the equilibrium rotation (46.34) and the calculated value of r, at zero time (83.85), which has already been obtained by application of eq 140. The substitution of these values in eq 139 gives the equation." °S=37.51×10− -.008031 +3.25X10-.0791+46.34. (142) If it is desired to use the natural logarithmic base, eq 142 is changed only by replacement of the base 10 by the base e, and by multiplying each of the exponents by 2.3026. The equation, which expresses the optical rotations as observed, is converted to a specific rotation by multiplying by the ratio of the equilibrium specific rotation to the observed equilibrium rotation. For example, in the mutarotation represented by eq 142, the equilibrium specific rotation of galactose was found from a separate experiment to be 80.2. The ratio of the equilibrium specific rotation to the observed equilibrium rotation is 80.2/46.34, or 1.7307. Multiplying eq 142 by this factor gives the mutarotation in terms of specific rotation. A summary of some mutarotation measurements, which have been conducted at the National Bureau of Standards during recent years, is given in table 149, p. 762 of this publication. The measurements reported therein were conducted as described in the following paragraph. (b) MEASUREMENT OF MUTAROTATION Mutarotation measurements are conveniently made in the following manner: The carefully purified sugar is powdered in an agate mortar and passed through a fine sieve. The weighed sample (about 2 g) is placed in a dry 100-ml glass-stoppered flask and about 50 ml of distilled water (preferably of known pH, or buffered with 0.001 N potassium acid phthalate,)2 at the correct temperature is added with agitation. The water can be added conveniently from a fast-draining pipette. Time, beginning with the addition of the water, is measured with a stop watch. After the sugar is dissolved, the solution is transferred to a water-jacketed polariscope tube and maintained at the desired temperature while optical rotation measurements are made. The work is preferably conducted in a room held at the temperature selected for the measurement; in any case, the water which circulates in the jacket of the polariscope tube should be held at constant temperature by a suitable thermostat. The optical rotations are measured directly after the solution of the sugar, and at such times thereafter as required to disclose the changes that occur. It is convenient for one person to make polariscope readings while another notes the times and records the results. It is usually advisable to make the observations in groups of 5 or 10 readings which (unless mutarotation is taking place rapidly) can be averaged for use in calculating the velocity constants. The method used for calculating the equations to represent the mutarotations and the mutarotation coefficients is given on page 444. The equilibrium specific rotation of the sugar is determined with a separate sample of the sugar. It is necessary to use the same concentration and temperature as those employed in the mutarotation measurements. 41 The optical rotation was read in sugar degrees. 42 0.2041 g of potassium acid phthalate (NBS Standard Sample 84) dissolved in 1 liter of water, (c) VELOCITY AND EQUILIBRIUM CONSTANTS FOR THE MUTAROTATION REACTIONS As already mentioned, the mutarotations of certain sugars consist of two or more reactions which involve three or more substances in dynamic equilibrium. The calculation of the separate velocity and equilibrium constants for all the mutarotation reactions is scarcely feasible at present because the number and character of the reactions are not known. By postulating that the mutarotation involves only two isomers, the separate velocity and equilibrium constants may be calculated from ki+k2 (eq 135, p. 443), and the equilibrium constant k/k2, which is obtained from the optical rotations by the equation Some values of k, and k2 thus calculated are given in table 60. TABLE 60.-Equilibrium constants calculated from optical-rotation measurements, assuming that only two isomers are present in dynamic equilibrium (d) EFFECT OF TEMPERATURE ON THE MUTAROTATION RATE In accordance with the general behavior of chemical reactions, the velocity for the mutarotation of a sugar is accelerated by a rise in temperature. Between 25° and 35° C the rates increase from one and one-half to three times, depending upon the sugar and upon the character of the mutarotation reaction. The normal alpha-beta pyranose interconversions have higher temperature coefficients than the rapid mutarotation reactions (pyranose-furanose interconversions). The effect of temperature on the rate of mutarotation is represented most satisfactorily by means of the integrated Arrhenius equation, in which k' and k' are velocity constants at the absolute temperatures, T and T2; R is the gas content; and Q is the heat of activation. In 1904 Hudson determined the effect of temperature on the velocity constants for the conversion of alpha to beta lactose and for the conversion of beta to alpha lactose. Subsequently, Lowry [4, p. 102] calculated, from Hudson's data, the following heats of activation: Application of the integrated Arrhenius equation to the data in table 60 gives the following heats of activation: It may be observed that the heats of activation for the alphapyranose isomers do not differ widely from the heats of activation for the beta-pyranose isomers. If the heat of activation for the alpha isomer equals that for the beta isomer, the value of Q obtained by application of the Arrhenius equation to the mutarotation coefficient (k1+k) likewise is equal to the same heat of activation. If the heats of activation of the alpha and beta isomers as calculated from k1 and k are not equal, the value of Q obtained from the mutarotation coefficient (k+k) is not a true heat of activation. Nevertheless, it is useful for comparing mutarotation measurements at different temperatures and for differentiating between mutarotation reactions of different types. Isbell and Pigman [11] found that the values of Q obtained from the mutarotation coefficients for the alpha-beta pyranose interconversions are larger than the values obtained from the mutarotation coefficients for the pyranose-furanose interconversions. (e) EFFECT OF TEMPERATURE ON THE EQUILIBRIUM STATE The effect of temperature on the equilibrium state can be ascertained most readily by observing the mutarotation which follows a change in temperature. When a sugar solution is cooled rapidly, a nearly instantaneous change in optical rotation takes place. This is followed by a mutarotation, the direction and rate of which furnish quantitative information concerning the shift in equilibrium. Mutarotations of this character are called thermal mutarotations. In 1909 Hudson [29] observed that when a solution of glucose, galactose, xylose, lactose, or maltose is cooled, a very small mutarotation takes place, from which he concluded that, at the higher temperature, the equilibrium solution contains more of the alpha sugar. The investigations of Isbell have shown that the equilibrium state between the alpha and beta pyranose modifications changes only slightly with changes in temperature, whereas the equilibrium state between the pyranose and furanose modifications changes considerably with temperature. Usually in the mutarotations of the freshly dissolved sugars, the changes due to the alpha-beta pyranose interconversions are large in comparison with those due to pyranose-furanose interconversions. In the thermal mutarotations, however, the changes due to the alpha-beta pyranose interconversions are small in comparison with those due to the pyranose-furanose interconversions. Consequently, the thermal mutarotations are useful for estimating the velocity constants for the pyranose-furanose interconversions. Some typical thermal mutarotations are given in table 61. The relatively large temperature effects for the pyranose-furanose equilibrium indicate that the heats of reaction are considerable; correspondingly small changes in the alpha-beta pyranose equilibrium indicate that the heats of reaction for the alpha-beta interconversions are small. The heat of reaction (AH) can be calculated from the equilibrium constants, but unfortunately in most cases these are not known. Application of the Van't Hoff equation to the equilibrium constants given in table 60 gives, for the heat of reaction in calories, values of +374, -59, +517, and -252 for the mutarotations of lyxose, glucose, mannose, and lactose, respectively. By direct measurement Brown and Pickering [30] found a thermal change of -835 calories per gram molecule for the mutarotation of levulose and smaller values for the mutarotations of dextrose, lactose, and maltose. Riiber and Minsaas [12] found that the rapid mutarotation reaction of a-d-galactose is accompanied by the absorption of heat, whereas the slow alpha-beta interconversion is accompanied by the liberation of heat. |