5. RELATIONSHIP BETWEEN BOILING-POINT ELEVATION AND CONCENTRATION OF SOLUTE

Substituting in eq 118 the value of po-p from eq 117, we have

in which Bo is the boiling-point constant and represents the relation existing between the vapor pressure of the solvent and the rate of change in vapor pressure of the solvent with temperature. T-To or AT is the boiling-point clevation at an atmospheric pressure corresponding to To.

This equation is satisfactory for dilute solutions and is useful in determining the molecular weight of various substances. At high concentrations, however, the equation does not hold, because it does not correct for the mutual attraction between the solute and solvent molecules; therefore the relationship existing between the boilingpoint elevation and the concentration must be determined experimentally for each substance.

6. RELATIONSHIP BETWEEN BOILING-POINT ELEVATION AND ATMOSPHERIC PRESSURE

The boiling-point constant at any atmospheric pressure may be determined from the approximate Clausius-Clapeyron equation

in which R is the universal gas constant and AH。 the molal heat of vaporization of the solvent at its boiling point, To.

If eq 122 is substituted for its value in eq 121, we have

which is the boiling-point elevation equation for concentration x. If this equation holds for any atmospheric pressure at which the boiling point of the solvent is To, then it is true for the pressure of 760 mm Hg. When we change the subscripts of the factors in eq 123 to correspond to these pressure conditions, we have

Inasmuch as AH780/AH, is the ratio of the molal heats of vaporization of the solvent under two pressure conditions, their values may be expressed in any unit, and we may rearrange eq 126 and write it as

where AT, is the boiling-point elevation at any pressure, p, at which the solvent boils at a temperature of T,, and L, is the latent heat of vaporization of the solvent at this temperature. AT700 is the boilingpoint elevation at a pressure of 760 mm Hg, in which case the solvent boils at a temperature of T760, which, for water, is equal to 373.16° K, and L is the latent heat of vaporization of the solvent at this temperature expressed in the same units as L. This equation, which is sometimes referred to as Tishchenko's equation [5], may be used to determine the boiling-point elevation at pressures other than that for which the values have been experimentally determined.

7. DERIVATION OF BOILING-POINT ELEVATION TABLE

As has been stated elsewhere, empirical equations were calculated from Spengler's observed data. These equations were developed in the following manner:

Inasmuch as no observations were made at a pressure of exactly 1 atmosphere, the first step was to adjust the values determined at the pressure nearest 1 atmosphere for each concentration and purity to the value it would have at exactly 1 atmosphere. This was done by means of eq 127 expressed in the form

in which L/L780 was determined for each observed temperature by the equation

Lp
L780

=1.1074-1024tX10-6-510-9,

(129)

where t is the temperature in degrees centigrade corresponding to the observed temperature, T,, which is expressed in degrees Kelvin, or

Values given by eq 129 in the range 60° to 130° C are in agreement with values of L, according to Osborne, Stimson, and Ginnings [6]. The use of eq 128 to adjust the observed values of the boiling-point elevation to the boiling-point elevation which the solution would have at 1 atmosphere resulted in a very small change from the observed values. In all cases this change was less than 0.10° C.

These adjusted values were fitted to four empirical equations, one for each purity reported, by the method of least squares. They have the form

log104T760=aX3+bX2+cX+d,

where AT700 is the boiling-point elevation of the solution at 1 atmosphere; X is the concentration of solids in solution, in percent (Brix); and a, b, c, and d are constants from the least-squares data. The equations on page 366 show the values of the constants for each of the four equations.

Boiling-point elevations at other pressures were calculated from the values found by these empirical equations by means of eq 127. The values so calculated deviate from the observed values by a lesser amount than they do from the graphic-method values.

8. REFERENCES

[1] H. Claassen, Z. Ver. deut. Zucker-Ind. 54, 1161 (1904).

[2] A. L. Holven, Ind. Eng. Chem. 28, 452 (1936).

[3] O. Spengler, S. Böttger, and E. Werner, Z. Wirtshaftsgruppe Zuckerind. 88, 521 (1938).

[4] H. S. Taylor, A Treatise on Physical Chemistry (D. Van Nostrand Co., Inc., New York, N. Y., 1931).

[5] I. A. Tishchenko, Soviet. Sakhar Nos. 11/12, 31-3 (1933); Chem. Zentr. 2, 352 (1934).

[6] N. S. Osborne, H. F. Stimson, and D. C. Ginnings, J. Research NBS 23, 261 (1939) RP1229.

XXIV. CANDY TESTS

1. INTRODUCTION
(a) GENERAL

The need of a standard or reference procedure as a starting point for a rational development of various types of candy tests has been felt for some time. The method outlined below for simple barleysugar tests, as well as the special equipment specified for carrying it out, has been developed at this Bureau, not only as a basic procedure but also as a standard procedure for the routine testing of commercial sucrose with respect to heat stability. It is founded upon an old procedure,20 which generally is attributed [2, 4, 5, 7, 9] to S. C. Hooker, whose directions, as transmitted to various laboratories under his supervision were stated in approximately the following words.

21

(b) HOOKER TEST

Half a pound (227 g) of sugar is placed in a copper casserole of the following dimensions, 416 inches diameter at the top, 24 inches diameter at the bottom, and height 2 inches (inside measurements). After the addition of 3 oz (89 cc)22 of distilled water, the casserole is placed over the naked flame of a burner. The flame should be regulated previously to such a size that the total time of heating required to bring the temperature to 350° F (177° C) is 21 to 25 minutes. (It has been found that this condition will be fulfilled if 200 cc of water at room temperature is brought to a point of vigorous boiling in 41⁄2 to 5 minutes.)

20 The procedure was described in 1897 by Wiechmann [1], not as a control test but as a method of preparing "amorphous sugar" to be used in a study of allotropy in sucrose. The two sections of the description, separated in his paper, cover roughly every point of the Hooker procedure almost word for word. The paper includes analytical data on a dozen different candy plaques, one of which had been stored under a bell jar with calcium chloride desiccant while it developed a crystallizing area, of which there is presented a record of the rate of growth to a diameter of 51 mm and an excellent photograph at this stage.

"Hooker's directions are quoted here, because no exact statement of them is known to be readily available elsewhere.

"In certain copies of Hooker's directions, which probably were intended for use with wet-packed confectioners' sugars, the quantity of water was stated as "87 cc."

The contents of the casserole are continuously stirred until the sugar has dissolved, and the stirring rod is removed. If the size of the flame has been properly adjusted the solution should start to boil in about 5 minutes after being first put over the flame. At this point an inverted watch glass is placed over the casserole; otherwise the sugar will be apt to crystallize as the evaporation proceeds.

After the heating has continued precisely 15 minutes from the time when the casserole was first placed over the flame, the watch glass is removed and the solution is then thoroughly and constantly stirred without a moment's interruption until the boiling point has reached exactly 350° F (177° C), the thermometer being used as a stirring rod. The casserole is than instantly removed from the flame and its contents are as rapidly as possible emptied upon a polished copper slab 14x14x4 inches in size. In a few minutes the candy becomes brittle and can be broken up for any tests it is desired to make.23

The Hooker procedure is deficient chiefly in reproducibility. Experiments conducted at this Bureau indicate that most of this variability can be eliminated through the use of more definite specifica

COPPER NO.168.WG.

OAK

FIGURE 89.-Copper casserole as used in Hooker's procedure.
The drawing is adapted from the illustration presented by Murphy [5].

tions for the apparatus and procedure and by the omission of handstirring of the boiling sirup [4]. As a result of this study, a method has been developed which is designated the "National Bureau of Standards simple barley sugar test.'

2. NATIONAL BUREAU OF STANDARDS METHOD FOR BARLEY SUGAR

The Bureau method varies from the Hooker procedure in several respects, as summarized later in this discussion. All of these modifications are important to the convenience and uniformity of the test procedure, as also to the precision and reliability of the results, especially as obtained by different operators, and particularly as obtained in different laboratories. The following is the improved procedure.

n Most candy and sugar technologists regard commercial sucrose as being the "weaker" the greater the degree of hydrolysis which it undergoes upon conversion into hard candy under standardized conditions (2, 4, 5, 9, 10, 11]. Hooker's procedure originally was intended to indicate, through direct polarization of the resulting candy project, the relative "strength" of any lot of sugar, conceived as the apparent resistance of the sugar to hydrolysis under such conditions. In Hooker's laboratory no other tests of the candy product were made. In later development of candy test methods, various other observations have been applied to the candy product as criteria of the quality of the sugar. When Osborn [2], in 1912, introduced candy test methods as a means of control of quality in beet sugar production, substituting porcelain casseroles for those of copper, he immediately gave heed to the rates of crystallization of the individual candy products and also devoted special attention to the color of the candy and to the tendency of the sirupy mixture to "foam" upon first coming to a boil in the candy test. He finally omitted the direct polarization in most cases. Empirical means of roughly estimating in quantitative form, the tendencies of the sugar to cause foaming and caramelization were developed somewhat later by Proffitt [4].

(a) PROCEDURE

1. Weigh 250.00 ±0.05 g of the sugar sample on a dry basis and make up to a weight of 350.00 +0.05 g with cold equilibrium water 24 in a 600-ml chemical-resistant glass beaker (provided with a thermometer clasp, as specified on p. 375) previously tared with the thermometer and the notched watch-glass cover.

2. With the thermometer used as a stirring rod, loosen the compacted crystals from the bottom of the beaker, and mix them evenly with the liquid to form a homogeneous suspension. Continue the stirring until the crystals easily remain in suspension for some time, or until the temperature has ceased falling.

3. Replace the thermometer in its clasp (to avoid injury of the thermometer and the dripping of sirup), and set the beaker upon its supports in the stove with the burner alight and with the flame in correct stable adjusment. Immediately resume stirring of the mixture with the thermometer to prevent settling of the undissolved crystals.

4. On the instant the starting temperature of 30° C (86° F) is indicated, note "zero time" in the heating cycle (as for example, by the starting of a stop watch or a second counter).25 Proceed with the stirring until a temperature of 70° C (158° F) is indicated, when crystals of fine or medium granulated sugar ordinarily should be practically all dissolved.26 Clasp the thermometer at its proper working level, which will bring the bottom of the bulb to the position indicated in the drawing (fig. 90). Immediately cover the beaker with the watch glass as indicated in the drawing. Observe the sirup closely as the boiling point is approached" for its behavior during the transition interval between quiescent heat absorption and steady boiling is an important criterion of the probable stability of the sugar in storage as well as in candy making. There should be no considerable increase in the apparent volume of the sirup, not more than a trace of foamy scum should collect on the surface, and the transition interval should last not more than 30 seconds.28 Steady boiling usually is barely established when the thermometer indicates a temperature about 6° C (11° F) higher than it would indicate in boiling water in the same beaker. This is assumed to be the initial boiling temperature of the sirup.

5. Allow the sirup to boil under cover until its indicated temperature is just 120° C (248° F) [4] (which in a 23-minute cooking interval occurs approximately 15 minutes after the start of heating). On the instant this temperature is indicated, lift the watch glass at one edge and tip it to drain most of the adhering condensate down the side of the beaker into the boiling sirup. Do not disturb the sirup in any other manner. Place the wet watch glass into a drying oven at a temperature of about 105° C (221° F) without washing, for it may retain a small amount of sirup.

24 Equilibrium water is defined on p. 271.

25 If temperature-gradient data are desired, record elapsed time against a previously prepared schedule of temperatures. Such gradients are a valuable means of interpreting results in certain cases.

26 If grains still can be felt with the thermometer or can be seen, remove the beaker from the stove and proceed with the stirring without further heating until the refractory grains have disappeared. Return the beaker to the stove, and stir the sirup again until the temperature of 70° C is regained. Do not include the time consumed in these operations in the recorded duration of the cooking interval.

27 Remove the watch glass during the transition interval only if dew formation on the undersurface interferes with observation, or if its removal is required for the measurement or the quelling of foam. (See b (1), p. 373).

If a layer of sudsy foam accumulates on the surface of the sirup, proceed as indicated under b (1), p373.