Katlo ial Bureau of Standards

library, H.W. Bldg

JUN 2 81963

NBS MONOGRAPH 64

Refractive Indices and Densities of

Aqueous Solutions of Invert Sugar

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Refractive Indices and Densities of

Aqueous Solutions of Invert Sugar

Carl F. Snyder and Albert T. Hattenburg

National Bureau of Standards Monograph 64

Issued June 7, 1963

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington IS, D.C. - Price IS cents
Contents

Page

1. Refractive index at various temperatures 1

1. 1. Introduction 1

1. 1. 1. Historical discussion 1

1. 2. Preparation of sugars 2

1. 2. 1. D-Glucose 2

1. 2. 2. D-Fructose 2

1. 3 Preparation of solutions 2

1.4. Determination of refractive indices 2

1.4.1. Results 3

2. Density at various temperatures 4

2. 1. Introduction 4

2. 1. 1. Historical discussion 4

2. 2. Determination of density 5 2.2.1. Results 5

3. References 6

Library of Congress Catalog Number: 63-60029

II
Refractive Indices and Densities of Aqueous Solutions

of Invert Sugar

Carl F. Snyder and Albert T. Hattenburg

The refractive indices and densities of aqueous solutions of invert sugar have been de- termined, at temperatures of 15, 20, 25, and 30° C, for concentrations up to about 82 percent

of invert sugar (by weight). From the results, equations have been derived which relate the refractive index and percent of invert sugar (weight in air) at each temperature. Other

equations relate the absolute density and percent of invert sugar (weight in vacuum) at each

temperature. Five-decimal tables giving the refractive indices and densities of invert sugar solutions containing 1 to 85 percent of sugar are given for each percentage of invert sugar at the four temperatures.

1. Refractive Index at Various Temperatures

Carl F. Snyder

1.1. Introduction

The increasing use of refractometric methods

for determining the dissolved soHds in commercial,

liquid sugar-products has made it desirable to obtain more-complete data on the refractive indices

of aqueous solutions of pure invert sugar at various

' temperatures. These refractive indices have,

therefore, been determined for concentrations up

i to about 82 percent (by weight), at 15, 20, 25,

and 30° C. From the results, an equation was

j derived relating refractive index and percent of

j invert sugar (by weight) at each temperature.

From the four equations thus obtained, values of

j the index for equal increments of concentration

j were calculated.

1.1.1. Historical Discussion

Although fragmentary data on the refractive

indices of solutions of some sugars had previously

been reported, StoUe [1] ^ is generally credited with

the first systematic study of the refractive indices

of sugars other than sucrose. He observed little

i difference in the indices of the different sugars in

solutions of the same concentration. Tolman and

I Smith [2], using an Abbe refractometer, found that,

for a number of sugars and related compounds, a

solution of a given percentage by weight has

approximately the same refractive index. In

, neither of these investigations were measurements

made on solutions of invert sugar. StanSk and

Vondrak [3] showed that the refractive index of an

I invert sugar solution is lower than that of a

sucrose solution of the same concentration. The

same observation was made by Schneller [4]. Most of the solutions measured by Schneller were

prepared by the acid hydrolysis of sucrose and

contained various proportions of invert sugar and

' This Monograph is based on work partly supported by the Sugar Research Foundation, Inc.

2 Figures in brackets indicate the literature references at the end of this Monograph.

sucrose. Subsequently, de Whalley [5] studied

the refractometric estimation of dissolved solids

in sirups containing invert sugar; he measured 17

solutions of invert sugar prepared by dissolving

equal weights of pure D-glucose and D-fructose, for the range of 9.61 to 66.72 percent (by weight).

The index was measured on an Abbe refractometer,

and the observed refractive index was converted

to percent solids by means of the table of the

refractive indices of sucrose solutions. Both

Schneller and de Whalley found that an appreciable difference exists between the refractive index

of a solution of sucrose and one of invert sugar of

the same concentration. Thus, estimation of the

total solids in a sirup containing invert sugar (with

or without sucrose) by conversion of the observed

refractive index to the equivalent sucrose (from

the sucrose table) gave results which were too low.

From iais experimental results, de Whalley calculated an average correction of 0.022 for each

percent of invert sugar present; this was to be

added to the refractometric result for solids ex- pressed as sucrose. Later, Zerban [6] showed

that, for the data of both Schneller and de Whalley,

the magnitude of the correction varies with the

concentration. Zerban and Martin [7] then

determined the refractive indices of invert sugar

solutions at 20 °C for the range of 0 to 80 percent

(by weight), and devised the following equation

where p is the percent by weight of invert sugar

solids.

riz)^° (invert sugar solutions) = 1.33299 + 1.411210X10-^i? +0.5198919

X 10-^p2+ 1.56855X 10-«p^

-0.3776638X10-V- (1)

Since the above measurements of the refractive

index of invert sugar solutions were made only at 20 °C, it was deemed desirable to repeat these

measurements and to extend them to other

temperatures.

1
1.2. Preparation of Sugars

1.2.1. D-Glucose

The purest form of commercial dextrose hydrate that was readily available was dissolved in

sufficient hot, distilled water to make a solution

of approximately 60 °Brix ; the solution was treated

with vegetable charcoal and filtered. The filtrate was warmed and refiltered through hardened

filter-paper until all traces of charcoal had been

remoyed. The final filtrate was concentrated

under diminished pressure to a_ sirup containing

about 80 percent of dextrose (by weight) ; this was heated to 55 °C, nucleated with anhydrous

D-glucose, and placed in a rotating crystallizer

enclosed in an insulated cabinet thermostated at 55 °C. The crystallization was usually complete

within a few hours. The temperature within the

cabinet was then lowered until the mass had

reached a temperature of about 30 to 35 °C, and

the crystals were separated from the mother

liquor by centrifuging and thoroughly washed

with absolute ethanol. Recrystalnzation was

repeated until analysis of the product showed that

the sugar was of the required purity. The final crystals were air-dried and then contained less than 0.1 percent of moisture. The sugar was

finely powdered, dried at 60 °C, and stored in vacuum desiccators over suitable drying agents.

1.2.2. D- Fructose Relatively pure o-fructose (levulose) was

available from the stock prepared at the National

Bureau of Standards from tubers of the Jerusalem

artichoke [8]. The sugar had already been re- crystallized from water and it consisted of large

crystals having a purity of over 99.9 percent.

For this investigation, the sugar was further purified by the procedure of Jackson and Mathews [9]. A solution of the sugar in about an equal weight

of water was treated with vegetable charcoal and

the suspension was warmed and filtered. The

filtrate was refiltered through hardened filter- paper to remove all traces of the charcoal, and

concentrated at diminished pressure to a sirup

containing 82 to 85 percent of D-fructose. The

thick sirup was mixed with absolute ethanol and

nucleated with crystals of D-fructose, and the

suspension was rotated in a motor-driven apparatus at room temperature until crystallization was

complete. The crystals were removed by centrifuging, thoroughly washed with absolute ethanol,

air-dried, finely powdered, dried in a vacuum oven

at 50 °C for about 1 hour, and stored in vacuum

desiccators containing suitable desiccants.

1.3. Preparation of Solutions

The measurements of the refractive indices and

densities were made on solutions prepared by

dissolving a mixture of equal weights of pure

D-glucose (dextrose) and pure D-fructose (levulose) in distilled water.

A suitable quantity of dry D-fructose was placed

in a tared glass-stoppered flask, and the flask and

contents were weighed and then dried to constant weight in a vacuum oven at 50 °C. An

equal weight of dry D-glucose was transferred to the flask, and the flask and contents were weighed

and then dried in a vacuum oven at 50 °C to constant weight. The final weight of the contents represented the weight of dry invert sugar. Enough water to yield a solution of the desired

j concentration was added. The flask was mechanically rotated in an inclined position on an apparatus so constructed that its rotating shaft extended

into an air bath fitted with heaters and a thermostat. For the solutions in the lower range of

concentrations, elevated temperatures were not

necessary, but, in the higher range,' the air bath was heated to the lowest temperature that would

ensure complete solution. When all of the sugar

had dissolved, the flask was cooled to room temperature (if necessary) and weighed. From the

weight of the solution and the weight of invert

sugar taken, the composition of each solution was

calculated in percent by weight (in air).

1.4. Determination of Refractive Indices

The solution of invert sugar was kept at room

temperature for 24 hours to establish mutarotational equilibrium. Determinations of the refrac- tive index were made with a Bausch and Lomb

precision refractometer (Serial 6326), using a sodium lamp. For all readings, the instrument was adjusted to read (approximately) correctly

for distilled water and the scale was calibrated by

means of test plates of known refractive index.

The instrument was kept in a room whose temperature was regulated to within about 1 °C.

Water from a large water-thermostat was continuously circulated through the prism jackets to maintain the same temperature of the solution

and prisms to within 0.01 or 0.02 °C.

For each series of measurements, the temperature of the room and water bath was adjusted to the desired value. A series of readings was taken

with distilled water, the prism faces were thoroughly dried, and the instrument was filled with

the solution of invert sugar. After a series of

observations had been made on the solution, the

prism faces were cleaned and a series of readings was taken with distilled water These operations were repeated until the required data had been

obtained.

On completion of the series of measurements at one temperature, the temperature of the room and

water bath was adjusted to a different temperature and a set of measurements was made at the

new temperature. A random order was followed

with respect to the measurements at different

temperatures.

The observed readings on the instrument scale were converted to their equivalents in refractive

index by means of the tables furnished with the

instrument.

2
1.4.1. Results 72z>^^= 1 .3325026 + 1 .4 1 14 X 10-='2? Measurements of the refractive indices were made on 39 solutions of invert sugar of concentrations ranging from about 5 to 82 percent by

weight (in air). Each solution was measured at two or more of the selected temperatures (15,

20, 25, and 30 °C). From the data obtained at each temperature, an equation relating refractive

index and percent of invert sugar by weight (in

air) was derived (by the method of averages)

The four equations are as follows:

7! i>i^= 1 .3333872 + 1 .4292 X 10-3^)

+0.515855X10-^ +0.1 153 XlQ-y (2) V°=1 .3329877 + 1 .4 149 X 10-^^

+0.52729 X 10-y +0.1 105 XlO-y (3)

+0.51088X10-y+0.1244X10-V (4)

7! d'°= 1.3319403 + 1. 4016 XlO-^i?

+0.5134 X lO-V+0.1249 X lO-y (5) The experimental values obtained at each

temperature for the invert sugar solutions of

known composition and the values calculated

from the corresponding equation are given in table 1. By employing equations (2) to (5) , the refractive

indices at equal increments of concentration were

calculated; they are given in table 2. These values

(table 2) for the refractive indices at 20 °C are

slightly higher than those reported by Zerban and

Martin [7].

Table 1. Refractive indices of invert sugar solutions

at 15 °C at 20 °C at 25 °C Ho at 30 °C

Obs. Calc. Calc. -Obs. Obs. Calc. Calc. -Obs. Obs. Calc. Calc. -Obs. Obs. Calc. Calc. -Obs.

1 34049 1 34053 +0 00004 1 34001 1 34006 +0 00005 1 33956 1 33956 0. 00000 1 33888 1.33895 +0. 00007

1 34076 1 34070 00006 1 34024 1 34023 00001 1 33973 1 33972 —. 00001 1 33913 1.33911 -. 00002

1 34768 1 34770 + 00002 1 34712 1 34717 + 00005 1 34665 1 34664 -.00001 1 34593 1. 34598 +. 00005

1 34779 1 34776 00003 1 34724 1 34722 -. 00002

1 34997 1 34995 00002 1 34871 1. 34873 +. 00002

1 35055 1 35052 00003 1 34994 1 34997 + 00003 1 34936 1 34942 +. 00006 1 34871 1. 34875 +. 00004

1 35225 1 35220 00005 1 35171 1 35163 00008 1 35109 1 35108 -.00001 1 35051 1. 35040 -.00011

1 35615 1 35608 00007 1 35542 1 35549 + 00007 1 35499 1 35492 -.00007 1 35420 1.35421 +. 00001

1 35627 1 35629 + 00002 1 35570 1 35570 00000 1 35504 1 35513 +. 00009 1 35433 1. 35442 +. 00009

1 35805 1 35814 + 00009 1 35753 1 35754 + 00001 1 35698 1 35696 -.00002 1 35629 1. 35624 -. 00005

1 35855 1 35847 00008 1 35786 1 35786 00000 1 35729 1 35728 -. 00001 1 35656 1. 35656 . 00000

1 36203 1 36210 + 00007 1 36143 1 36147 + 00004 1 36085 1 36087 +. 00002 1 36010 1. 36013 +. 00003

1 36407 1 36414 + 00007 1 36360 1 36350 00010 1 36290 1 36289 -. 00001 1 36228 1. 36214 -.00014

1 36365 1 36362 00003 1 36305 1 36301 -. 00004

1 37265 1 37259 00006 1 37197 1 37190 00007 1 37128 1 37125 -. 00003

1 37268 1 37264 00004 1 37132 1 37129 -.00003

1 37581 1 37587 + 00006 1 37509 1 37516 + 00007 1 37434 1 37449 +. 00015 1 37360 1. 37368 +. 00008

1 38138 1 38128 00010 1 38060 1 38054 00006 1 37991 1 37984 -. 00007

1 38283 1 38294 + 00011 1 38213 1 38220 + 00007 1 38134 1 38149 +. 00015 1 38073 1.38064 -.00009

1 38639 1 38634 00005 1 38566 1 38561 -.00005

1 38994 1 39004 + 00010 1 38929 1 38926 00003 1 38864 1 38852 -.00012 1 38761 1.38764 +. 00003

1 39753 1 39745 00008 1 39678 1 39666 -.00012

1 40390 1 40391 + 00001 1 40299 1 40308 + 00009 1 40223 1 40226 +. 00003 1 40124 1. 40133 +. 00009

1 40946 1 40937 00009

1 41958 1 41958 00000 1 41869 1 41870 + 00001 1 41774 1 41780 +. 00006 1 41680 1.41681 +.00001

1 42420 1 42422 + 00002 1 42325 1 42332 + 00007 1 42230 1 42240 +. 00010 1 42134 1.42140 +. 00006

1 43005 1 43003 00002 1 42909 1 42911 + 00002 1 42810 1 42816 +. 00006 1 42709 1.42714 +. 00005

1 43771 1 43773 + 00002 1 43677 1 43679 + 00002 1 43583 1 43581 -.00002 1 43484 1.43477 -.00007

1 44090 1 44086 00004 1 43994 1 43991 00003 1 43900 1 43892 -.00008 1 43804 1.43787 -.00017

1 45114 1 45108 00006 1 45017 1 45010 00007 1 44923 1 44908 -.00015 1 44814 1. 44800 -.00014

1 45166 1 45161 00005 1 45070 1 45064 00006 1 44859 1.44853 -.00006

1 45974 1 45962 00012 1 45880 1 45863 00017 1 45772 1 45758 -. 00014 1 45656 1.45648 -. 00008

1 46454 1 46452 00002 1 46359 1 46352 00007 1 46249 1 46245 -. 00004 1. 46137 1. 46134 -.00003

1 47010 1 47000 00010 1 46898 1 46899 + 00001 1 46786 1 46791 +. 00005 1 46685 1. 46678 -.00007

1 47563 1 47573 + 00010 1 47482 1 47470 00012 1 46365 1 46361 -. 00004

1 47584 1 47589 + 00005 1 47494 1 47486 00008 1 47385 1 47377 -.00008 1. 47268 1.47263 -.00005

1 48203 1 48206 + 00003 1 48096 1 48102 + 00006 1 47984 1 47992 +. 00008 1. 47867 1. 47877 +.00010

1 48687 1 48701 + 00014 1 48568 1 48596 + 00028 1 48469 1 48485 +.00016 1 48365 1. 48369 +.00OO4

1 49347 1 49351 + 00004 1 49221 1 49245 +. 00024 1 49114 1 49133 +. 00019 1 48987 1.49016 +. 00029

3
Table 2. Refractive indices of invert sugar solutions* Table 2—Continued

Invert at Invert

ht

ir) 15 °C 20 °C 25 °C 30 °C

0 1 33339 1 33299 1 33250 1 33194

1 1 33482 1 33441 1 33392 1 33335

9 1 33627 1 33584 1 33535 l 33476

3 1 33772 1 33728 1 33678 1 33619

4 1 33919 1 33873 1 33823 1 33763

5 1 34066 1 34020 1 33969 1 33908

6 1 34215 1 34167 1 34116 1 34054

7 1 34364 1 34315 1 34264 1 34201

8 1.34516 1 34465 1 34413 1 34349

9 1. 34668 1 34616 1 34563 1 34498

10 1 34821 1 34768 1 34714 1 34648

11 1 34975 1 34920 1 34866 1 34800

12 1 35130 1 35075 1 35020 34952

13 1 35286 1 35230 1 35174 1 35106

14 1 35444 1 35386 1 35330 1 35260

15 1 35603 1 35544 1 35487 1 35416

16 1 35762 1 35702 1 35644 1 35573

17 1 35923 1 35862 1 35803 1 35731

18 1 36085 1 36023 1 35964 1 35891

19 1 36248 1 36185 1 36125 1 36051

20 1 36413 1 36348 1 36287 1 36213

21 1 36578 1 36513 1 36451 1 36375

22 1 36746 1 36679 1 36616 0UU03

23 1 36913 1 36846 1 36782 1 36706

24 1 37082 1 37014 1 36949 1 36871

25 1 37252 1 37183 1 37118 1 37038

26 i 37424 1 37354 1 37287 1 37207

27 1 37596 1 37525 1 37458 1 37377 28 1 37770 1 37698 1 37630 1 37548 29 1 37945 1 37873 1 37803 1 37721

30 1 38122 1 38048 1 37978 1 37895

31 1 38299 1 38225 1 38154 1 38070 32 1 38478 1 38403 1 38331 1 38246 33 1 38658 1 38582 1 38509 1 38423

34 1 38840 1 38763 1 38689 1 38602

35 1 39022 1 38944 1 38869 1 38782 36 1 39206 1 39128 1 39052 1 38964

37 1 39391 1 39312 1 39235 1 39146 38 1 39578 1 39498 1 39420 1 39330

39 1 39766 1 39685 1 39606 1 39515

40 1 39955 1 39873 1 39793 1 39702

41 1 40145 1 40063 1 39982 1 39890

42 1 40337 1 40254 1 40172 1 40079

43 1 40530 1 40446 1 40363 1 40270

44 1 40724 1 40640 1 40566 1 40462

weight

(in air) 15 °C 20 °C 25 °C 30

45 1 40920 1 40835 1 40750 1 40655 46 1 41117 1 41031 1 40945 1 40849

47 1 41315 1 41229 1 41142 1 41045 48 1 41515 1 41428 1 41340 1 41243 49 1 41716 1 41628 1 41539 1 41442

60 1 41919 1 41830 1 41740 1 41642

51 1 42122 1 42033 1 41942 1 41843

52 1 42328 1 42238 1 42146 1 42046

53 1 42534 1 42444 1 42351 1 42251

54 1 42742 1 42651 1 42568 1 42457

55 1 42952 1 42860 1 42766 1 42664

56 1 43163 1 43070 1 42975 1 42873

57 1 43375 1 43282 1 43186 1 43083

58 1 43589 1 43495 1 43398 1 43294

59 1 43804 1 43710 1 43612 1 43507

60 1 44020 1 43926 1 43827 1 43722

61 1 44238 1 44143 1 44043 1 43938

62 1 44458 1 44362 1 44262 1 44155

63 1 44679 1 44582 1 44481 1 44374 64 1 44901 1 44804 1 44702 1 44695 65 1 45125 1 45027 1 44925 1 44817

66 1 45350 1 45252 1 46149 1 45040

67 1 45577 1 45479 1 46375 1 46265

68 1 45805 1 45706 1 45602 1 45492

69 1 46035 1 45936 1 46830 1 45720

70 1 46266 1 46166 1 46060 1 45950

71 1 46499 1 46399 1 46292 1 46181 72 1 46734 1 46633 1 46525 1 46414 73 1 46970 1 46868 1 46760 1 46648

74 1 47207 1 47105 1 46997 1 46884

75 1 47446 1 47343 1 47236 1 47121

76 1 47687 1 47583 1 47474 1 47360

77 1 47929 1 47825 1 47716 1 47601

78 1 48172 1 48068 1 47958 1 47843

79 1 48418 1 48313 1 48203 1 48087

80 1 48664 1 48559 1 48449 1 48333

81 1 48913 1 48807 1 48696 1 48680 82 1 49163 1 49057 1 48945 1 48828

83 1 49414 1 49308 1 49196 1 49079

84 1 49668 1 49560 1 49449 1 49331

85 1 49922 1 49815 1 49703 1 49684

*A condensed form of this table was published in the Proceedings of the Twelfth Session of the International Commission for Uniform Methods of Sugar Analysis, 1958, page 26.

2. Density at Various Temperatures

Albert T. Hattenburg and Carl F. Snyder

2.1. Introduction

Densimetric methods are applicable to the

determination of dissolved solids in commercial

liquid-sugar products. The true densities of 15

solutions of invert sugar of various concentrations were determined at 15, 20, 25, and 30 °C. By

using the experimental data at each of these

temperatures, an equation was derived relating true density and percent of invert sugar by weight

(in vacuum). From the four equations thus

obtained, the values of the density at equal increments of concentration (percent of invert sugar

by weight) were calculated.

2.1.1. Historical Discussion

The determination of the densities of sugar

solutions of various concentrations and teiiipera- tures has been the subject of extensive investigation. Because of the commercial importance of sucrose, the densities of its aqueous solutions have

received the most attention. Since their publication in 1900, Plato, Domke, and Harting's

tables of densities of sucrose solutions [10] have

been generally accepted as being the most accurate

that were available. Although, strictly, these

tables are applicable to solutions of pure sucrose

only, they are frequently employed for expressing

the total content of dissolved solids in a sugar

solution containing other dissolved solids besides

sucrose. For such materials, the values have

been expressed as apparent percent of sucrose or

as "sucrose equivalent."

By basing calculations on the values of Plato

and co-workers [10] for the densities of sucrose

solutions, many other tables have been prepared.

Among these is the expanded table of Sidersky

[11] which gives the number of grams of sucrose per 100 g and per 100 ml of solution for concentrations up to 30 percent by weight at t/4 °C and

t/15 °C (between 10 and 30°). Domke [12] published a table of apparent specific gravities at 4
20 °C/20 °C for aqueous solutions containing 0

to 90 percent of sucrose by weiglit. Bates and

Bearce [13] calculated a table giving the Baunie

equivalents in specific gravities at 20 °C/4 °C

and 20 °C/20 °C. A table of weights of sucrose per gallon and per cubic foot of aqueous solutions was computed by Snyder and Hammond [14]. For use in the tropics, a table of specific gravities

of sucrose solutions at 27.5 °C/4 °C was calculated by Dowes-Dekkar and Erlee [15] and at 28 °C/4 °C by Sidersky [llj. For use in Hawaii,

a table giving apparent specific gravities at 27.5

°C/27.5 °C was given in the Methods of Chemical

Control of the Association of Hawaiian Sugar

Technologists.

The densities of aqueous solutions containing

up to 30 percent of D-glucose were determined by

Jackson [16] and by Riiber [17]. Subsequently,

Jackson and Matthews [9] determined the densities of aqueous solutions containing up to 70

percent of D-fructose.

The lack of published data on the densities of

aqueous solutions of invert sugar led to the ex- perimental determinations now reported.

2.2. Determination of Density

Data on the densities of invert sugar solutions were obtained from a series of determinations

made at 15, 20, 25, and 30 °C, for solutions of 15

different concentrations prepared as described in

section 1.3. The weight of invert sugar and the

weight of the solution (in air) of each of the solutions were converted to weights in vacuum, and

the percent (by weight) of invert sugar (in vacuum)

was calculated. The measurements were made

by the use of a pycnonieter which consisted of a long cylindrical ghiss body of about lOO-rnl capacity. Access to the body was provided ljy

two capillary tubes whose upper ends proli'uded

into a small bowl fitted witli a ground-glass cover. The small bowl served to contain the solution

which spilled out of tiie tubes upon removal from

a high-temperature bath.

2.2.1. Results

From the data at each temperature, an equation relating absolute density (in g/ml) and per- cent of invert sugar by weight (in vacuum) was

derived by the method of averages. The four equations are as follows :

d'5°=0. 9991266 +0.3895362 X 10-^2+0.124621

X lO-Y+0.4632 X 10- Y-0.21854 X 10-Y (6)

d2('°=0.9982343 +0.3863641X 10-^2+0.1214466

X lO-V+ 0.5417 X 10- Y-0.25882 X lO'Y (7)

d25° =0.9970770 +0.3827780 X 10-^2 +0.1261903

X10-V+0.4235X10-Y-0.1661X10-Y (8)

d3o° =0.9956780 +0.3798374 X 10-'2 +0-1264516

X10-Y+0.4180X10-V-0.1533X10-Y (9) Table 3 shows the observed densities for each

concentration at each temperature and the values

calculated from the corresponding equation.

By means of equations (6) to (9), the absolute

densities at equal increments of concentration were calculated; they are given in table 4.

Table 3. Densities of invert sugar solutions

Invert Density (g/ml) at

sugar by

wt. (In vacuo)15 ° C 20° C 25 ° C 30 ° C

Obs. Calc. Calc. -Obs. Obs. • Calc. Calc. -Obs. Obs. Calc. Calc. -Obs. Obs. Calc. Calc.-Obs. %

4. 9086

9. 6649

11. 4917

15. 1604

18. 7575

1. 01857

1. 03798

1.04563

1.06116

1. 07685

1. 01855

1. 03798

1. 04560

1. 06120

1.07686

-0. 00002

. 00000 -.00003 +. 00004 .+. 00001

1. 01754

1. 03674

1. 04436

1.05972

1. 07532

1. 01750

1. 03676

1. 04432

1. 05978

1. 07531

-0. 00004 +. 00002 -.00004 +. 00006 -.00001

1.01619

1.03527

1. 04282

1. 05812

1. 07358

1. 01617

1. 03529

1. 04279

1.05815

1. 07358

-0. 00002 +. 00002 -.00003 +. 00003

. 00000

1. 01462

1.03360

1.04110

1. 05629

1.07165

1. 01463

1. 03361 1.04106

1. 05631

1.07163

+0. 00001 +.00001

-.00004 +. 00002 -.00002

26. 9360

30. 9614

34. 8913

42. 2733

52. 4482

1. 11394

1. 13282

1. 15184

1. 18875

1. 24276

1. 11388

1. 13285

1. 15186

1. 18887

1. 24274

-.00006 +. 00003 +. 00002 +. 00012 -.00002

1. 11204

1. 13085

1. 14975

1. 18653

1. 24023

1. 11204

1. 13087

1. 14974

1. 18653

1. 24014

. 00000 +.00002

-. 00001

. 00000 -.00009

1. 11010

1. 12875

1. 14757

1. 18408

1. 23743

1. 11008

1. 12879

1. 147.55

1. 18411

1. 23740

I-. 00002 +. 00004 -.00002 +. 00003 -.00003

1. 10790

1. 12650

1. 14514

1. 18150

1. 23458

1. 10790

1. 12650

1. 14515 1.18151

1. 23455

.00000

.00000 +.00001

+.00001

-.00003

58. 8461

64. 9138

70. 7899

75. 5211

82. 7439

1. 27846

1. 31327

1. 34828

1. 37725

1. 42273

1. 27833 1.31329

1. 34827

1. 37723

1. 42276

-.00013 +. 00002 -. 00001 -. 00002 +. 00003

1. 27564

1. 31030

1. 34531 1.37418

1.41967

1. 27559

1. 31044

1.34532

1. 37420

1. 41964

-.00005 +. 00014 +. 00001 +. 00002 -.00003

1. 27276

1. 30728

1.34216

1. 37094

1. 41642

1. 27266

1. 30736

1.34214

1. 37097

1.41641

-.00010 +. 00008 -.00002 +. 00003 -.000011. 26971 1.30418

1. 33890

1. 36764

1. 41309

1. 26967

1. 30424

1.33891

1.36768

1.41304

-.00004 +.00006

+.00001 +.00004

-.00005

5
Table 4. Densities of invert sugar solutions

Invert

sugar by

wt. (in vaccum) %

0

123

4

5

10

1112

1314

15

16

1718

19

20

2122

23

24

2526

27

28

30

3132

33

34

35

36

37

38

39

40

4142

4344

45

4647

48

49

50

51

62

5354

6556

57

58

59

60

6162

63

64

65

70

717273

74

7576

7778

79

80

81

8283

84

86

Density (g/ml) at

15 °C 20 °C 25 °C 30 °C

0. 99913 0. 99823 0. 99708 0. 99568

1. 00303 1. 00211 1. 00092 . 99949

1. 00697 i. UUbUi I. UU^/o 1 nnQQ^i 1. yjyjoo6

1. 01093 1. 00994 1. 00868 1. 00719

1.01491 1. 01389 1. 01259 1. 01108

1. 01892 1. 01786 1. 01654 1. 01499

1. 02296 1. 02186 1. 02051 1.01893

1. 02702 1.02589 1. 02450 1. 02290

1.03111 1. 02995 1.02853 1. 02690

1. 03523 1.03403 1. 03258 1. 03092

1. 03937 1. 03814 1. 03666 1. 03497

1. 04354 1. 04227 1.04076 1. 03904

1. 04774 I. U4D44 1. U44yU 1. 04315

1. 05197 1. 05063 1.04906 1. 04728

1.05622 1. 05484 1. 05325 1.05144

1.06051 1. 05909 1.05747 1. 05563

1. 06482 1. 06337 1.06171 1. 05985

1. 06916 1. 06767 1. 06599 1. 06410

1. 07353 1. 07200 1. 07030 1. 06837

1. 07793 1. 07637 1. 07463 1. 07268

1. 08235 1. 08076 1. 07899 1. 07701

1. 08681 1.08518 1. 08339 1. 08138

1. 09130 1. ooyoo 1. 0»7»i 1. 0!50/

1. 09581 1. 09411 1. 09226 1. 09020

1. 10036 1. 09862 1. 09674 1. 09465

1. 10494 1. 10316 1. 10126 1. 09913

1. 10954 1. 10773 1. 10580 1. 10365

1. 11418 1. 11233 1. 11037 1. 10819

1. 11885 1. 11697 1. 11498 1. 11277

1. 12355 1. 12163 1. 11961 1. 11738

1. 12828 1. 12633 1. 12428 1. 12201

1. 13304 1. 13105 1. 12897 1. 12668

1. 13783 1. 13581 I. loo7U 1. 13138

1. 14265 1. 14060 1. 13846 1. 13612

1. 14750 1. 14542 1. 14325 1. 14088

1. 15239 1. 15027 1. 14807 1. 14567

1. 15730 1. 15516 1. 15293 1. 15050

1. 16225 1. 16007 1. 15781 1. 15536

1. 16723 1. 16502 1. 16273 16025

1. 17224 1. 17000 1. 16768 1. 16517

1. 17729 1. 17502 1. 17266 1. 17013

1. 18236 1. 18006 1. 17768 1. 17512

1. 18747 1. 18514 1. 18273 1. 18014

1. 19261 1. 19025 1. 18780 1. 18519

1. 19778 1. 19539 1. 19292 1. 19027

1. 20298 1. 20057 1. 19806 1. 19539

1. 20821 1. 20577 1. 20324 1. 20054

1.21348 1.21101 1. 20845 1. 20573

1. 21878 1. 21629 1. 21369 1. 21094

1. 22411 1. 22159 1. 21896 1. 21619

1.22947 1. 22693 1. 22427 1. 22148 L 23487 1. 23230 1. 22961 1. 22679

1. 24030 1. 23771 1. 23498 1. 23214

1. 24576 1. 24315 1. 24039 1.23753

1. 25120 1. 24861 1. 24583 1. 24294

1. 25678 1. 25412 1. 25130 1. 24839

1.26233 1. 25965 1. 25681 1. 25388

1. 26792 1. 26522 1.26235 1. 25939

1. 27354 1. 27082 1. 26792 1. 26494

1. 27920 1. 27646 1.27353 1. 27053

1. 28488 1.28112 1. 27917 1.27615

1. 29060 1. 28782 1. 28484 1. 28180

1. 29635 1. 29355 1. 29055 1. 28748

1. 30214 1. 29932 1. 29629 1. 29320

1. 30795 1.30511 1.30206 1. 29896

1. 31380 1. 31094 1. 30787 1. 30474

1. 31968 1. 31680 1.31371 1. 31056

1.32559 1. 32269 1. 31958 1. 31642

1.33153 1. 32862 1. 32548 1. 32231

1. 33750 1.33458 1. 33142 1. 32823

1. 34351 1. 34057 1. 33740 1. 33418

1. 34954 1. 34659 1. 34340 1. 34017

1. 35561 1. 35264 1. 34944 1. 34620

1. 36171 1. 35872 1. 35551 1. 35226

1. 36784 1. 36484 1.36162 1. 35835

1. 37400 1. 37099 1.36776 1. 36447

1. 38020 1.37717 1. 37393 1. 37063

1. 38642 1.38337 1. 38013 1. 37682

1.39268 1.38962 1. 38637 1.38305

1.39896 1. 39589 1. 39264 1 38931

1. 40528 1. 40219 1. 39895 1. 39560

1.41162 1. 40852 1. 40528 1. 40193

1. 41800 1. 41488 1. 41165 1. 40829

1. 42441 1. 42128 1. 41805 1. 41469

1. 43084 1. 42770 1. 42449 1.42111

1. 43731 1. 43415 1. 43095 1. 42757

The authors gratefully acknowledge the help of

Charles T Collett who designed the pycnometer

used for the measurements of density and who

rendered advice and assistance while the work

was in progress.

3. References

[1] F. Stolle, Z. Ver. deut. Ziicker-Ind. 51, 469 (1901).

[2] L. M. Tolman and W. B. Smith, J. Am. Chem. Soc.

28, 1476 (1906).

[3] V. Stanek and J. Vondrdk, Z. Zuckerind. cechoslov. Rep. 45, 203 (1920-1921).

[4] M. Schneller, J. Assoc. Offie. Agr. Chemists 9, 156

(1926).

[5] H. C. S. deWhalley, Intern Sugar J. 37, 353 (1935).

[6] F. W. Zerban, J. Assn. Official Agr. Chem. 26, 143

(1943).

[7] F. W. Zerban and J. Martin, J. Assoc. Offic. Agr.

Chemists 27, 295 (1944).

[8] R. F. Jackson, C. G. Silsbee, and M. J. Proffitt, B. S.

Sci. Paper 519 (1926).

[9] R. F. Jackson and J. A. Mathews, BS J. Research 8, 404 (1932) RP426.

[10] F. Plato, J. Domke, and H. Harting, Z. Ver. deut.

Zilcker-Ind. 50, 982, 1079 (1900).

]11] D. Sidersky, Les densit^s des solutions sucr^es k

differentes temperatures, Paris (1908).

[12] J. Domke, Z. Ver. deut. Ziicker-Ind. 62, 302 (1912).

[13] F. J. Bates and H. W. Bearce, BS Tech. Paper, T115

(1918).

[14] C. F. Snyder and L. D. Hammond, NBS Circular C457 (1946).

[15] K. Dowes-Dekker and T. J. D. Erlee, Arch. Suikerind. Ned. en Ned.-Indie 38, III 697 (1930).

[16] R. F. Jackson, BS Sci. Paper 293 (1916).

[17] C. N. Riiber, Ber. 56, 2185 (1923).

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