0660 0.079O 0.0920
11
1
15
0.00764 0,02026 0.04123
1
I
* plCrepresents the ionic strength, in concentration units, due t o iodide and added salts; its value for each series is given above the curve in figure 1 corresponding thereto. t Formation of HS0.i- has been considered in calculating (Hi); the uncertainty of this correction precluded measurements in more concentrated sodium sulfate solutions. of reasonable magnitude, reaction 4 is altogether without the exponential salt effect predicted by the Bronsted theory (2). Before these conclusions are discussed, we shall consider briefly the results of a group of experiments
861
THIRD ORDER IONIC REACTION
designed to reveal whether reaction 4 has appreciable salt effect a t low ionic strengths. I n these experiments the iodine formed could be accurately titrated with Shiosulfate before any marked concentration change occurred, so that the TABLE 2 S u m m a r y of experimental results i n figures 1 and 8, and table 1 SERIES
1
we*
k10
i
kl
Ba(C10& as added salt It
0,0572
0.69
3
7
0.381 0.543 0.972 1.677 3.07
0.84 0.91 1.08 1.40 2.41
10.4 10.8 10.7 10.2 10.2 10.3 10.2
8 9 10 11 12 13 14 15
0.156 0.264 0.451 0.648 0.850 1.040 1,700 3.70
0.75 0.78 0.85 0.93 1.00 1.07 1.33 2.26
10.7 10.5 10.2 10.8 10.3 10.0 10.8 10.5
’
1
NanSOc as added salt 16
~
0.25
1
0.74
10.4
Arithmetic mean of kl values. . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . .10.4 & 0.06$‘
* hLcrepresents the ionic strength, in concentration units, due t o iodide and added salt.
t These values were obtained without added salt (see reference 7) and are not plotted in figure 1. $ The average error of the mean has been computed from a “least squares” formula; this procedure seems applicable, for the value of kl for each series was determined independently of the other data-Le., no attempt was made to select “best” values of kl after all the data were at hand. ”method of constant rates” (1, 8) could be employed. To the reaction mixture, a t room temperature and containing starch as indicator, thiosulfate solution was added from a buret at the minimum rate that would prevent the appearance of the starch blue, while the flask containing the
862
HERMAN A. LIEBHAFSKY AND ALI BIOHABIMAD
mixture was kept in constant m ~ t i o n . The ~ thiosulfate consumed in a minute measures the rate at which iodide is oxidized in reaction 1; from this rate, ?c‘/(I-)may be calculated. Values thereof obtained a t different values of (H+) have been plotted against (H+) in figure 3; in table 3 the results are summarized. The results in table 3 demonstrate that this experimental method is capable of less accuracy than the “analytical method” (7) employed to obtain the data in table 1; further, since reaction 4 is responsible, on the average,
FIG. 2. SALTEFFECT ON REACTION 3 (Cf. table 2 )
for only one-tenth of the absolute rate, experimental errors will appear greatly magnified in ICl. We believe, however, that the large number of experiments tends to compensate these inaccuracies; and since the results 3 Gradual addition of the thiosulfate so that no great excess of it is ever present seems preferable t o initial addition of the whole amount, for its oxidation by the hydrogen peroxide is thus greatly reduced. (Cf. Abel: Monatsh. 28, 1239 (1907).) This oxidation is accelerated somewhat by hydrogen ion; the difference between the kl values of table 2, and 10.4, the value from table 1, may conceivably be due t o some reaction like this. Our experimental method is a modification of that first used by Harcourt and Esson (Phil. Trans. Roy. Soc. 167,117 (1867)).
863
THIRD ORDER IONIC REACTIOK
I
050
0
I
I
2
I
I
I 4
I
6
I
I
1
1
1 12
10
8
io3 (H') FIQ.3. ADDITIONALSALTEFFECT MEASUREMENTS Cf. table 3. The radius of the circles corresponds to a change in ( k ' / ( I - ) ) of 0.02. TABLE 3 Data for experiments of figure 3 (H202)= 1.23 X 10-2 moles per liter; (H+)variable SERIES NO.
I I1 I11
(I-) X 103
1
I i: 1 1.06
(NaClOa)
0.00 0.113 0.568
1 ~
k10
(23")
0.63 0.68 0.65
1
ki (23")
:::;
1
11.7
~
~
kiO ( 2 5 ' )
0.74 0.79 0.76
1
1
hi (25")
13.2*
13.8 13.2
Corresponding table 1 values: k10 = 0.69(1), 0.75(11), and 0.89(111); k l = 10.4 (all three series). *0.005 is an average value for the ionic strength of Curve I, figure 3. The dotted line below this curve has been drawn through k'/(I-) values, each corrected for the positive salt effect on kI0. Only for the point a t highest acid is this correction, which was determined in additional experiments, appreciably larger than the experimental error; the dotted line gives kl = 12, which is lower than the values a t higher ionic strengths. (Did the Bronsted theory apply, it should be higher.) We have given the uncorrected value in table 1 because the correction is itself uncertain. Since p c does not change greatly along Curves I1 and 111, a similar correction need not be ttpplied.
864
HERMAN A. LIEBHAFSXY AND ALI MOHAMMAD
are self-consistent, we do not hesitate to offer them as confirmatory evidence for the conclusion that reaction 4 is without salt effect. Emphasis should be placed, not on the difference between 13 (the approximate table 3 value of kl) and 10.4 (the accurate table 1value), but on the fact that the table 3 values agree with each other. Although the experimental error is rather large (=t 10 per cent seems a fair estimate), it is probably not over one-fourth the change in y2 over the range of ionic strengths covered in table 3. We must conclude, therefore, that the experiments of figure 3, covering ionic strengths from pclc= 0.005 (see footnote to table 3) to p c = 0.5, furnish no evidence for the exponential salt effect predicted by the Bronsted theory. DISCUSSION O F RESULTS
In discussing the experimental results we shall employ a terminology differing slightly from what is usual.* An inspection of figure 2 makes evident that, below p c = 2, k10 may be considered a linear function of the ionic strength. As is well known, such an effect may be interpreted as an equilibrium salt effect if the intimate mechanism
+ +
Rapid equilibrium: HzOz I- H202.IRate-determining: H202.1- --+ HzO IO-
+
(3a) (3b)
is assumed for reaction 3 : the concentration of HzOz.I- could vary linearly with the ionic strength, for I- and this complex each carry a single negative charge and therefore have similar activity coefficients. (Thus, for series
E*times as large as for series 1.) The 0.69 curvature, which becomes pronounced as p o increases above 2, might well be due to a superimposed medium effect, more marked with barium perchlorate; this superimposed effect might be responsible also for the steeper 5, table 1, (HzOz.I-) would be
4 By the general term “salt effect” we understand the effect, t o a first approximation similar for all electrolytes, on the rate of a reaction of changing the ionic strength. (Skrabal (Z. physik. Chem. 3B, 247 (1929)) prefers the more accurate term “electrolyte effect,” which he has been using for many years.) Three kinds of salt effects may now be recognized: equilibrium salt effects, caused by the shift in an equilibrium, which accompanies a change in ionic strength and alters the concentration of a substance involved in a rate-determining step; kinetic salt effects t o which no definite cause can be assigned, but with which the various attempts t o introduce activity coefficients into rate laws (the activity theories of reaction rate) are principally concerned; and medium effects, which result when electrolyte addition has been so large that the reaction now proceeds in what is virtually a new solvent. There seems t o be no sharp line of demarcation between medium effects and pronounced kinetic salt effects. Our ‘
