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 (ki+k2) likewise is equal to the same heat of activation. If the heats of activation of the alpha and beta isomers as calculated from k, and k2 are not equal, the value of Q obtained from the mutarotation coefficient (k+k2) 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-furanosc 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.

TABLE 61.-Thermal mutarotation for sugars exhibiting complex mutarotation.

(f) EFFECT OF ACIDS AND BASES ON THE MUTAROTATION RATES

The acceleration of the mutarotation rates of the sugars by acids and bases has been the subject of many investigations. The early workers attributed the catalytic effect of acids and bases to the hydrogen and hydroxyl ions, but subsequent work has revealed that catalysis is not the exclusive property of the hydrogen and hydroxyl ions. Experiments by Lowry and coworkers, [4, p. 111,] by Brönsted and Guggenheim [31], and others have disclosed the catalytic activity of molecules of undissociated acids, of anions of weak acids, and of cations of weak bases. In general, amphoteric solvents are complete catalysts for the mutarotation, while hydrocarbons, chloroform, and carbon tetrachloride do not promote mutarotation.

It may be observed from the curve given in figure 108 that the velocity for the mutarotation of glucose in aqueous solutions does not change appreciably in the range from pH 2.5 to 6.5. However, in more

FIGURE 108--Variation of the mutarotation constants with pH [10].

strongly alkaline or acid solutions, the velocity rises rapidly with increasing concentrations of the hydrogen and hydroxyl ions. If carefully purified distilled water, free from carbon dioxide, is employed in mutarotation measurements, the velocity constants are substantially higher than those obtained in slightly acid solutions. Fortunately the region of minimum velocity falls in the pH range of distilled water containing carbon dioxide, such as the water ordinarily used for mutarotation measurements. Minute quantities of bases suffice to cause large alterations in the rate, and therefore it is difficult to obtain satisfactory velocity constants except in the presence of an acid-base buffer. Mutarotation measurements made with unbuffered solutions in nickel, brass, or copper tubes give substantially higher velocity constants than those made in glass tubes [32]. The higher constants appear to be due to an alteration in the acidity caused by the metallic oxide from the tubes which dissolves in the sugar solution.

Precautions are necessary in making mutarotation measurements to avoid accidental catalysis. In order that results from different sources be placed on a comparable basis, the use of 0.001 N potassium acid phthalate is recommended as a solvent for mutarotation measurements. According to Hudson, the catalytic activity of water in the mutarotation of glucose may be represented by the equation

k=0.0096+0.258 [H+]+9750 [OH-].

The equation shows that the alterations caused by the hydrogen and hydroxyl ions are proportional to their concentration but that there is a residual catalytic activity which is now considered to be due to undissociated water molecules.

In the mutarotation of glucose at pH 4.7, the contribution of the hydroxyl ion to the catalysis is about 40,000 times that of the hydrogen ion, and the residual catalytic effect of the water is nearly 500 times that of the combined catalytic effect of the hydrogen and hydroxyl ions. Lowry and Faulkner [33] showed that pure pyridine and pure cresol do not promote mutarotation; however, a mixture of 1 part of pyridine with 2 parts of cresol does accelerate the rate for the mutarotation of tetramethyl glucose to 20 times that obtained in water solution. Lowry explained this seemingly anomalous behavior by assuming that for the mutarotation to take place the solvent must possess acid and basic properties simultaneously. Pyridine and cresol, or pyridine and water, or water alone, can act both as an acid and as a base, but pyridine alone can act only as a base and cresol alone can act only as an acid. In this connection the acid and basic functions are used in the Brönsted sense, that is, the ability to give or to accept protons. The molecules of an undissociated acid can give, and the anions of a weak acid can accept, a proton, as follows:

CH3COOH- gives H++CH,COO

CH,COO accepts H+ CH3COOH

The ammonium cation can give a proton, and ammonia can accept a proton as follows:

NH,+ gives H+, leaving NH3

NH, accepts H+, giving NH4+

Undissociated water accepts a proton and forms the H3O+ ion or gives a proton and forms the hydroxyl ion. The anions of highly ionized strong acids and metallic cations do not give or accept protons and hence do not exhibit catalytic activity. In harmony with this concept, calcium chloride, sodium sulfate, and other metallic salts of strong acids do not accelerate the mutarotation reaction, while salts of weak acids, like sodium acetate, have marked catalytic action. Isbell and Pigman [10] have shown that the mutarotation of levulose and the rapid mutarotation of galactose are extremely sensitive to the catalytic action of acids and bases. The extreme sensitivity of the pyranosefuranose interconversions to acid and basic catalysts furnishes a convenient means for distinguishing them from the alpha-beta pyranose interconversions.