M . A. ROSANOFF AND H . M. POTTER.
248
CORRBCTION. On page I 74 of the February number read K On page 176 (near the bottom) : read stead of . .
. - 5 K-K’).s
=
k,’
k , e e , instead of k =KO&.
.... -
‘-0
ko”
~(K-K”S
=
K , in-
K.
[CONTRIBUTION FROM THE CHElluCAL ~ABORATORX&S OF CLARK UNIVERSITY.]
A RE-IIWESTIGATIOff W THE VELOCITY QB SUGAR HYDROLYSIS. SECOND COMMUNICATION: THE ROLE OF WATER.I B Y M. A. ROSANOFF AND H. M.POTTER. Received January 13, 1913.
In a former communication it was shown that sugar hydrolysis is strictly unirnolecular with respect to the sugar itself. In the present communil be made to show that water plays a double role an attempt d in the reaction: on the one hand, it takes part in the reaction and contributes to its velocity according to the law of mass action; on the other hand, it acts as a negative catalyzer by its dissociating power. With respect to this retarding effect, the reaction will be shown to follow a catalysis primiple which is also obeyed by several other reactions investigated here within the past few years. I . The Anomaly of the Reaction. In course of his classic researches on the strength of acids, Ostwald discovered a puzzling anomaly in the hydrolysis of cane sugar: contrary to the mass law for a unimolecular reaction, the velocity of hydrolysis was found to be a function of the initial concentration of the sugar.2 Shortiy afterward Spohr advanced the idea that the cause of this phenomaion lies in the changing ratio of the concentrations of acid and water : the less sugar in the solution initially, the more water, therefore the “weaker” the acid and the slower the hydrolysis.3 Three experiments reported by Spohr, in which different amounts of sugar were dissolved in equal amounts of tenth-noma1 hydrobromic acid, appeared to support this view, the three velocity coefficients being equal, or nearly so. But similar experiments with formic acid carried out in these laboratories have yielded velocity coefficients varying regularly with the initial amount of sugar. This shom that Spohr’s observation was not of a general character and, hence, that his explanation of the anomaly is incorrect. Kor does the explanation appear plausible in the light of the dissociation theory: the more water in place of sugar, the greater must be the dissociaz
Presented befor? the New York Section of the Am Chem Soc. on October
It)[?
Ostwald J pn~kt Llzem , [ z ] S ~ n l i r Ibid 33, 2 6 - (18%)
31, 3xci
I
11,
RE-INVESTIGATION OF THE VELOCITY OF SUGAR HYDROLYSIS.
249
tion of the acid, and hence the greater its catalytic power; while in Ostwald’s experiments a decrease in the initial amount of sugar resulted in a decrease of the reaction velocity. A new interpretation was proposed in 1897 by Ernst Cohen.’ This investigator believes that in a more concentrated solution the reaction is faster because the available volume is smaller, the sugar molecules filling, and rendering unavailable, part of the volume. Accordingly, he introduces an impirical volume, correction analogous to the quantity b of the van der Waals equation and to the similar correction proposed by A. A. Noyes for van’t Hoff’s ideal law of osmotic pressure.2 If, however, we consider’that according to the mass law the velocity of hydrolysis should be the same whether the volume (or its reciprocal, the initial sugar concentration) is large or small, whether the whole of the apparent volume is available or not, Cohen’s volume correction appears to emphasize the discrepancy between theory and fact, rather than account for it. Still another idea, advanced by A r r h e n i ~ s may , ~ be briefly stated as follows: The law of mass action, as deduced by van’t Hoff thermodynamically, refers, not to concentrations, but to osmotic pressures. The customary employment of volume concentrations in place of osmotic pressures is admissible only a t infinit dilution. At finite concentrations i t is erroneous in principle and must lead ,to apparent discrepancies like that found by Ostwald. No discrepancy should appear if the mass law were applied to the osmotic pressures involved. Unfortunately, the partial osmotic pressures of cane sugar in solutions undergoing inversion and containing both cane sugar and invert sugar, are unknown. Nevertheless, we were able to test Arrhenius’ idea indirectly. If, namely, we assume, with Arrhenius, that active masses are to be measured by osmotic pressures, and denote by 7c the pressure at the time t , we get: dz/dt = - hn. We must expect, then, that the relative change of x per unit time will be constant during a single process and the same for different processes independently of the initial osmotic pressures involved. Denoting by 7ro the initial osmotic pressure and integrating : I
-
t
log
= k. x T O
For pure cane sugar solutions Arrhenius gives:4 G = o.0541(+ 0.0132+~),
+
Cohen: 2. physik. Chem., 23, 442 (1897).
A. A. Noyes: 2. physik. Chem., 5, 53 (1890). Arrhenius, Ibzd., 28, 319 (1899). Arrhenius, Ibid., 28, 320.
M. A. ROSANOFF AND H. M. P O W E R .
250
where G is the depression of the freezing point (which is very nearly proportional to the osmotic pressure) and p is the number of grams of sugar per IOO cc. of solution. If this expression held true also in the presence of invert sugar, then, substituting' 0 ,5504 ( a- urn ) for fi, we should have:
As a matter of fact, owing t o the presence of invert sugar, the osmotic pressures here taken into account are more or less different from the true partial osmotic pressures, and therefore the velocity coefficient k calculated from the observed rotations cannot be expected to remain constant. But if the calculated coefficients are plotted against the time, extrapolation to t = o must give the true value of the coefficient k for osmotic pressure; for in the beginning of the reaction no invert sugar is present, and as t = o is approached] the unknown partial osmotic pressures approach the known osmotic pressures of pure sugar solutions. (We neglect, with Arrhenius, the presence of acid.) Applying this process to Ostwald's four series of different initial osmotic pressures] we expect, then, the four extrapolated values of k to be the same, if Arrhenius' view of the anomaly is correct and it is the relative variation of osmotic pressure, and not of volume concentration, that should be the same for the different solutions The results are shown in Tables I to I V below. Since Ostwald counted time from the arbitrary instant of the first reading, while our extrapolation requires knowledge of the time a t which the reaction really began, we assumed the true a, to have been 14.04' in the IO% solution (according to Ostwald, Zoc. czt., p. 309) and proportional to the percentages (grams per IOO cc.) in the remaining solutions It was then easy to calculate the initial times and change correspondingly the t's recorded by Ostwald TABLEI . S O L U T I O N CONTAINING 40 GRAMSOF SUGAR PER k X 10'
t (min ). 0 11
7' 127 178 226 351 W
9
U
-IO -I
x
104
tvol concentrations) (osmotic pressures).
56 1 6 O 50.46 28.30 73 60 4 44
-
CC.
IOO
k.
88 87 j .98 I
138.61 28 84 29 2 5 29 21 29 32 29 00
29 I 2
On the basis of Ostwald, loc. c t t . , p. 309.
37.5 36.9 36 0 35 5 33 7
RE-INVESTIGATION OF THE VELOCITY OF SUGAR HYDROLYSIS.
TABLE1 I . S O L U T I O N
CONTAINING 20
1
a.
13.2 64 127 I77 225
350 m
GRAMS OF SUGAR PER 100 cc. k x 104 k . X IO4
(vol. concentrations).
28.08~
0
25 I
25.62 16.76 I O . 30
6.00 2 ' 74 - 2.61 - 8.35
(osmotic pressures).
... ...
b7.3 1
22.66
....
22.85 22.82
26.6 26.2
22.91
26.0 25.3 ....
....
22.88 ... 22.82
TABLEI I I . S O L U T I O N
CONTAINING IO
GRAMS OF SUGAR PER
k X IO' (vol. concentrations).
cc.
100
k . x 104 (osmotic pressures).
t.
a.
0
14.04'
... ...
....
71
12.90 8.98
20.23
23.I
127 I77
5.94 3.79
20.53 20.81
22.8 22.8 22.5 21 .g
13.8
224
2.25
349 m
- 0.46 - 3.91
20.78 20.52
...
-
[23.41
....
20.57
TABLE1 V . S O L U T I O N CONTAINING 4 GRAMS OF SUGAR PER t.
348 00
IO0
cc.
t& x 101 (vol.concentrations). (osmotic pressures). k X lo4
(1.
5.27 3.82 2 -63 I .88 I .2g 0.09 - I . 42
.... 18.63 19.46 19.12
18.88 19.40
.... .... 19.6 19.3 19.2
....
19.IO
The bracketed figure in the fourth column.of each table represents the velocity coefficient found by graphic extrapolation to t = 0. In the course of each series the coefficients based on vblume concentrations remain constant, those based on osmotic pressures diminish regularly. The latter coeflFidents would come out constant if, owing to the appearance of invert sugar, the true osmotic pressures of cane sugar were proportional to the volume Concentrations. In that case,however, there would be no advantage in htroducing osmotic pressures in place of the usual volume concentrations.
2 -52
M. A . ROSAKOFF .4ND H . M. POTTER.
But what concerns us most in the present connection is that the four extrapolated coefficients, =,E! 6, 2 ; >, 23 4, and 19 7 ) are unequal; 1. t , that the relative variation of osmotic pressure is by no means independent of the initial osmotic pressures of the solutions.‘ .4nd so it is plain that whether osmotic pressures or volume concentrations are used in connectior, with the law of mass action, this law alone is incapable of fully describing the phenomena of sugar hydrolysis New Theory. I n a previous communication2it was shown that in the course of any single experiment sugar hydrolysis is strictly unimolecular with respect to the sugar itself, in accord with the stoichiometric equation: C,,H,,Oll 4 H,O = C,H,,O, C,H,,O,. There is no doubt but the reaction follows the mass law also with respect to the reacting water; so that if S represents the initial concentration of the sugar, W the initial concentration of the water, and x the amount of sugar inverted a t the time t , the reaction proceeds as follows: tlx/dt - k ( S --- x)(W x). On account of the large molecular weight of cane sugar, the molar concentration of the water, W, is generally large compared with S and with z, and therefore the equation may be simplified into, dx dt = kW(S -- x). The velocity coefficient” obtained, as usual, by the unimolecular equation is thus the Froduct of the true velocity coefficient L and the water concentration W. I n order to find the true coefficients corresponding to Ostwald’s and Spohr’s measurements, we were obliged to determin how much water was present in their solutions per unit volume. For this purpose we ;eprepared their solutions, weighing the several ingredients, including the water. Ostwald’s four solutions were found to have contained, respectively, 3 9 . 2 S , 46 11, 49 4s and 5 1 43 mols of water per liter. His coefficients, kW x IO*, are respectively 2 9 . 1 6 , 2 2 . 8 7 , 2 0 . 6 3 , and 19.14. Dividing these by the values of W just given we obtain, as the true velocity coefficients: o . 0 0 0 0 7 4 2 , 0.0000496, 0 . oooo4x 7, and 0 . While, unimolecular coefficients change in the ratio of 3 tQ 2 , ted coefficients change in the greater ratio of 2 to I , so that the 2.
+
calculations show that in Ostwald’s four series 0 is proportional h i x e d system of active masses is sfarc matter of fact, $he proportionaiity found by hrrhenius do&s+aotappear at ai4 when the mixed system is applied to the results reported in Tables V I 1 to XI11 of the present communication. - Rosanoff, Clark and Sibley, THE JOI-RTAL, 33, 191; and 1921 ( 1 9 1 1 ) . ~t[ d x / d l ] l =
RE-INVESTIGATION OF
THE VEWCITY OF SUGAR HYDROLYSIS.
253
anomaly is e m greater thaaa it appears when the mass &n of the water is not taken into account. Let us now apply to the reaction the views of homogeneous catalysis recently formulated by one of US.^ According to these, chemical reactions, in general, wodd Be fully described by the mass law only if the influence of medium were reduced to nothing, as in the gaseous state a t Mnit dilution. Under real working conditions, and when the concentrations of the substances forming the medium suffer changes, the mass law must lead to changing velocity coefficients. Such changes, which are outside the scope of the mass law itself, must be subject to a special catalysis law. I n connection with a number of reactions, a general catalysis equation, of which the following is the simplest form, has been found to represent the experimental data with precision: Iz
=
KC
toe
.
Here k is the velocity coefficient of the mass law, C the concentration of the principal substance determining the nature of the mediwm, and K the catalysis coefficient of that substance. In Ostwald’s experiments the medium consisted principally of water, b u t the concentration W of the water was quite differenf.in the four series. From the above point of view, therefore, variation of the velocity coefficient K from series to series must be expected; and since increasing dilution (i. e . , increasing concentration of the water) causes great diminutions of the velocity coefficient, water must be recognized as a powerful negative catalyzer of sugar hydrolysis. Its coefficient K in the above equation should, accordingly, be a negativ constant. Tables 17, VI and XIV show this to be the case. Tables V and VI are based on Ostwald’s and Spohr’s measurements, respectively. Table XIV is based on seven new series of measurements. While Ostwald and Spohr used respectively hydrochloric and hydrobromic acids, we used formic acid to make sure that the anomaly of sugar hydrolysis is not somehow connected with the abnormal properties of strong electrolytes, and also for the purpose of testing the catalysis equation on a more extensive series of experiments than those of Ostwald and of Spohr. Our measurements are reported in Tables VI1 t o XIII. TABLEAPPLICATION Grams sugar per liter.
4* 2 w
Io0
OF THE CATALYSIS
EQUATION TO OSTWALD’S
\xi
(mols water per liter).
39.28 46.11 49.48 51.43
40 Rosanoff, Tms
JOURNAL,
kW.
0,002916 0.002287 0.002063 0.001914 35, 173 (1913).
k observed.
O.OOOO742 0.0000496 O.OOo0417 O.ooOo372
MEASUREMENTS.
k calculated.
0.0000742 0.oO00504
0.0000416 -373
0*
254
M. A. ROSANOFF AND H. M. F'O"&R.
The values under " b calculated " are given by the equation:
k
=
log,, k
o.ooo688~e~0~05669w,
=
4.83778
- 0.024621W.
TABLSVL-APPLICARONOF m CATALYSISEQUATION To Spomt's M ~ J M U R S ~ W ~ ~ . Grams sugar per liter.
300 200 I00 20
k observed.
\V.
kW.
42.71 45.55 48.12
0.002421
5 0 32
0,002047
f
0.002721 0 . CWZIOO(
?)
k calculated.
0.0000637 O.ooOo531 0 .oooo436(?) 0 ooo0407
o.oooo633 o.oooa536 o.ooo0461 o .ooo0406
The values under " k calculated " are given by the equation :
TABLEVII,-HYDROLYSISAT 2 7.00' f 0 . 0 1 5 O,
THE SOLUTION CONTAINlNG PSR
LITER
57.50 GRAMSFORMICACID,400 o GRAMSSUGAR, AND 705.4 GRAMSWATER. t (hours).
LW.
0.
....
1 7 .jo
E74.73'1 53.51
0.00595
20.75
50.64
0.0Oj80
24.39 27.38 30.58 40.83 44.87 48.17
47,:6 44.30 41.46 32 7 5
52.58 65.45 69.75 74.66 7 8 SO
24.72 16.85
0.00563 0.00579 0.00579 0,00583 0.00576 0 .w 5 7 6 0.00576
0
89.50 93.92 98.50 102 58 113.35
co
29.92
27.74
0.00578
14.30
0.00582
11.80
0.00582 0.00579
IO.13
0.00587
4.90 3.50
0.00581
.36
0.00589 0.00587
I
0.Oj
0.00590 .. .
- 3.45 -24.82
Mean kW
w
-
= 0.00581
39.'5
k = 0.0001484
RE-INVESTIGATION OF THE VELOCITY OF SUGAR HYDROLYSIS.
255
TABLE VIII.-HYDROLYSIS AT 27.00 f TABLE IX.-HYDROLYSIS AT 27.00 f o.o15O,THE SOLUTION CONTAINING PER 0.01 5 O, TEE SOLUTION CONTAININ@ PER LITER57.50 GRAMSFORMICACID,300 LITER 5 7 . 5 0 GRAMS FORMIC ACID, GRAMS SUGAR, AND 768.52 GRAMS 200 GRAMS SUGAR. AND 829.60 GRAMS WATER. WATER. [55.p0] 40.36 37.78 35.29 33 .00 31 .oo 24.70 22.63
17.43 20.66 24.28 27.27 30.66 40.75 44.70 48.08 52.45 65.32 69.77 74.77 78.54 89.50 93.92 98.66 102.58 W
kW.
a.
1. 0
20.60
18.50 12.84 11.15 9.45 7.70 4.I5 2.65 1.49 0.50
, ,
.
..
0.00566 0.00572
0.00568 0.00575 0.00568 0.00573 0.00570 0.00576 0.00574 0.00572 0.00570 0.00567 0.005 76 0.00576 0,00581 0.00578 0.00578
.....
-18.30
t. 0
kW.
a.
4.08 5 . IO 7.75 16.75 19.50 20.80 21.70 30.50 30.75 43.08 48.08 65.08 68.08 75.33 80.00 gr .00 93.15 95.15 W-+
Mean kW = 0.00570 W. = 42.65 k 0.0001337
..... 0.00541 0.00549 0.00538 0.00540 0.00545 0.00548 0.00543
[34.7r01 32.40 31.80 30.45 25.95 24.60 23.95 23.65 19.93 19.80
0.00544
0.00545 0.00549 0.00541 0.00538 0.00544 0.00544 0.00537 0.00549 0.00543 0.00545
15.15
I3 ' 73 8.93 7.98 6.28 5.45 2.89 2.69 2.26 -11.85
.....
Mean kW = 0.00544 W -46.04
k
=
0.0001182
TABLEX.-HYDROLYSIS AT 27.00 f TABLE XI.-HYDROLYSIS AT 27.00 f o.0qo,THE SOLUTION CONTAINING PER 0.015 O, THE SOLUTION CONTAINING PER LITER 57.50 GRAMSF o w c ACID, 160 LITER57.50 GRAMSFORMICACID, 140 GRAMS SUGAR, WATER. t. 0
2.83 3.83 10.83 20.83 24.42 31.66 34.75 45.52 49.00 51.17 54.75 58.90 69.90 74.50 78.75
AND
855.52 GRAMS
a.
[29.21~] 27.89 27.44 24.49 20.41 18.82 16.51 15.54 11.91 11.53 IO.84 9.76 9.I7 6.69 5.59 4.76
kW.
GRAMS SUGAR, AND 867.60 GRAMS WATER. t.
. ., .,
0'
0.00549 0.00531
7.33 17.83 20.53 27.33 31.33 42.66 46.90 51.42 55.25 66.05 69.57 73.57 78.90 9 0 . I7 96.52
0.00522
0.00538 0.00556 0.00546 0.00545 0.00566 0,00553 0.00547 0,00554 0.00538 0.00542 0.00550
0.00544
a.
[50.47'] 44.79 37.35 35-40 31.17 29.20
a3.34 21.00
19.26 17.71 13.29 13.02 10.38 8.97 5.35 3.65
kW.
.
.
0.00530
0.00535 0.00543 0.00544 0.00533 0.00532 0.00541 0.00534 0.00532 0.00537 0.00537 0.00543 0.00536 0.00544 0.00546
M. A . ROSANOFF AND H. M. POTTER.
256
TABLEX (contznued). t.
4
82 50
93 16 97 2 5 I O 0 90 106 50 rrg 45
21
0
36 66 I 35 o 64
1.
0 00552
I
00556 o 00548 o 0054; o ooj66
Mean kb'
w
103.90
00547
2
--o 89 -9 4 -
ot.
TABLEXI (continued).
h \cr
0
m
hW.
Ut
0.00546 .....
1.86
-16.60
-
Mean kViT = 0.00538 W = 48.15 k = O.OOOIII~
o 00548 47 48 o 0001156
= =
k = TABLEXII-HYDROLYSIS AT 2 7 00 i TABLEXIII.-HYDROLYSIS AT 27.00 & o 015", THE SOLUTION CONTAININGPER 0 .015O, THE SOLUTION CONTAININGPER LITER57.50 GRAMSFORMIC ACID, 6a LITER57 j o GRAMSFORMIC ACID,100 GRAMS SUGAR,h A D 892 82 GRAMS GRAMS%GAR, AND 916.86 GRAMS. WATER. WATER. t
23
i. 0
u
0
25
!17. 47'1 I I 69
26 z j
IO
29.00
IO
33 08 43 75 47 2 5 50 75 53.08 56 58 67 OS 7' 33 74.50 77.16 81.16 98 33 104.75 116.16
9 45 7 56 6 ;I 6 58 6 06 5 71 4 00 3.39
51.17
j j . 50
65 75 70.17 75.66 79.66 89.45 94.11 99.20 103.45 113.45 '
2.99
2.83 2.26
-
m
53 o 08 56 0
-6
00
21.66 44.25 47.17
91 31
2 . 2 j
O.OOj23, 0.00551 0,00542 0.00540~ 0.00523 o ,005 1j
2 .OS
0.00500.
1.37 1.23 0.42 0.18
0,00533 0.0052 I
0.0543. O.OOj42 0,00534-
4 . 0 2
-0.37 4 . 5 2 -4. I 2
0.00550.
0.00517-
.....
Mean &W = 0.00531 W = 50.88
30
L Mean kW
sn-. .....
