THEEFFECTOFELECTROLYTESUPONTHERATEOF HYDROLYSIS O F DIETHYL ACETAL1s2 LEONARD C. RIESCHa
AND
MARTIN KILPATRICK
Laboratory of Physical Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania Received August $3, 1934
.
The kinetic method for the determination of the dissociation constant of benzoic acid in potassium chloride solutions has been shown to yield results in agreement with the electrometric method (7, 10). In order to determine the dissociation constants of acids in solutions of other salts, it is necessary to calibrate the reaction for these salt solutions. This involves a study of the primary kinetic salt effect of the reaction. The present paper extends the study of Kilpatrick and Chase to eight solvent salts. The results are not only of value for th.e determination of hydrogen-ion concentrations, but in themselves they are of interest as a study of primary kinetic salt effect in a reaction of the zero kinetic type, Ao + B- --+ products. The rate-determining step may be regarded as the formation of the complex as postulated by Bronsted (2,3) or the decomposition of the intermediate complex in equilibrium with the reactants (1). In either case the equation which expresses the kinetic salt effect for this type of reaction is In
k 3 0 +=
In kko+
+ (P + P’
- P”>C
(1)
where lC~~o+ represents the velocity constant for molar hydrogen ion a t the concentration C of the uni-univalent salt, and is the velocity constant for molar hydrogen ion a t zero electrolyte concentration. P is the salting-out constant for acetal in the equation, Info = PC
(2)
1 An abstract of this paper was presented a t the Eighty-sixth Meeting of the American Chemical Society, held a t Chicago, Illinois, September, 1933. Abstracted from the dissertation of Leonard C. Riesch which was presented to the Faculty of the Graduate School of the University of Pennsylvania in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June, 1934. George Lieb Harrison Fellow in Chemistry, 1933-1934. 561
562
LEONARD C. RIESCH AND MARTIN KILPATRICK
and 8’ and p” are the salting-out terms for the ions in the expression, lnf =
- adi? + 8’
(or p”)C
(3)
where p, p’, and p” depend upon the specific electrolyte. Equation 2 has been shown to hold over wide ranges of concentration in certain cases (11). Equation 3 would not be expected to hold over a wide range of concentration. An examination of the results in the literature indicates that the magnitude of the electrolyte effect varies greatly. Two typical examples are given in figure 1, in which log
C
kH30f
log
k’30+
is plotted against the
electrolyte concentration C.
acefm -Iodine Reucfion
I
I
I
2
I
I
-
4
J
€/ecfm&Te Concentrcrton Mo/arr/fy
FIQ. 1. THEVARIATIONOF TEE B VALUESWITH ELECTROLYTE CONCENTRATION 0,KCl; A, NaCl; 0 , LiCl; @, KN03; V, NaN03
The points represent the values of B , which equals 2.3 ( p + 0’- p ” ) , a t the various concentrations. It is to be noted that in the case of the acetone-iodine reaction B is small and fairly constant, while in the case of the hydrolysis of sucrose B decreases until an electrolyte concentration of approximately one molar is reached, after which B remains almost constant. For small values of B and low concentrations, equation 1 reduces to the form, kHS0+ = k&O+
+ xc
(4)
EFFECT OF ELECTROLYTES ON RATE OF HYDROLYSIS
563
This equation has been subjected to many experimenta! tests in dilute solution and has been shown to hold within the accuracy of the measurements (4). In the case 6f diethyl acetal the B value is large, and equation 4 cannot be expected to hold, but through the range of concentration where equation 3 is valid, log kH,O+should be a linear function of the concentration. A few experiments reported by Bronsted and Wynne-Jones (6) apparently show this to be the case. Bronsted and Grove ( 5 ) have studied the primary salt effect in the hydrolysis of dimethyl acetal, and find that while the magnitude of the effect depends upon the particular electrolyte, equation 1 holds up to a concentration of 0.2 molar. The results reported herein indicate that equation 1 does not hold very exactly even in dilute solutions, but that B becomes 'fairly constant at high concentrations. EXPERIMENTAL PART
The course of the reaction was followed dilatometrica.lly, the apparatus and the method of calculation being the same as that used by Kilpatrick and Chase (10). The acetal was purified by fractional distillation after treatment with anhydrous potassium carbonate, the fraction boiling between 102.5-103°C. (760 mm.) being used. It was essential that the acetal be free from acidic impurities. Frequent tests for acidic impurities were made by adding 0.5 cc. of acetal to 50 cc. of carbon dioxide-free water containing bromothymol blue. During the course of the work it was found necessary to keep the acetal in tightly stoppered bottles to prevent the formation of acetic acid. Apparently a trace of moisture and acid result in the hydrolysis of the acetal to acetaldehyde, which on oxidation yields acetic acid thereby increasing the amount of acid present and the rate of hydrolysis. The salts were purified when necessary. The sulfonates were recrystallized several times from alcohol after decolorization with activated charcoal. An inspection of table 1 indicates that there is apparently a slight o + increasing concentration, and a difference between increase in k ~ ~ with the acids; however, this is probably within the experimental error of the measurements. We have therefore taken k$o+ as 2.469. Table 2 gives the results with lithium chloride solutions. The magnitude of the electrolyte effect is thirteen-fold a t three molar, and even at 0.2 molar it is 27 per cent. Table 3 summarizes the kH30+values for the other salts. The specific effect of the various salts is evident. The kHIO+ values vary over 100 per cent a t some concentrations. Table 4 gives the B values calculated as for figure 1, From this table it is evident that the B values are much greater than those given in figure 1 for other reactions,
,
564
LEONARD C. RIESCH AND MARTIN KILPATRICK
TABLE 1 f
Results at low electrolyte concentration
.4CID
CONCENTRATION
(OBSERVED)
,k/ca,cid = kHaO+
k
moles per liter
.
HCl.. .. . . . . . . . . . . . . . . . . , HC1. . . , , . . . . . . . . . . . . . . . . HCl.. , . . . . . . . . . . . . . . . . . . , HC1.. . . . . . . . . . . . . . . . . . . , HCl.. . , . . . . . . , . . . . , . . . . . . HC1. . . . . . . . . . . . . . . . . . . . . ,
0.00502 0.010096 0.01004 0.01004 0.01506 0.02008
0.01221 0.02478 0.02456 0.02447 0.03736 0.05021
2.432 2.454 2.445 2.439 2.480 2.501
HNOa . . . . . . . . . . .
0,00510 0.01020 0.01020 0.01530 0.02040
0.01244 0.02507 0.02569 0.03776 0.05066
2.439 2.458 2 ..520 2.468 2.484
.. . . . . . . .
0.00510 0.01020 0.01020 0.01530 0.02040
0.01246 0.02559 0.02497 0.03803 0.05104
2.443 2.508 2.447 2.485 2.502
.
HClO4..
TABLE 2 Electrolyte e$ect at 0°C. in lithium chloride solutions HC1
LiCl
moles per liter
moles per liter
0.010096 0.010096 0.010096 0.010096 0.010096 0.010096 0.010096 0.010096 0.010096 0.010096 0.005048 0.005048 0.005048 0.003029 0.002019
,
0.040 0.090 0.140 0.190 0.240 0.290 0.390 0.490 0.590 0.790 0.995 1.495 1.995 2.497 2.998
k (OBSERVED)
0.02620 0.02819 0.02967 0.03164 0.03296 0.03432 0.03781 0.04182 0.04564 0,05406 0.03185 0.04782 0.07310 0.06588 0.06892
2.60 2.80 2.95 3.13 3.27 3.40 3.75 4.14 4.52 5.35 6.31 9.47 14.48 21.75 34.13
E F F E C T O F ELECTROLYTES ON RATE O F HYDROLYSIS
565
and that equation 1 is only approximately in agreement with experiment even in dilute solution. The value of B apparently decreases with concentration and becomes fairly constant a t the higher concentrations. If the assumption that equation 2 holds js correct, the change in B must be due to the fact that equation 3 does not express the change of the activity coefficient of the TABLE 3 k ~ ~ at o 0°C. + for various electrolytes
- __ ELECTROLYTE CONCENTRATION
NaCl
KCI
2.58 2.76
2.79
NaCIO4
CeHaSOaNa
2.55 2.63 2.73 2.81 2.89 3.06 3.19 3.35 3.47 3.65 3.75 3.97
--LiNOs
NaNOa
KNOa
2.77
2.72
2.74
3.05 3.30 3.55 3.85 4.14
3.01 3.19 3.50 3.76 3.95
2.89 3.09 3.31 3.51 3.73
4.80
4.43
5.51
4.99
4.08 4.27 4.49 4.62 4.88
7.85
6.51
10.98
8.32
15.06 21.08
10.60 12.97
moles per lite1
0.05 0.10 0.15 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.oo 1.10 1.20 1.25 1.50 1.75 2.00 2.25 2.50 3.00
3.08 3.43 3.73 4.08 4.48
3.73 4.37
2.61 2.84 3.04 3.21 3.60 4.04 4.52 5.01
5.27
5.08
5.98
6.16
5.74
7.08
3.11
7.47 9.09 7.95 10.44 10.83 12.43 13.06 10.96 15.15 15.69 18.49 18.90 14.34 22.43 27.64 19.42 31.50
2.58 2.68 2.74 2.82 2.93 3.06 3.23 3.40 3.49 3.63 3.75 3.80
4.45 5.04 5.62
ions with increasing electrolyte concentration. equation 3 is
The more exact form of
where b is the mean ionic diameter of the given ion and the ions in the solution. Other equations of this type have been used by other investigators (13),’but in all cases for this type of reaction the resulting equation for the salt effect has the same form as equation 1.
LEONARD C. RIESCH A N D MARTIN KILPATRICK
-
I
?
-T 6 e1 h
r 3 . w
z 6
w
-9.
s m
mm.lrl0
t-wwmm
0 0
0
0 0 0 0
0 0 0 0 0
83 v
M
"M?"
""l""
567
EFFECT OF ELECTROLYTES ON RATE OF HYDROLYSIS
The temperature coeficient The acetal reaction is so sensitive to hydrogen ion that k ~ o +cannot be determined accurately by direct measurement above 0°C. The method employed was the two-thermostat method of Rice and Kilpatrick (12). Portions of the same solution were placed in two similar dilatometers in
HC1 (APPROX.)
I
moles per liter
TABLE 5 Electrolyte effect on the temperature coeflcient SALT
I
kslkas
I
moles per liter
3.372 3.402
DEVIAZTZf~$RROY
calories
cnlories
-
0.0001 0.0002
I
E
22,199 22,360
124 37
22,474 22,458 22,600 22,843 23,139 22,611 22,388 21,666
151 138 277 520 816 288 65 657
22,270 22,963 21,934 21,277
53 640 389 1,046
KC1 0.00015 0.000125 0.0001 0.00004 0.00004 0.00004 0.00004 0.00004
3.423 3.420 3.447 3.493 3.550 3.449 3.407 3.275
0.10 0.50 1.oo 2.00 2.00 3.00 3.00 3.00
NaCl 1.oo 2.00 2.00 3.00
0.00007 0.00004 0.00004 0.00004
1
0.0001
1.00
3.385 3.516 3.323 3.206
I
3.326
1
21,949
j
I
21,942
1
~~
374
KNO:
I
3.325
...... . . . . . . . . . . . . , . . .
3.395
0.00005 Average.
1
3.00
I
I
22,323
-1
,
381
-1370
thermostats a t 35°C. and 25"C., respectively. The temperature interval was determined by a calibrated resistance thermometer, and the thermostats were controlled to f 0.005"C. Equivalent portions of acetal were added to each and kobsd. was calculated in the usual manner. The quotient k36/k26 yielded the temperature coefficient directly. Table 5 gives the results and the energy of activation calculated from the Arrhenius equation.
568
LEONARD C. RIESCH A N D MARTIN KILPATRICK
Apparently the value of the energy of activation remains constant in the presence of neutral salts within the experimental error of measurement. DISCUSSION
As already stated the results cannot be expressed by equation 1. Upon examination the deviations are found t o be hyperbolic functions of the concentration. Equations which express the experimental results within 2 per cent are given below.
+
NaC104 log k = 0.392 0.62C LiCl log k = 0.392 0.5%' NaCl log R = 0.392 0.55C log k = 0.392 + 0.53C KC1 LiN03 log k = 0.392 0.50C NaN03 log L = 0.392 + 0.45C KNOa log k = 0.392 + 0.43C CGH~S03Na log k = 0.392 0.40C or p-CsH4(CH3)SOaNa
+ + + +
(40.0576 + 0.104C2 - 0.24) (40.00292 0.0482C2 - 0.054) (l/O.OlO + 0.0535C2 - 0.10) (40.0256 + 0.07870 - 0.lG) (40.0049 + 0.0438C2 - 0.07) (40.0225 + O.OG39C2 - 0.15) (d0.0144 + 0.0697C2 - 0.12) (40.000225 + 0.0418C2 - 0.015)
+
TABLE 6 Correlation between velocity constant and acidity junction KC1 IN MOLES
PBR LITER
0.00
1 .oo
2.00
3.00
1
HO
log k
0.389 0.759 1.040 1.288
1.05 0.88
0.75 0.60
log k
+ Ho
1.44 1.64 1.79 1.88
Mammett (8, 9) has recently tried t o show a relationship between the velocity constant of a reaction and the acidity function. He finds that the rate of the inversion of sucrose, and the rate of the hydrolysis of ethyl acetate and cyanamide in salt solution, can be expressed by the equation: log k
+ Ho = log
k2
where k is the velocity constant of the reaction, Ho, the acidity function, is equal to - log uH+ fB/fHB, and kz is a constant. In order t o test the relationship for the acetal reaction, our values of log k and the corresponding H Ovalues for potassium chloride solutions determined by Hammett are given in table 6. The last column shows that log IC2 is not constant. I n the case of the inversion of sucrose by trichloroacetic acid Hammett interprets the lack of constancy as indicating general acid catalysis. In the case of the acetal reaction it might seem that catalysis by acids stronger than H30+ exists.
EFFECT OF ELECTROLYTES O N RATE OF HYDROLYSIS
569
The order of the effect of the anions is Clod > C1 > NO3 > RSOs, which might favor this view. However, the fact that changing the concentration of the hydrogen ion does not change the value of kH30+ argues against this view. If molecule cata.lysis were present an increase in the concentration of H30+ should alter the ratio of acid molecule to hydrogen ion and k ~ ~ o calculated +, on the assumption that the hydrogen ion is the sole catalyst, should vary. Further evidence against the view that acids other than H30+catalyze this reaction will be presented in a later paper. SUMMARY
1. The primary kinetic salt effect of nine saltp has been determined for the hydrolysis of diethyl acetal catalyzed by strong acids in aqueous solution. 2. The temperature coefficient has been determined, and the heat of activation was found to be independent of the electrolyte concentration within the experimental error of measurement. 3. The reaction has been calibrated to determine the hydrogen-ion concentration of buffer solutions. REFERENCES
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
BJERRUM: Z. pbysik. Chem. 108, 82 (1924). BRONSTED:Z. physik. Chem. 102, 169 (1922). BRONSTED:Z. phyaik. Chem. 116, 377 (1925). BRONSTED:Trans. Faraday SOC. 24, 630 (1928). BRONSTED AND GROVE:J. Am. Chem. SOC. 62, 1394 (1930). BRONSTED AND WYNNE-JONES: Trans. Faraday SOC.26, 59 (1929). CHASEAND KILPATRICK: J. Am. Chem. SOC. 63, 2589 (1931). HAMMETT AND DEYRUP: J. Am. Chem. SOC. 64, 2721 (1932). AND PAUL: J. Am. Chem. SOC. 66, 827-32 (1934). HAMMETT KILPATRICK AND C H A S ~J. : Am. Chem. SOC. 63, 1732 (1931). OSOLAND KILPATRICK: J. Am. Chem. SOC. 66, 4430 (1933). RICEAND KILPATRICK: J. Am. Chem. SOC.46, 1401 (1923). See SAMARAS: J. Phys. Chem. 37, 436 (1933).
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