NOTES ON ANALYTICAL PROCEDURES Determination of Reducing Sugars Mathematical Expression of Reducing Action in the Lane and Eynon and Volumetric Ferricyanide Methods
F. W. ZERBAN, W. J. HUGHES, AND C. A. NYGREN N e w York Sugar Trade Laboratory, N e w York,
IN
T H E determination of reducing sugars by direct titration against Fehling solution according to Soxhlet, Violette, or Pavy, it has been generally assumed that the concentration, x, of sugar solution, multiplied by the volume, y, required for complete reduction of a fixed quantity of copper solution, is constant (xy = C). But Soxhlet (6) showed as early as 1878 that this simple relationship holds only if the concentration of the unknown sugar solution is approximately the same as that used for standardization of the Fehling solution. Later, Lane and Eynon ( 4 ) found that the "factor" (C/lOO) may vary as much as 5% for a range of 15 t o 50 ml. of sugar solution used. When it became apparent about two years ago that copper salts might be difficult to obtain, it was decided to devise a substitute for the Lane and Eynon method, and alkaline ferricyanide solution was tried, as first proposed by Ionescu and Vargolici (f), with methylene blue as indicator of complete reduction. When the results were plotted by Louis Sattler, of this laboratory, it was discovered that there is a straight-line relationship not between x and y, but between their logarithms, and t h a t the results can be expressed by the equation log y = log b or
- m log x
y = bx-m
Table
=
log b
m log b
Deviation Average Maximum
M1.
M1.
0.023 o,013 0.012
0.08 o,04 0.04
10 ml. of Fehling solution
l n ~ ~ ~ ~ ~ $ ~ m 1.0341 1,0166 o f 3.7886 3,7405 0.2730 o,2718 Plus 5 grams of sucrose 1.0030 3.6848 0.2722
"-
erose lo grams Of 0.9830 3.6240 Plus 25 grams of sucrose 0.9552 3.5308 Dextrose 1.0354 3.7789 1.0315 3.7966 &;&hydrate 0.9759 3.8444 Lactose hydrate 1.0010 3.8348
0.2713
0.067
0.21
0.2698 0.2740 0.2717 0.2512 0.2610
0.109 0.017 0.023 0.008 0.057
0.28 0.04 0.06 0.03 0.14
0.018
0.05 0.04 0.05 0.04 0.05 0.04
25 ml. of Fehling solution Invert sugar 1.0124 4.1270 0.2453 D ~ ~ o ~ ~ r a m o f s u c r 1.0086 ose 4.1130 0.2452 1.0121 4.1138 0.2458 Levulose 1,0108 4.1362 0.2444 Maltose hydrate 0.9597 4.1932 0.2289 Lactose hydrate 0.9760 4.1593 0.2344
O.Oo9 0.022 0.016 0.024 0.016
(1)
the method of averages from 18 pairs of values for milligrams of sugar in 100 ml. of solution and the corresponding titers given in the Lane and Eynon tables ( 3 ) . A detailed comparison between
(2)
the figures in the table for invert sugar alone, with 10 mi. of Fehling solution, and those calculated from the equation is shown in Table I. I n this particular case m was found to be 1.0341, and log b = 3.7886. In Table I1 the values of nz and log b, calculated as explained, are shown for all the sugars and sugar mixtures studied by Lane and Eynon, together with the maximum and average deviations of the calculated titer from t,hat given in their tables. I n two of the equations the value of m is so close to unity that the formula y = C / x could be used without serious error. The ratio of m to log b for invert sugar is about midway between the ratios for dext,rose and levulose. W t > hincreasing quantities of sucrose added to invert sugar both m and log b decrease, m more rapidly than log b, as shown by the ratio between the two. The agreement between the titers given in the Lane and Eynon tables and those calculated is remarkably close, the average deviations being in most instances around 0.02 ml. or less and the maximum deviations well within 0.1 mi. Larger discrepancies are found in the case of invert sugar in the presence of 10 or more grams of sucrose, titrated against, 10 ml. of Fehling solution. Lane and Eynon have pointed out that the total time of boiling has a pronounced effect on the reducing pow-er of invert sugar mixed \vith large amounts of sucrose. The maximum discrepancies occur usually when the titer is very high, close t o 50 ml.
1.
EQUATIONS FOR LANE AND EYNON METHOD
T o test the validity of this 1aTv of reducing action for the Lane and Eynon method, the values of m and log b were calculated by
I.
Comparison between Lane and Eynon Titers and Those Calculated from Equation I for Invert Sugar A l o n e (10 ml. of Fehling solution) Sugar Sugar Sugar in Solution, Solution, 100 hll. L. & E. Equation 1 Difference Mo. M1. hll. Ml. 336 15 13.00 0.00 298 17 16.98 -0.02 267 19 19.03 4-0.03 242.9 21 20.98 -0.02 0.00 222.2 23 23.00 204.8 25 25.02 4-0.02 190.4 27 26.98 -0.02 177.6 29 29.00 0.00 166.3 31 31.04 4-0.04 156.6 33 33.03 4-0.03 147.9 35 33.04 4-0.04 140.2 37 37.03 4-0.03 133.3 39 39.01 +0.01 127.1 41 40.98 -0.02 121.4 43 42.98 -0.02 116.1 45 45.01 +0.01 111.4 47 46.97 -0.03 107.1 49 48.92 -0.08 Average difference *0.023 Maximum difference -0.08
Table
Constants in Equation 1 for Reducing Effect of Various Sugars, as Determined b y Lane and Eynon m
where b and m are constants. The original equation, = C, or y = C / x , is a special case of the general equat'ion Y = C/xm, with m
II.
N. Y.
An interesting case is presented by lactose, titrated against 10 ml. of Fehling solution. Here the factor, C/lOC, found experimentally by Lane and Eynon decreases between 15- and 3064
ANALYTICAL EDITION
January, 1946
65
mixture of invert sugar with 10 grams of sucrose. It must be considered, however, that Lane and Eynon did Titer not publish their original experimental Invert Sugar + Invert Sugar + Invert Sugar + Invert Sugar + Invert Sugar values, and that those given in their 1 G r a m of Su3 Grams of Su5 Grams of Su10 Grams of SuAlone crose crose crose crose Invert tables are probably taken from Sugar Found Calcd. Found Calcd. Found Calcd. Found Calcd. Found Calcd. smoothed curves. .Nevertheless, the No. lesser precision of the ferricyanide 400 14.30 14.28 14.12 14.11 14.11 14.00 13.89 13.84 13.62 13.64 360 15.93 15.95 15.79 lL76 15.64 15.64 15.52 15.48 16.16 15.15 method is indicated by the fact 320 18.00 18.05 17.78 17.83 17.64 17.70 17.56 17.54 17.14 17.17 280 2 0 . 8 3 20.77 20.49 20.51 2 0 . 2 8 20.36 2 0 . 1 2 20.20 19.71 19.79 that neither the m nor the log b 260 2 2 . 4 5 22.46 22.18 22.16 22.01 22.01 21.78 21.85 21.39 21.41 240 values in Table IV show a regular 24.50 24.43 24.08 24.10 23.92 23.94 23.85 23.79 23.49 23.32 220 26.70 26.77 26.46 26.40 26.31 26.23 26.01 26.09 25.50 25.58 trend, contrary to those in the Lane 200 29.60 29.60 29.11 29.18 28.99 28.99 28.91 28.86 28.39 28.31 180 33.08 33.07 32.51 32.60 32.36 32.38 32.25 32.28 31.51 31.67 and Eynon method. The ratio of m 160 37.41 37.43 36.99 36.87 36.58 36.64 36.56 36.57 35.81 35.89 to log b, however, increases regularly with an increase in added sucrose, wherew in the Lane and Evnon ml. titer, and then increases again up to 50-ml. titer. This method the trend is donmward. On the whole, the Lane and would mean that in the lower range m is greater than unity, but Eynon method appears to be preferable. in the higher range smaller than unity, and would explain the unIonescu and Vargolici claim that a solution may contain aa usual discrepancies observed when the entire range is considered t o have only one value for m. But it is also possible that the exmuch as 30% sucrose in addition to 0.5% glucose without affectception is only apparent and caused by experimental difficulties ing the titer. The figures in Table I11 show that this is not genin maintaining a uniform rate of boiling and addition of sugar erally true, but that sucrose does affect the reducing power of solution, which affects the results obtained with disaccharides invert sugar, as in the Lane and Eynon method. more than it does with monosaccharides. Table
Ill. Invert Sugar Table for I O MI. of A l k a l i n e Ferricyanide Solution, Diluted with PO MI. of Water
Jackson and Mathews (2) have called attention to the fact that the Lane and Eynon factors found by different operators or with different batches of Fehling solution may vary somewhat from those given by Lane and Eynon, and recommend that each analyst standardize his own analyses x i t h solutions of the pure sugar. This Can now be readily done by plotting two or more points on double log paper and drawing a straight line through them. V O L U M E T R I C FERRICYANIDE M E T H O D
I n this method the concentrations of the potassium ferricyanide and potassium hydroxide were increased over those specified by Ionescu and Vargolici, in order that titers between 15 and 50 ml. of sugar solution might correspond to approximately 400 to 100 mg. of invert sugar in 100 ml. of solution, similar to the range of the Lane and Eynon method. A solution containing in 1 liter 56.000 grams each of potassium ferricyanide and potassium hydroxide answered these requirements. Of this solution, 10 ml. were transferred to a 250-ml. Erlenmeyer flask, and diluted with 20 ml. of water. The determinations were then carried out exactly as in the Lane and Eynon method, 5 drops of methylene blue indicator being added toward the end of the titration. I n each case the incremental method of titration was used in the first experiment, and in the subsequent experiments almost all of the sugar solution was added a t one time, and the titration completed by dropwise addition of’ the sugar solution. The titers were determined in this manner for solutions containing invert sugar alone, and in the presence of 1, 3, 5, and 10 grams of added sucrose in 100 ml. of solution.
It was found that the precision of the ferricyanide method is not as high as in the Lane and Eynon method. When the titer lay between 35 and 50 ml., duplicate tests often varied by 0.2 to 0.3 ml. It is therefore advisable with this reagent to keep the titer within 15 and 35 ml., as was done by Main (6) in his pot method with Soxhlet solution. The titers found in this range for invert solutions, containing 400 to 160 mg. of invert sugar in 100 ml., are shown in Table 111. The values of constants m and log b in Equation 1, calculated from the experimental titers in Table 111, are given in Table IV, together with the ratios of m to log b and the average and maximum deviations of the calculated from the found values. The titers calculated from the equations are shown in Table 111, next to the found values. The average deviations of the found from the calculated values are slightly larger than the corresponding figures for the Lane and Eynon method, even though the titer range is only from 15 to 35 ml. The same is true of the maximum deviations except for the
Table IV. Constants in Equation 1 for Reducing Effect of Invert Sugar upon Alkaline Ferricyanide Reagent in Absence and Presence of Sucrose m ~
m Invert suear alone Invert s u i a r plus 1 gram of sucrose Invert sugar plus 3 grams of sucrose Invert sugar plus 5 grams of sucrose InGert sugar plus 10 g r a m of sucrose
log h
1 ,0520 3 . 8 9 1 9
log h
Deviation Average Maximum .W. .1-I 1 .
0.2703
0 043
0.07
1 ,0481 3 . 8 7 6 8 0.2704
0.049
0.12
1 0497
~
3.8777
0.3707
0.043
0.11
1,0603 3.9001
0.2718
0.049
0.08
1.0639 3.9001
0.2728
0,073
0.16
S U M M A R Y AND C O N C L U S I O N S
When the titers, y, found in the determination of reducing sugar by the Lane and Eynon met,hod, or by a similar direct volumetric determination with alkaline ferricyanide solution, are plotted against t,he concentrations, x , of the reducing sugar, the equation of the resulting curve is y = bx-m, or log y = log b - m log 2, a straight-line equation in which b and m are constants. These constants have been calculated for all sugars and sugar mixtures used by Lane and Eynon, with both 10 and 25 ml. of Fehling solution, as well as for invert sugar and mixtures of invert sugar with sucrose, determined by means of an alkaline ferricyanide solution. The agreement betweer, the titers calculated from the equations and those given in the Lane and Eynon tables is very close. The precision of the alkaline ferricyanide method is somewhat lower; best results are obtained if the titer range is kept’ within 15 to 35 ml. Sucrose affects the reducing power of invert sugar not only in the Lane and Eynon method, but also in the alkaline ferricyanide method. LITERATURE CITED
(1) Ionescu and Vargolici, Bull. SOC. chim.Romania, 2, 38 (1920). (2) Jackson and Mathews, Bur. Standards J. Research, 8 , 403 (1962). (3) Lane and Eynon, “Determination of Reducing Sugars by Fehling’s Solution with Methylene Blue as Indicator”, London, Norman Rodger, 1934. (4) Lane and Eynon, J . SOC.Chem. Ind.. 42, 32T (1923). (5) Main, Intern. Sugar J . , 34,213, 460 (1932). (6) Soxhlet, Z. Ver. deut. Zuckerind., 28,368 (1878).
