160 THE ANALYST, THE VOLUMETRIC DETERMINATION OF REDUCING SUGARS. Part 11.-The Limits of Accuracy of the Method under Standard Conditions. BY ARTHUR R. LING, F.I.C., AND G. CECIL JONES, S.C.G.I., F.I.C. (Read at the X e c t i i i g , Marcl~ 4, 1908.) IN a previous paper one of us and T. Rendle brought forward a modification of the method of estimating reducing sugars by titration with Fehling’s solution, based on the use of a new indicator, ferrous thiocyanate (ANALYST, 1905, 30, 182). The method was recommended mainly on account of its greater accuracy as compared with the one usually adopted of titrating sugars with Fehling’s solution, in which a solution of potassium ferrocyanide acidified with acetic acid is used as indicator. Daily experience of this modification of the volumetric method since the previous com- munication was published has confirmed the view that in practised hands it is capable of yielding results little, if at all, inferior in accuracy to those obtained by the gravimetric method; still, in order to establish once for all its limits of accuracy, it.THE ANALYST.161 seemed desirable to submit it to a stringent critical investigation. In carrying out the experiments necessary for this work, we have to acknowledge the assistance of Messrs. T. Rendle, G. McLaren, and R. C. Denington, and take this opportunity of thanking these gentlemen. The Indicator.-In the previous paper a misprint in the directions given for preparing the indicator was overlooked, and this, we fear, may have led many workers to abandon all attempts to use the method.The amount of hydrochloric acid pre- scribed should have been 5-0 c.c., and not 50 C.C. (Zoc. cit., p. 184). Such a high proportion of acid a8 this renders the indicator absolutely unworkable. Recently we have carried out a series of experiments in order to determine the effect of varying the constituents on the sensitiveness or otherwise of the indicator. As a result of these, we find that hydrochloric acid is the most satisfactory acid to employ, but that for the quaratities of the other constituents previously given 5.0 C.C. is too much. Better results are obtained when the amount of acid is decreased and that of ammonium thiocyanate increased. We find that the following proportions give the most satisfactory indicator : Ammonium thiocyanate ...... ... ... 1.5 gram. Ferrous ammonium sulphate ... ... ... 1.0 ,, Ordinary concentrated hydrochloric acid ... ... 2.5 C.C. Water.. . ... ... ... ... ... 10.0 ,, As previously stated, it will usually be necessary to decolorise the indicator by the addition of a trace of zinc dust immediately after its preparation, and again after it has been kept for some time. When decolorised too often in this way, the indicator loses sensitiveness. Before commencing the titration, about a dozen small drops of the indicator should be placed on a glazed porcelain or opal glass slab. A drop of the assay liquid should then be removed from the titration-flask and brought in contact with the middle of one of the drops on the slab. If the margin of the drop of indicator is touched with the assay liquid, the results are less satisfactory, possibly because of the greater risk of aerial oxidation.I n any case, it is necessary to perform the test as rapidly as possible. The various sugars used for the determinations to be described were all of high purity and practically free from ash. The dextrose, laevulose, and maltose were specially prepared for the purpose of another piece of work to be published by L. Eynon and J. H. Lane in conjunction with one of us. The dextrose wa8 prepared by hydrolysing cane-sugar with an acid. The product was repeatedly recrystallised from alcohol until the rotation was constant. The final specific rotatory power (c = 8) was [u],, 1 7 ~ + 52-65', The laevulose was prepared from Schering'e com- mercial product.This, after being many times recrystallised from alcohol, had a constant specific rotatory power (c = 10) [.ID- 18.50 - 93.83O. The maltose was pre- pared by J. L. Baker's method by the action of barley extract on soluble starch (Jown. Chem. SOC. Trans., 1902, 81, 1177). I t was repeatedly recrystallised from 80 per cent. alcohol, the specific rotatory power being determined after each recrystallisation on a portion kept in a vacuum over sulphuric acid until its weight was constant. Rzferred to the anhydrous sugar, the final value obtained (c=6)162 THE ANALYST. was [.II, 17.50 137.8", a value substantially identical with that of Brown, Morris, and Millar (Journ. C'hem. SOC. Traits., 1897, 71, 112). Instead of weighing out definite amounts of dextrose, lsvulose, and maltose, the purified sugars were dissolved in water to a concentration of about 6 grams per 100 C.C.The exact concentration in grams per 100 fluid grams was then determined from the specific gravities of the solutions at 15*5°/15*50 by means of the solution factors determined recently by L. Eynon and J. H. Lane in conjunction with one of us; this work will be published later on. Quantities of the solutions corresponding with the required weights of the several sugars were then accurately weighed out and made up to the necessary volume. The invert sugar was made by hydrolysing pure sucrose with hydrochloric acid in the manner described in the previous paper (Zoc. cit.). It will be seen that the values given for invert sugar so prepared are substantially the mean of those obtained with dextrose and lievulose (compare, how- ever, below).I n the paper by one of us and Rendle, previously referred to, the weight of the various reducing sugars equivalent to 10 C.C. of Fehling's solution was given. I t was known that this quantity varied slightly with the concentration, and it was therefore recommended that the concentration of the sugar solution should be so adjusted that 20 to 30 C.C. were required to reduce 10 C.C. of Fehling's solution. The varia- tion of the reducing power due to varying concentration has now been determined with some accuracy, which extends the range of concentration of solutions which can be directly titrated and increases the possible accuracy of any results obtained by the method.Solutions of invert sugar, of dextrose, of lawulose, and of maltose, prepared ac1 above described, were titrated against 10 C.C. of Fehling's solution, with the following results : 1)es trose. Lzv\-nlose. - h A. 13. c'. B. c. 0.125 41.0 195.1 44.2 181.0 0.15 33.8 197.2 35.9 185.7 0.20 24.6 203.2 26% 188.0 0.25 19.4 206.2 21.4 -186.9 Invert. A. 13. C. 0.125 42.4 188-7 0.15 34.7 192.1 0.20 25.7 194% 0.25 20.2 198.0 0.30 0.35 - - 0.40 - - - - JIaltose. 7-' - - 13. c. - - - - 40-7 122.9 32.6 122.7 27.15 122.8 23.3 122.6 20.55 121-7 Column A gives the concentration of the sugar solutions in grams per 100 C.C. Columns B give the C.C. required by 10 C.C. of Fehling's solution. Columns C give the C.C. of Fehling's solution equivalent to 1 gram of sugar. When these numbers are plotted on squared paper, with the concentrations for abscisse, and volumes of sugar solution for ordinates, curves are obtained which, like those given by Brown, Morris, and Millar (Jouru.Chem. SOC. Trans., 1897, 71, 280),THE ANALYST. 163 connecting weight of sugar present with copper oxide reduced under their standard conditions, entirely fail to discover the errors of observation. When, however, the concentration is plotted against the volume of Fehling’s solution equivalent to 1 gram of sugar, the errors are greatly magnified and their extent can be measured. We are only justified in drawing the straight line which makes the sum of the errors of observation least. This we have done, and from it have obtained the numbers given in columns L’, D’, 1’, and M’ of the accompanying table.The plotted results are not of sufficieut importance to justify the expense of reproduction, but the limits of accuracy of the volumetric method can be ascertained by plotting the first and last of these numbers against the corresponding concentrations, and drawing the straight line joining them. If, then, our experimental numbers are plotted on the same paper, it will be found that on the average they deviate from these straight lines by 1 in 400 in the case of dextrose and invert, 1 in 300 in the case of maltose, and 1 in 100 in the case of Iawulose. The lsevulose values are not good, but the mean line drawn through the points is probably determined with some accuracy, as the calculated invert curve-that is, the curve occupying the mean position between the dextrose and lEevulose curves-is a line exactly parallel to the invert curve con- structed from direct experiments and lying very close to it.The invert table has been constructed from the mean of the calculated and directly-determined invert curves. I n the case of maltose we have felt that the only reasonable conclusion to be drawn from our experiments is that for all practical purposes within our limits of concentration the reducing power is a constant. We have, therefore, drawn not the straight line which makes the sum of the errors of observation least, as this would show the reducing power very slightly falling with increasing concentration, but the horizontal straight line which best satisfies this condition. The average error of the method is thus seen to be about 1 in 300, and with the exception of the lamdose numbers, no single observation of ours shows an error so great as 1 in 200.Brown, Morris, and Millar (ibid., 1897, 71, 106) place the maximum experimental error by the gravimetric method for maltose at 0-5 per cent. In their paper dealing with the constants of dextrose, lamdose, and invert sugar (ibid., 1897, 71, 275), they do not discuss the limits of accuracy of their work, which, however, we may assume, represented the highest order of accuracy of which the gravimetric method is capable. Long ago we were struck by the apparently anomalous variation of the numbers in the columns heEtded ‘‘ CuO corresponding to 1 gram ” sugar in the table given by Brown and his co-workers (Zoc.cit., 281). We accordingly plotted these numbers against the amounts of dextrose and Izvulose, and obtained a strange arrangement of points-strange, that is, because the table from which they were taken was not a statement of experimental results, which might well have yielded an irregular figure, but a calculated table for practical use, presumably derived from a smoothed-out curve or calculated equation. We can only conclude that they were derived from the curve connecting weight of sugar present with weight of copper oxide reduced, which, as we have said, is incapable of discovering experimental errors. We next plotted the actual experimental numbers of these workers and compared the amount of sugar present, not with the amount of copper oxide reduced, but with the amount of copper oxide reduced per gram of sugar in varying concentration-that is to say, we subjected their results to the same164 THE ANALYST. rigid test which we applied to our own.By grouping the results of these authors there are obtained four points on a curve in the case of laevulose and five points in the case of dextrose, and from these we are enabled to judge of the limit of accuracy of the gravimetric method in their hands. The average error in the case of dextrose appears to be 1 in 250, in the case of lmulose 1 in 300, and the maximum errors about 1 in 150. This is in close agreement with the limit they themselves place on their maltose values-0.5 per cent. Had we not overlooked that statement, we might have been saved the analysis of their results, which were undertaken with a view to determining how far, if at all, the volumetric process fell in accuracy below the gravimetric under the best conditions.The curves which we have been at the pains t o draw, however, place it in our power to recalculate the table of Brown, Morris, and Millar (Zoc. cit., 28l), and perhaps it may be worth while to extend the same treatment to the maltose table (Zoc. cit., 100). We think we have said enough to show that in our hands thevolumetric method is not only much more rapid, but quite as accurate, as the gravimetric method, to which some workers appear to cling because of the seeming accuracy of a method which gives a precipitate which, however incomplete, can be weighed accurately to 1 in 2,000.Although we have confined our experiments on the development of the volumetric method to the case in which 10 C.C. of Fehling's solution are employed, there are circumstances in which it is desirable to work with a greater or lesser volume of Fehling's solution. I t is interesting to note that, assuming the concentration of the sugar solution to be constant, the number of c.c.'s required for any titration is directly proportional to the volume of Fehling's solution employed-at all events, when this lies between the limits of 5 and 20 C.C. The experiments given in the following table prove this. Volumes of Fehling's solution varying from 5 to 20 C.C. were measured out, and in order to eliminate any possible error due to measurement, these volumes were also weighed and the volume calculated from the weights and the specific gravity of the Fehling's solution, which at 15-5"/15.5" was found to be 1-1618.Experiments with a solution of invert sugar (c = 0.2 gram) titrated against varying volumes of Fehling's solution : A 5 5 10 10 15 15 20 20 B 5.831 5.780 11.601 11.596 17.376 17.448 23.232 23.202 C 5.019 4.975 9.985 9.980 14.956 15.018 19-99 19.97 D 12.9 12.8 25-7 25-7 38.6 38.6 51.3 51.4 E 194.6 194.3 194.9 194.1 193.7 194.6 194.8 194.3 Column A gives the volumes of Fehling's solution as measured out with a Column B gives the weight in grams of the volumes under A. Column C gives the volume in C.C. (fluid grams) calculated from the weights pipette. under B and the specific gravity of Fehling's solution at 15*5"/15*5".THE ANALYST.165 Column D gives the volume of sugar solution in C.C. required for the titration. Column E gives the C.C. of Fehling's solution equivalent to 1 gram of invert sugar calculated from columns C and D. We work with vessels graduated to contain grams of water at 15.5" C., but for the volumetric method it does not matter which system of graduation be adopted, provided the flasks and burette agree. Nor does it matter that a 10 C.C. burette fails to deliver 10 C.C. of a viscous liquid such as Fehling's solution, provided the same pipette be used in standardising and in analytical work. Every preparation of Fehling's solution will need standardising, and this can be easily and quickly conducted under the exact conditions in which it will be used. Our work was carried out with a preparation of Fehling's solution of which 10 C.C.required under our conditions 25-65 C.C. of a, 0.2 per cent. solution of invert sugar, and the table we give is constructed on this basis. Volumc of Solu tioii required by 10 C.C. l~eliling's S o h tion. C.C.. 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 ~ DEXTROSE. Gra111, 0-2427 0.2332 0,2226 0.2138 0,2056 0.1981 0.1911 0.1846 0.1784 0.1728 0.1675 0.1625 0-1577 0.1532 0.1490 0.1450 0.1412 0.1377 0.1343 0.1310 0-1 279 - - - C. c. 206.0 205.1 204.2 203.4 202.6 201.9 201.3 200.7 200.1 199.6 199.1 198.6 198.2 197.8 197.4 197.0 196.7 196.4 196.0 195.8 195.5 - - - LEVU LOSE. Gram. - - 0.24 11 0.2312 0.2222 0.2138 0-2060 0.1988 0.1921 0.1857 0-1798 0-1743 0.1691 0.1642 0.1596 0.1552 0.1511 0-1472 0.1 435 0.139 0.1366 0.1334 0.1298 0.1274 C.C.- - 188.5 188.0 187.5 187.1 186.7 186-3 186.0 185.6 185.4 185.1 184-8 184.6 184.3 184.1 183.9 183.6 183.4 183.3 183.1 182.9 182-8 182 6 INVERT SUGAR. Cram. 0,2412 0.2311 0.2218 0.2132 0.2052 0.1980 0.1910 0.1846 Oe.1787 0.1731 0.1678 0.1629 0.1583 0.1539 0.1497 0,1458 0.1421 0.1385 0.1349 0.1319 0.1288 0.1259 - - C . C . 197.5 196.8 196.0 195.5 194.9 194.3 193.9 193.4 193.0 192.5 192.2 191.8 191.5 191.2 190*9 190.6 190.3 190.1 189.8 189.6 189.4 189.2 - - Gmni. 0.3888 0.3711 0.3550 0.3402 0.3266 0.3140 0.3023 0.2915 0.2815 0.2721 0.2633 0.2551 0.2474 0.2401 0.2332 0,2268 0.2206 0.2148 0.2093 0.2041 - - - 122.5 -166 THE ANALYST. If any other worker finds that 10 C.C. of his Fehling’s solution require under his conditions only 25 C.C.of, 0.2 per cent. invert sugar, to use our table he will need to reduce the numbers in columns D, L, I, and M, and increase those in columns D’, L’, 1’, and M’ proportionately. These numbers have been given to four significant figures; the fourth, on our own showing, has no claim to accuracy, but is given to enable the third to be selected accurately when interpolating. I n practice, for example in the analysis of a mixture of dextrose and lmulose, or of dextrose and maltose, it will be sufficiently accurate to take the factor (c.c. Fehling’s solution per gram sugar) to the nearest third place; the maximum error which can be thus introduced is 1 in 250, and will usually be much less. Suppose a, solution of pure laevulose is being examined, and that 25-0 C.C.of it am required to reduce 10 0.c. of Fehling’s solution. Opposite 25 in the first column is found 0.2138 in column L ; the percentage of laevulose in the solution titrated is thus given direct. If 25-2 c.c., or other quantity not a whole number, is required to reduce 10 C.C. of Fehling’s solution, the percentage of lmdose can be easily found by inter- polation between the numbers in column L. The numbers in columns D’, L’, 1’, and M’ are given for another purpose- namely, the separate determination of two reducing sugars in a mixture, by a modification of the method of Morris (Jozcm. Fed. Inst. Brewing, 1898, 4, 162), which depends on the reducing power and the reading in the Ventzke-Scheibler half-shadow polarimeter, when observed in a 200 mm.tube in 10 per cent. solution. An illustra- tion will again best explain this use of the table. A commercial invert sugar gave a reading in 10 per cent, solution in a 200 mm. tube of - 4.7 divisions, and 10 C.C. of Fehling’s solution required 36-45 C.C. of 0.20 per cent. solution for reduction. After hydrolysis with acid only 35-95 C.C. of 0.20 per cent. solution were required to reduce 10 C.C. of Fehling’s solution. The difference between this reading and the last gives the amount of cane-sugar present in terms of invert sugar. From the table, column I, we find 36-45 C.C. =0.1441 per cent., and 35.95 C.C. =0.1460 per cent. The 0.20 per cent. solution of the sample under examination therefore contains cane- sugar equivalent to (0.1460 - 0.1441) = 0.0019 gram invert sugar-that is to say, (0.0019 x 0.95) = 0.0018 gram cane-sugar, or 0.9 per cent.on the sample. A 10 per tent. solution of the sample after fermentation gave a reading in a 200 mm. tube of -0.1 division, and 40.0 C.C. were required to reduce 10 C.C. of Fehling’s solution. Opposite 40 C.C. in colunin I we find 0.1319, the reducing power in terms of invert of the unfermentable residue in 10 per cent. solution. I n 0.20 per cent. solution, therefore, the unfermentable matter would raise the apparent content of invert sugar 0.0026 per cent. In a concentration such that 10 C.C. of Fehling’s solution require from 36 to 37 c.c., a difference of 0,0037 per cent. of invert sugar makes a difference of 1 C.C. in the burette reading; unfermentable reducing sub- stances equivalent to 0-0026 per cent.invert would tberefore reduce it 0.70 C.C. Ten C.C. of Fehling’s solution would therefore require (36.45 + 0.70) = 37.15 C.C. of the 0.20 per cent. solution if this were free from unfermentable reducing substances, or 1 gram of the sample contains dextrose and laevulose equivalent to 10+(37.15 x 9.002) = 10~0.0743 =- 134.6 C.C. Fehling’s solution. The manner of using the table is best explained by an illustration;THE ANALYST. 167 In concentrations such as that in which our first reduction experiment W&8 made-namely, where 10 C.C. Fehling’s solution require 36.45 C.C. of sugar solution- 1 gram dextrose = 196.6 C.C. Fehling’s solution, and 1 gram lavulose = 183.8 C.C. Fehling’s solution (columns D’ and L’) ; but 1 gram of our sample requires 134.6 C.C. Fehling’s solution. If we represent the percentage of dextrose in the sample by D and the percentEtge of Itevulose by L, we have the equation- 1.966 D + 1.838 L = 134.6( 1). The sample was found to contain 0.9 per cent. cane-sugar ; a 0.09 per cent. solu- tion of cane-sugar gives a reading of (3.85 x 0.09) = + 0.3 division when read in a 200 mm. tube in the Ventzke-Scheibler polarimeter. The actual reading ( - 4.7) must therefore be corrected for this amount as well as for the reading of the unfermentable residue ( - 0*1), in order to arrive at the reading due to the dextrose and Iaevulose alone - 4.7 - 0.3 - ( - 0.1) = -- 4.9 divisions, Since 1 per cent. solutions of dextrose or Izvulose give readings of 3.05 and -5.32 divisions respectively, we have 0.305 D - 0.532 L = 4*9( 2). From equations (1) and (2) D = 39-0, L = 31.5 per cent.