MUTXROTATIOPL’ IV. COXSECUTIVE REACTIONS I S THE MUTAROTATIOPL’ O F GLUCOSE AXD GALACTOSE BY FREDERICK PALLISER WORLET AND JOHN CLARK ANDREWS
Experimental investigation of the mutarotation of glucose has hitherto failed to afford any definite indication that the process is other than the direct attainment of simple equilibrium between CY glucose and p glucose, represented by the equation K1
CY
glucose
-+p glucose. K?
The reaction appears to be strictly unimolecular from each end, but since the velocity is enormously affected by alkalies and to a smaller extent by acids, the catalyst should appear on each side of the equation’, the reversible reaction being probably bimolecular. I n the polarimetric method of following the course of the change, optical rotations of the substances present are taken as proportional to their concentrations. It is found that the rate of change of rotation at a given time is proportional to the difference between the rotation a t this time and a t equilibrium, this ratio being the velocity coefficient. It can easily be shown that this should be the case if the reaction is a reversible unimolecular change or a reversible bimolecular change in which the second reactant on each side of the equation remains constant. Furthermore, the velocity coefficient of mutarotation of LY glucose and ,!3 glucose determined in K P = K. this manner under similar conditions should be the same, viz. Kl If in the reversible reaction
+
K1
CY
glucose
a ,!3 glucose KP
the initial concentrations of LY and ,!3 glucose be a and o respectively, and if the amounts of a glucose converted to ,!3 glucose a t time t and a t equilibrium be xLand xc.respectively, then a t time t dx/dt = K1 (a-xt) - K2xt a t equilibrium
K1 (a-x,)
=
x, =
KZx, Kla KI Kz
+
a t time t dxjdt (a-xt) - (a-x,)
_ _ _dxjdt _ xc. - xt
,308
FREDERICK PALLISER WORLEY A S D JOHS CLARK ANDREWS
- Kl(a-xt) - K2xt
Kla ~-
Ki = Ki
+ Ky
xt
+ K?
Hence in the polarinietric method of following the mutarotation
in which a ~a2, and a , are the rotations a t t,, t 2 and t,. IC2 in The velocity constant as usually determined should t,hus be K1 the case of both a glucose and /3 glucose. It has been amply shown that the reaction over the very large portion investigated is strictly unimolecular and that the velocity coefficients of mutarotation of a glucose and p glucose are identical under similar conditi0ns.l It has also been shown that if a and p glucose be mixed in the proportion calculated to be present a t equilibrium both in the case of water and of methyl alcohol, on the assumption that the reaction is expressed by the abovr simple equilibrium, and dissolved in the respective solvents, there is no detectable change of rotation after dissolution2 indicating that there is no third substance present a t equilibrium capable of detection by the physical method:: employed. These considerations, however, do not eliminate the possibility of mutarotation proceeding in two, or more stages, but show that if an intermediate substance is formed, the rate of its transformation into a and /3 glucose must be very much greater than that of its formation. If the velocity of transformation were a large multiple of that of the reverse change, there would be only a small percentage of the sugar in the intermediate form a t equilibriuni. and, since the physical methods employed in the mixture experiments are dependent on the rr’ife’e,ence between the physical properties of the intermediate form and those of the mixture of a and @ glucose from which it is formed, this small amount of a third substance would not be detected in the experiments. Its formation should, however, be indicated by the course of the reaction at the beginning of mutarotation. If we assume that starting from (Y glucose, the original concentration is ( I and that at time t the amount left is a - y and the amount of the intermediate substance S formed is 5 , the concentration of 6 glucose will be y - x according t>othe equation. Kl L X /3 Glucose a Glucose Ky K, a - y Y y-x
+
a
_______
’Roux: Ann. Chim. Phys., 30, 422 (1903); Hudson and Dale: J. Am. Chem. Soc.. 39, 320 (1917); Andrews and Worley: J. Phys. Chem., 31, 882 (1927). ~ R O I I Ann. X : Chim. Phys., (7) 30, 422 (1903); Riiber: Rer., 56, 2185 (1923); .lndren.s and Korley: J. Phya. Chem.! 31, 1880 (1927).
309
MUTAROTATION
From the fact that there is no detectable amount of an intermediate substance present a t equilibrium] it follows that KP K4 must be large in K3 k. The rate of formation of X comparison with K1 and K3. Let Kl is given by dx/dt = Kl(a - y) K3 (y - x) - (Kz K4) x = K 3 (a - x) k (a - y) - (Kz K4) x If k = 0,dx/dt becomes zero, z reaching a maximum when K3 (a - x) = (Kz K4) x thereafter 2 remains constant during the remainder of mutarotation until equilibrium is attained. If k has a positive or negative value, dx/dt becomes zero and z reaches a maximum when K I (a - x) k (a - p) = (Kz K4) x If k is positive z will reach a maximum and thereafter decrease as a - y decreases until equilibrium is reached. If, however, k is negat'ive z will increase as long as a - y decreases, that is, during the whole course of mutarotation. Consider first the simpler case when KI = K3. I n the mutarotation of either a glucose or p glucose, the concentration of the intermediate substance will increase from zero to a maximum and thereafter be constant during the remainder of mutarotation, the concentration a t maximum depending on the ratio of K 3to Kz K4, Accompanying the gradual increase in the concentration of the intermediate substance] whether we start from a glucose or 0 glucose, there will be a corresponding increase in the rate of formation of the other isomer until the maximum amount of the intermediate form is present. There will thus be initially an apparent retardation in the rate of mutarotation which will be the same whether we start with a glucose or 0 glucose. If K1 is not equal to K3, there will also be an initial retardation, but the effect in the case of a glucose will be somewhat different for that in the case of p glucose. If Kl > K3, the retardation with glucose should be more pronounced, but of shorter duration than with glucose and vice versa. I n the polarimetric method of following the course of mutarotation, an additional complication is introduced by the optical activity of the intermediate substance. The retardation will be modified according as the intermediate substance has a high or a low rotation. If high, the retardation in the case of a glucose will appear more pronounced, while in the case of p glucose, it may be diminished, obscured, or possibly converted into an apparent acceleration. I n the light of the above analysis of the problem, various initial effects may be expected according as Kl is greater than, equal to, or less than K I , and according as the intermediate substance has a high or low rotation. I n the case of galactose] Riiberl followed the course of mutarotation by methods dependent on ( I ) the change in volume of the solution and ( 2 ) the
+ +
+
+ +
+ +
+
+
+
'Ber., 59, 2266
(1926).
+
310
FREDERICK PALLISER WORLEY AND JOHN CLARK ANDREWS
change in refractivity as well as by (3) the polarimetric method. By the dilatometer method he found that in the initial stages of mutarotation of CY galactose the reaction departed considerably from the unimolecular nature of the subsequent part of the mutarotation. There was, however, no observable departure in the case of /3 galactose. He assumed the formation of a third or intermediate form of galactose and by an elaborate mathematical investigation, arrived a t the four velocity constants and the proportions of the three forms present at equilibrium. By the refractometric method, a slight and doubtful divergence from the subsequent uniform unimolecular nature of the reaction was observed in the initial stages. By the polarimetric method no departure was indicated. I n the case of the glucose, Riiber found no evidence for the existence of an intermediate form, the reaction appearing regular from the beginning when treated as a simple unimolecular balanced action. Mutarotation of Glucose and Galactose at 0°C
It is possible that a t 2 5 " any retardation in the mutarotation of glucose may occur only in the short interval after dissolving the sugar when the polarimetric readings are not taken or are discarded owing to the possibility of the temperature not having become constant. In order to examine the initial stages more minutely, we have carried out experiments a t 0°C with CY and p glucose and CY and p galactose in aqueous solution, the velocity of mutarotation being very much less a t this temperature than a t z s " , and any initial retardation correspondingly protracted. The polarimetric tube was imbedded in crushed ice in a box considerably longer than the tube. Extension tubes attached to the polarimetric tube passed through holes in the box. The sugar and the water were mixed a t o°C and quickly transferred to the polarimetric tube imbedded in the crushed ice. Readings were taken a t frequent intervals after mixing and afterwards at longer intervals. I n Tables I-IV are given the results of four typical experiments made with CY and /3 glucose and (Y and p galactose respectively. Each rotation is the mean of five readings taken a t intervals of ten seconds. The results of the above four experiments are shown graphically in Figs. I to 3. I n Figs. I and 2 the observed rotations are plotted as ordinates and the times as abscissae, the curves thus representing the course of mutarotation as indicated by the change in optical rotation. I n the case of both CY and @ galactose (Fig. I ) there is an initial flattening of the curve indicating an initial retardation which is more pronounced in the case of the /3 sugar. I n the case of glucose (Fig. 2 ) there is an initial flattening or retardation in the case of a glucose, but an initial acceleration in the case of p glucose. I n Fig. 3 the logarithms of the differences between the specific rotations a t the various times and the specific rotation at equilibrium are plotted as ordinates against the times as abscissae. I n order to plot the curves in one diagram, the logarithms of CY galactose and CY glucose have been diminished by 0.10and 0.1j respectively and those of p galactose increased by 0.03 throughout. If the velocity of mutarotation be in accordance with the re-
MUTAROTATION
FIG.I
FIG.2
FIQ.3
311
FREDERICK PALLISER WORLEY A S D JOHN CLARK A S D R E W S
312
TABLE I Glucose 0.4793 gms. in 25.100 gms. water d: = 1.00580
TABLE I1
0Glucose
CI
Times
Observed Rotation
5 min. IO
15
20 25
30 35 40
50 60 io
0,5771 gms. in
d:
1.2j0
1.592
40
I . 2;o
4.564 4.530
45 55
I.
1.338 1.358 1.430
I . 192
1.216 1.234
25
105
4.322
I3 5
2.236
ca
TABLE I11 Galactose 0.4378 gms. in 25.100 gms. mater d: = 1,00534 Observed Rotation
5.830 5.830
1
490
2.834
gms. water dp = 1.00870 Times
3 min.
5
20
5.686
20
25
5.656
25
30 35 45 55 65
5.632 5.604
30 35
j . jj0
40
5 504
75 85 95
5.398 5.352 5.304
45 55 65
10;
I Z j
5 ' 264 5 224 5.180
I3 5
s
3.310
I55
I I j
286
I . 306
TABLE I\;
5.808 5.750
5,452
I , 260
C,3 Galactose 0.62jr gms. in 25.100
I5
IO
I . 1;o
20
IO0
CY
1.1j2
15
130
5
136
30 35
I.
IO
" 1 e3
3 min.
Observed Rotation
3 min. 5
65
Times
1.00819
4.736 4 . i30 4,730 4.710 4.696 4.666 4.650 4,636
1.494
33
=
Times
4.46~ 4.426
80 90
25.100
gms. water
IO
I5
75 85
95 I1j
m
Observed Rotation
3.080 3.076 3.080 3.080 3.082 3.082 3.080 3.092 3.1'4 3.136 3.160 3.192 3.220
3.244 3,304 3.358 3.398 3.460 4.726
MUTAROTATION
313
quirements of a unimolecular balanced action, as has already been found to be the case during the greater part of the mutarotation, a straight line should be obtained, the slope of the line affording the value of the velocity coefficient. This method of expressing the results clearly shows the nature and duration of the initial divergence from the unimolecular character of the change obtaining during the subsequent mutarotation. I n the case of cy galactose the initial retardation is seen to be followed by an acceleration before the niutarotation becomes regular as expressed by the straight part of the curve, the initial divergence extending for about twenty minutes. I n the case of fl galactose, there is an apparent complete arrest of mutarotation for about thirty minutes, after which the action becomes normal. The slope of the two curves when they become straight lines is approximately the same, that for cy galactose, however, being slightly the greater. I n the case of cy glucose, the retardation extends over about fifteen minutes before the curve becomes a straight line. The initial divergence in the case of p glucose is an acceleration extending for about twenty-five minutes, the subsequent straight part of the curve having the same slope as that of cy glucose. The possibility of the initial divergence being due to the temperature not having become constant has been considered, but although a portion of the divergence may be due to a temperature effect, it appears that such portion must be small in comparison with the total effect observed. Four or five experiments were carried out in each case and the general form of the curves for each sugar found always to be the same. We consider that the different characters of the initial divergences are to be explained principally by the magnitude of the rotation of the intermediate substance and by the relation of IG to KB. These results we regard as definite evidence against mutarotation being a simple unimolecular balanced action between the cy and the fl sugar. They appear to be in agreement with the requirements of an action which proceeds by the formation of an intermediate substance and represented bycy
sugar
*
X
+/3 sugar
in which the rate of formation of X is very slow in comparison with the reverse changes.. Although the possibility is not excluded of mutarotation proceeding in more than two stages with the formation of more than one intermediate substance, there is no evidence that more than one intermediate substance is formed, and it is reasonable to assume provisionally that one only is present. I n the case of galactose, the more prolonged initial divergence from the uniformity of the subsequent course of mutarotation compared with that of glucose, considering also the greater speed of mutarotation of galactose, indicates that the difference between the rate of formation of the intermediate substance and the reverse changes is considerably greater in the case of glucose than in that of galactose, with the result that the amount of the intermediate form present during mutarotation and a t equilibrium will be considerably greater for galactose than for glucose.
314
FREDERICK PALLISER WORLEY AND JOHN CLARK ASDREWS
Temperature Coefficient of Velocity of Mutarotation The velocity coefficients a t o'C and 2 5 O C are given in Table V. Tne values a t 0°C being the means of five determinations in the case of a glucose and a galactose and four determinations in the case of /3 glucose and ;3 galactose. TABLE V 0°C
glucose /3 glucose mean a galactose /3 galactose mean cy
o 00073 0.000j3
0.00073 0.00092
o.00090 0.00091
25°C
o 0096 0.0096 0.0096 0.0134 0.0134 0.0134
I
