KINETICS OF THE HYDROLYSIS OF CHLORINE
April, 1962
701
THE KINETICS OF THE HYDROLYSIS OF CHLORINE. 111. THE REACTION IN THE PRESENCE OF VARIOUS BASES, AND A DISCUSSION OF THE MECHANISM BYASSALIFSHITZ AND B. PERLMUTTER-HAYMAN Department of Physical Chemistry, Hebrew University, Jerusalenz, Israel Reeeiued September 87, 2061
The hydrolysis of chlorine in the presence of various anions of weak acids HA has been investigated. The values of kk-, the rate constant for the reaction between chlorine and a given anion A-, are found to be correlated with the corresponding acid dissociation constants K , by the equation: k+-.= 1.6 K,-0-6*. Since this is the Brgnsted catalytic law, the reaction mechanism may be expected to involve rate-determining proton transfer. A different mechanism involving rate-determining rupture of the C1-C1 bond and formation of AC1 is ruled out by further considerations which concern the rate of the back reaction, and the lrnown rate of formation of compounds of the type AC1. The two mechanisms consistent with all the known facts are either a reaction in a single step, or a two-step mechanism in which C1,OH- is formed in a rate-determining proton transfer between A- and the hydrate of chlorine. Theoretical considerations favor the two-step mechanism.
Introduction The hydrolysis of chlorine in pure waterlJ was found to proceed according to CIA
+ HrO
kHeO
-& HOCl
f C1-
+H+
(I)
and not Clz
+ OH-
kmr___t
HOCl
+ C1-
(2)
In the presence of a ~ c t a t ethe , ~ reaction is much faster and was shown to proceed mainly according to HZ0
+ Clz + AC--
kAo-
HOCl
+ C1- + HAC
(3)
with some contribution by reaction 1, and a possible contribution by reaction 2. In the presence of other anions A- of weak acids HA we may expect analogous reactions of the type H20
+ Clz -I- A-
kA-
HOCl
--i,
+ C1- + HA
(4)
to take place. ,4, knowledge of the values of k ~ for different anions might give some insight into the actual mechariism of the reaction. We thereforc investigated the hydrolysis in the presence of the following ions (given in the order of increasing basicity) : CHCl2COO-, SO4-, CI12ClCOO-, HCOO-., and HPOI-. Experimental The experimental' procedure was the same as that described in our previous work.2+s The acids and salts employed were either "chemically pure" or "analytical reagent." The temperature was again 9.5".
Results The Reaction in the Presence of Monochloroacetate.-Several experiments were carried out in the presence of chloroacetate-chloroacetic acid mixtures. Details of three runs are given in Table I. The initial stoichiometric chlorine concentration is designated by a; the amounts hydrolyzed a t zero time, and at the end of the reaction by xo and x e ; the initial concentrations of acid and anion by [HA10 and [A--]o. Column 8 shows the value (1) E. A. Shilov and 13. M. Solodushenkov, Compt. rend. mad. sci' U.R.S.S.,1 , 96 (1936); Acta Physicochim. U.R.8.9..30, 667 (1945); J . Phys. Chem. (U.S.S.R.), 19,404 (1945); 22, 1159 (1947). (2) A. Lifshitzand B. Perlmutter-Hayman, J . Phys. Chem., 64,1663 (1960). (31 A. Lifshitz and B. Perlmutter-Hayman, ibid., 66, 753 (1961).
of AHI1 the heat of reaction 4, calculated' from the total heat effect, ATo - AT- (0.20 to 0.25'); column 9 shows the value calculated from data in the literature. The rate constants k ~ are defined by the rate equation representing the two parallel reactions 1 and 4, uix. dzr/dt = ( a - zr) [ka20 4- k ~ - ( [ A - l a - st)] (1 - p) (I) where cp is the relative contribution of the back r e a c t i ~ n . ~ The . ~ values of xi were calculated3 from the measured values of AT,, and those of kA- by a trial and error method described b e f ~ r e . ~ The application of this method was slightly more tedious than in the case of acetate because the ratio
+
k ~ z ~ l [ k ~k p~ ([A-lo ~-
- rtl)
(11)
is somewhat higher, i.e., the relative contribution of reaction 1 Is higher. Furthermore, any un~ ~ 0 a larger uncertainty certainty in 1 ~ introduces into kA-, the higher the value of the ratio 11. For this reason, and also in order to obtain a sufficient degree of hydrolysis, we employed higher - values of [A-l0 than in the case of acetate. In spite of this, the reaction is comparatively slowonly about 2 to 3 times faster than in pure water. Figure 1 shows that ICA- as defined by equation I is constant during each runlaand does not change appreciably from one run to the other, in spite of the variations in [A-Io and [HAl0. This fact confirms the rate equation assumed. The average value of the rate constant is ~ C H ~ C I C O O= -
57.3 f 2.2 mole-' 1. see.-'.
The Reaction in the Presence of Formate.The details of 3 runs again are shown in Table I. Figure 2 shows that the appropriate second order plots again yield straight, parallel lines. From the slopes we get ~HCOO-=
193 i 3.5 mole-' 1. see.-'
Unfortunately, formate is oxidized by chlorine. Whereas this reaction may be assumed to be too slow to make itself felt during the 0.07 sec. of observation, it somewhat affects the reliability of the analysis of the reaction m i ~ t u r e ,and ~ therefore (4) A. Lifshitz and B. Perlmutter-Hayman, Bull. Research Council l w a e l , SA, 200 (1960). (5) According to J. Thamsen (Acta Chem., Scand., 7 , 6 8 2 (1953)) the reaction takes place between formate and chlorine at a specific rate of 8.1 mole-' 1. eec.-L at 25'; the rate constant has not been measured at other temperaturea but may be expected to be appreciably lower at
ASSALIFSHITZ AND B . PERLYUTTER-HSYMAN
702
Vol. 66
TABLEI DETAILSOF EXPERIMENTS CARRIED OUT IN THE PRESENCE OF VARIOUS BASES Ka
Base
mmole 1. - 1
xo
49.0
Xe
14.15
[HAlo
-
[A-lo
kA-,
mole-’
1. sec.-l
39.8 48.8 48.2 50 12 53 7 61 95
I
-AH4 (kcal. mole-’)measured calcd.atb
50 4 146 57 10.65 148 60.5 7.10 53.5 30 5 14.6 291 55 7 45 51.3 14.35 23.7 192 189 5.78) HCOO35 9 252 194 63.0 16.1 0 250 196 6.18 SO*“ ’1.70 X 57.6 ... 0 212 -19 ... ... CHCLCOOd ~ X 5lo-’ 72.0 ... ... 0 308 ~ 1 6 ... ... a R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworths Scientific Publications, London, 1955, p. 496. 0 See reference 22. H. S.Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” Reinhold Publ. Corp., New York, N. Y., 1950, p. 514. “Handbook of Chemistry and Physics,” 40th ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1958, p. 1744.
...
The Reaction in the Presence of Phosphate, HP04=.--Tn the presence of HP04=a t initial concentrations between 0.028 and 0.035 M , all the thermistors registered identical temperature effects. This means that already a t the first thermistor, or after 8 msec., the amount hydrolyzed was equal to X e , and A T , had been reached-within the limit of experimental error. If we assume that the first nieasured value is actually equal to at least 0.95 (AT, - AT,), we can calculate a lower limit for the rate constant, vix.
h
H v
-48 X
12
i
k7 I
11
3 0
’”
6
5 10 $2
12
+ 9
k~p~,;
2
. .11
11
F!
2 10
lo
Y
0
0.01
0.02
0.03
0.04
0.05
f k 11 - q]dt, sec. Fig. l . - [ k ~ ~ ~ / k ~+- [a-], - a]-’ X L ( z ) against “corrected time”8,4 s (1 - ,+,)&, where L is defined by L = in [ ( k ~/ ~k o~ -+ [A-Io - z ) / ( a - x)]. Straight parallel lines confirm the assumed rate law. Reactions in the presence of chloroacetate.
. 20
20
h
ti
G, X 15
-
l5
rl
El
20
I lo 0
I
l5
-Fri 15 +
20
B 10
1
6-. 15
15
v
10
10 0
Fig. 2.-As
0.02 0.03 0.04 0.05 0.06 J k [l - q]dt, sec. in Fig. 1. Reactions in the presence of formate.
0.01
of the dilution ratio, and of the initial concentrations. On the other hand, according t o E. 4. Shilov and A. I. Slyadnev ( J . Phys. Chem (U.S.S.Z.), 22, 1312 (1948); Chem. Abstr., 45, 2495 (1949),formic acid also is attacked, though much more slowly.
9.5O.
2 2.5 X lo4 mole-’ 1. sec.-l
(The arbitrariness of this assumption does not materially affect the result.) ( I n order to slow down the reaction rate as far as possible, we did not employ HPO,= in excess, but rather at concentrations approximately equal to those of chlorine. I n some experiments, [HPO4=Io was even somewhat lower than a. It is interesting to note that in these cases the initial “instantaneous” temperature drop was followed by an additional small change lvhich QTas much slower. Clearly, this is due to a further reaction, namely that between chlorine and the H2P04- formed in the first, rapid part. We did not attempt to calculate ? C H ~ P O ~from this qualitative observation. The Reaction in the Presence of Dichloroacetate and Sulfate, S04=.-The details again are shown in Table I. I n the presence of these two comparatively weak bases we employed high values of [A-],, and chose [HAIo = 0. I n spite of this, the degree of hydrolysis vas small, so that ( A T , ATo) was low (only about -0.1’) and the percentage error in the measured values of ATt was larger than usual; furthermore, the contribution of reaction 1 now predominates over that of reaction4. For these two reasons, the experimental results cannot be expected to be very accurate. Therefore, certain approximations in the calculation of ICA- seem to be justified and we used the rate equation kHzo + kA- [A-l = 1.07 K ~
+ 3xe2
d In (2, - xt) dt
(W
Kh[r-]/Ka (Kh representing the hy%,here K drolysis COrlStant Of chlorine), [k-]iS the mea11
KINETICS OF
April, 1962
THE
HYDROLYSIS OF CHLORINE
value of [A-] during the reaction, and the factor 1.07 is the mean value of the expression ( K 3xe2)/(K xe2 xext xt2)-which actually changes gradually from -1.14 for xt = 20 to 1.00 for zt = ze. We thus ___ obtain approximate values of (kxI,o kA- [A-3) from simple first order plots of ln(ATt - AT,) vs. time. The experiments are not sufficiently accurate for a reliable calculation of AH,. Discussion The Br@sted Catalytic Law.-Our results show that k ~ is- higher the weaker the acid HA. In - pK,, including the Fig. 3 we plotled log k ~ vs. values obtained previously for water2 and acetate.a (The value of k E z O was divided by 55.5 to make it comparable t o all the other rate constants which are second order; similarly,6 we used K H ~ o = + 55.5.) We drew a straight line through the two most reliable points, acetate and monochloroacetate; the points for the other 4 bases are seen to deviate only slightly from this line. We thus get
+
+
703
+
+
+
k ~= - : 1.6K,-0-6‘
1 2 3 4 5 pKa. dependence of log k ~ on - pKa.
- 2 - 1 0 Fig. 3.-The
(IV)
This means that reaction 4 obeys the BrZnsted catalytic law.7 Discussion of Reaction Mechanisms.-The Brgnsted law usually applies to general base catalysis, or to other rea,ctions involving rate-determining proton transfer. However, a linear free energy relationshipsa is conceivable between the acid-base equilibrium and a reaction of the type Cls
+ A- +AC1 + C1-
(5)
Such a relationslhip also might leads to eq. IV. We therefore shall not consider the applicability of the Brflnsted Law as a conclusive proof for a mechanism involving proton transfer, and shall include in our discussion a reaction scheme which involves rupture of the C1-C1 bond in the ratedetermining stepl, namely reaction 5 followed by AC1 .+- HzO +AH
+ HOCl
(6)
(reaction scheme AI0). Other mechanisms to be discussed are either a one-step mechanism (reaction 4 as it stands), or Clz
+ HzO + A- +HOClz- + HA
+ C1The mechanism Clz + He0 +H&lO+ + C1HOClz-
----ic HOCl
(7) (8) (9)
(6) See R. P.Bell, ” Acid-Base Catalysis,” Oxford University Press, London, 1949, p. 45. (7) J. N. Brpinsted sirid X. J. Pedersen, 2. phusdk. Chem., 108, 185 (1924). (8) See, e.g., A. A. Frost and R. G. Pearson, “Kinetics and Mechanism,” John Wiley and 13ems, Inc., New York, N. Y., 1953, (a) p. 214 ff., (b) p. 118. (9) A correlation between “catalytic constant” and basic strength seems to exist in many reactions where we see no room for proton transfer. See, for instance, 13. M.Dawson and N. B. Dyson, J. Chem. Soc., 49 (1933), for the hydrolysis of bromoacetic acid; F. J. W. Roughton and V. H. Booth, Biochem. J., 32, 2049 (1948), for the hydration of Con (the reaction between COz and OH- which the authors consider to be uninfluenced by other catalysts may be interpreted as catalysis by OH-); A. Lifahitz and B. Perlrnutter-Hayman, J . Phys. Chem., 65, 2098 (1961), for the hydrolysis of CrzOv-. (10) See A. Lifshitz and B. Perlmutter-’Hayman. Bull. Ressarch Council Ismel, AS, 160 (1959), where ABr is suggested as one of two possible intermediates in the hydrolysis of bromine.
0
0.01
0.02
0.03 0.04
0.05
So( I - p)dt, see. of the expression (LA-], 4- kale /kA-).log + / k ~ -- z) - a log ( a = L’(z) against f (1 - dt, for reactions in the presence of acetate. Straight Fig. 4.-Plots
(L.i-10
~
H
~
5)
O
p)
lines would correspond to reactions 7 or 9 constituting a rapid pre-equilibrium. H&lO
+
+ A- +HA + HOCl
(10)
can be discarded immediately, since it does not account for the accelerating influence of A-, unless 9 is a rapid pre-equilibrium. However, the assumption that either reaction 9, or reaction 5 or 7 should constitute a rapid equilibum in their respective reaction schemes is not compatible with our kinetic results. For 5 or 9 to be a rapid equilibrium, the rate of reaction would have to be inversely proportional to the concentration of the chloride formed during the reaction, and the integrated form of the rate equation would be (LA-10 -I- kHlO/k.4-)
a In ( a
- zt)
In ([A-lo =
So“
(1
+
~ H Z O / ~ A -
- zd -
- p)dtSj4 _= 2.3 L’ (z)
(V)
Fig. 4 shows the appropriate plots for 3 typical experiments in the presence of acetate (taken from our previous paper3). Curved lines are obtained; this indicates that equation V does not fit our results. For reaction 7 to be a rapid pre-equilibrium, the reaction rate should be inversely proportional
ASSA LIFSHITZ AND B. PERLMUTTER-HAYMAN
704
Vol. 66
+
to ([HA], z t ) ; inspection of Table I and of the data reported for acetate-acetic acida shows that this is not the case. Furthermore, when acid and base are involved in a rapid pre-equilibrium, as in 7, we should expect spec> 1.3 X lo2 moles-’ 1. sec.-l. This assumption is a very reasonable one in view of the fact that the analogous c o m p o ~ n d s ~X3~ J are ~ known15 to be in mobile equilibrium with Xz and X-. Invoking again the principle of microscopic reversibility, we see that reaction 8 can be a fast following reaction under our experimental conditions. l6 Now, on the basis of our results both reaction scheme B and a one step reaction represent possible mechanisms. In fact the difference between them might seem trivial. In both schemes there is a rate-determining proton transfer from a water molecule to A-, and the concomitant formation of a chemical bond between the OH- of this water molecule and one of the chlorine atoms in Clz. The only difference is that in the one-step reaction the C1-C1 bond is broken simultaneously with all these rearrangements, whereas in scheme B it survives for a short but finite time after the reacting system has passed the main energy barrier. That the differentiation between the two is nevertheless meaningful17 is perhaps brought out more clearly when me again consider the back reaction. In scheme B the rate will be proportional to the -possibly small-concentration of C12OI-I-, and the number of collisions between this substance and HA. On the other hand, the rate of the one-step reaction is proportional to the number of ternary collisions. Now, theoretical considerations seem t o show that the binary collision frequency in solution is somewhat higher than in the gas p h a ~ e . 8 ~ J ~ , ~ ~ The same considerations lead to the conclusion k6’ >> k ’ ~ ~[Cl-1, or [Cl-]
