_a_ - 2_a_ʹ
_P_ = -----------.
_m_
For the copper reduction data the following are used:
_G_ = the weight of 100 cubic centimeters of the original solution:
_Gʹ;_ = the same for the inverted solution: Allowance must be made here
both for the dilution and for the 5 per cent increase of the inverted
sugar, but the latter number is so small that it need not be calculated
accurately.
_w_ = the weight of the original solution used for the estimation:
_wʹ_ = the same factor for the inverted solution:
_k_ = the weight of cupric oxid reduced by _w_:
_kʹ_ = the same factor for _wʹ_:
_p_ = the weight of cane sugar present in 100 cubic centimeters of the
original solution: The formula to be employed then is
_Gʹ kʹ G k_
_p_ = 0.4308(2 ------ - -----).
_wʹ w_
This method has been applied to the estimation of cane sugar in
molasses, apple juices and other substances. It is recommended by the
authors as a simple and accurate means of estimating sucrose in all
solutions containing it. The methods of making the copper reductions
will be given hereafter.
=99. Application of the Process.=—In practice the process of inversion
is used chiefly in the analysis of molasses and low grade massecuites.
In approximately pure sugars the direct polarization is sufficiently
accurate for all practical purposes. In molasses resulting from the
manufacture of beet sugar are often found considerable quantities of
raffinose, and the inversion process has been adapted to that character
of samples. In molasses, in sugar cane factories, the disturbing
factors are chiefly invert sugars and gums. The processes used for
molasses will be given in another paragraph. In certain determinations
of lactose the process of inversion is also practiced, but in this
case the lactose is converted into dextrose and galactose, and the
factors of calculation are altogether different. The process has also
been adapted by McElroy and Bigelow to the determination of sucrose in
presence of lactose, and this method will be described further on. In
general the process of inversion is applicable to the determination of
sucrose in all mixtures of other optically active bodies, which are not
affected by the methods of inversion employed.
=100. Determination of Sucrose and Raffinose.=—Raffinose is a sugar
which often occurs in beets, and is found chiefly in the molasses after
the chief part of the sucrose has been removed by crystallization. It
is also found in many seeds, notably in those of the cotton plant. In a
pure solution of sucrose and raffinose, both sugars may be determined
by the inversion method of Creydt.[63] The inversion is effected by
means of hydrochloric acid in the manner described by Clerget. The
following formulas are calculated for a temperature of observation
of 20°, and the readings should be made as near that temperature as
possible.
_C_ - 0.493_A_
(1) _S_ = --------------
0.827
_A_ - _S_ 6
(2) _R_ = --------- = 1.017_A_ - ------.
1.57 1.298
In these formulas _S_ and _R_ are the respective per cents of sucrose
and raffinose desired, _A_ the polarization in sugar degrees before
inversion, _B_ the polarization after inversion read at 20°, and _C_
is the algebraic difference between _A_ and _B_. It must be understood
that these formulas are applicable only to a solution containing no
other optically active substances, save sucrose and raffinose.
=101. Specific Rotatory Power.=—In order to compare among themselves
the rotations produced on a plane of polarized light by different
optically active bodies in solution, it is convenient to refer them all
to an assumed standard. The degree of rotation which the body would
show in this condition, is found by calculation, since, in reality,
the conditions assumed are never found in practice. In the case of
sugars and other optically active bodies, the standard of comparison
is called the specific rotatory power. This factor in any given case,
is the angular rotation which would be produced by any given substance
in a pure anhydrous state if it were one decimeter in length and of a
specific gravity equal to water. These are conditions which evidently
do not exist in the case of sugars, since crystalline sugar particles
have no polarizing power, and it would be impossible to pass a ray
of light through an amorphous sugar column of the length specified.
The specific rotatory power is therefore to be regarded as a purely
theoretical factor, calculated from the actual data obtained by the
examination of the solution of any given substance. If the length
of the observation tube in decimeters be represented by _l_, the
percentage of the polarizing body in 100 grams by _p_, and the specific
gravity of the solution by _d_, and the observed angle of rotation by
_a_, then the factor is calculated from the formula:
_a_. 100
[_a_]_{Dj} = ---------------.
_p_. _d_. _l_.
The symbols Dj refer to the character of light employed, D indicating
the monochromatic sodium flame, and j the transition tint from white
light.
If the weight of the polarizing body _c_ be given or known for 100
cubic centimeters of the solution the formula becomes
_a_. 100
[_a_]_{Dj} = ----------.
_c_. _l_.
The latter formula is the one easier of application since it is only
necessary in applying it to dissolve a given weight of the active body
in an appropriate solvent and to complete the volume of the solution
exactly to 100 cubic centimeters. It is therefore unnecessary in this
case to determine the specific gravity.
=102. Formulas for Calculating Specific Rotatory Power.=—In order
to determine the specific rotatory power (gyrodynat[64]) of a given
substance it is necessary to know the specific gravity and percentage
composition or concentration of its solution, and to examine it with
monochromatic polarized light in an instrument by which the angular
rotation can be measured. The gyrodynat of any body changes with its
degree of concentration, in some cases with the temperature, and
always with the color of the light. With the red rays the gyrodynat
is least and itprogressively increases as the violet end of the
spectrum is approached. In practice the yellow ray of the spectrum
has been found most convenient for use, and in the case of sugars
the gyrodynat is always expressed either in terms of this ray or if
made with color compensating instruments in terms of the sensitive or
transition tint. In the one case the symbol used is (_a_)_{D} and in
the other (_a_)_{j}. From this statement it follows that (_a_)_{D} is
always numerically less than (_a_)_{j}. Unless otherwise specified
the gyrodynat of a body is to be considered as determined by yellow
monochromatic light, and therefore corresponds to _a__{D}.[65]
=103. Variations in Specific Rotatory Power.=—The gyrodynat of any
optically active body varies with the nature of the solvent, the
strength of the solution, and the temperature.[66]
Since water is the only solvent of importance in determining the
gyrodynat of sugars it will not be necessary here to discuss the
influence of the nature of the solvent. In respect of the strength of
the solution it has been established that in the case of cane sugar the
gyrodynat decreases while with dextrose it increases with the degree
of concentration. The influence of temperature on the gyrodynat of
common sugars is not of great importance save in the case of levulose,
where it is the most important factor, the gyrodynat rapidly increasing
as the temperature falls. It is of course understood that the above
remarks do not apply to the increase or decrease in the volume of a
solution at changed temperatures. This influence of temperature is
universally proportional to the change of volume in all cases, and
this volumetric change is completely eliminated when the polarizations
are made at the temperatures at which the solutions are completed to
standard volumes.
=104. Gyrodynatic Data for Common Sugars.=—In the case of cane sugar
the gyrodynat for twenty-five grams of sugar in 100 grams of solution
at 20° is [_a_]_{D} = 66°.37. This is about the degree of concentration
of the solutions employed in the shadow lamplight polariscopes. For
seventeen grams of sugar in 100 grams of solution the number is
[_a_]_{D} = 66°.49. This is approximately the degree of concentration
for the laurent instrument.
For any degree of concentration according to Tollens the gyrodynat may
be computed by the following formula: [_a_]_{D} = 66°.386 + 0.015035_p_
- 0.0003986_p_², in which _p_ is the number of grams of sugar in 100
grams of the solution.[67] In the table constructed by Schmitt the data
obtained are as follows:
In 100 parts by weight Specific Rotation _a_
of solution. gravity Concentration for 100 mm.
Sugar _p_. Water _q_. at 20° C. _d_. _c_ = _pd_. at 20° C. [_a_]_{D}.
64.9775 35.0225 1.31650 85.5432 56°.134 65°.620
54.9643 45.0357 1.25732 69.1076 45°.533 65°.919
39.9777 60.0223 1.17664 47.0392 31°.174 66°.272
25.0019 74.9981 1.10367 27.5938 18°.335 66°.441
16.9926 83.0074 1.06777 18.1442 12°.064 66°.488
9.9997 90.0003 1.03820 10.3817 6°.912 66°.574
4.9975 95.0025 1.01787 5.0868 3°.388 66°.609
1.9986 98.0014 1.00607 2.0107 1°.343 66°.802
=105. Bi-Rotation.=—Some sugars in fresh solution show a gyrodynat
much higher than the normal, sometimes lower. The former phenomenon
is called bi- the latter semi-rotation. Dextrose shows birotation in
a marked degree, also maltose and lactose. After standing for a few
hours, or immediately on boiling, solutions of these sugars assume
their normal state of rotation. The addition of a small quantity of
ammonia also causes the birotation to disappear.[68] This phenomenon
is doubtless due to a certain molecular taxis, which remains after
solution is apparently complete. The groups of molecules thus held in
place have a certain rotatory power of their own and this is superadded
to that of the normal solution. After a time, under the stress of the
action of the solvent, these groups are broken up and the solution then
assumes its normal condition.
=106. Gyrodynat of Dextrose.=—The gyrodynat of dextrose, as has already
been mentioned, increases with the degree of concentration, thus
showing a property directly opposite that of sucrose.
The general formula for the anhydrous sugar is [_a_]_{D} = 52.°718 +
0.017087_p_ + 0.0004271_p_². In this formula _p_ represents the grams
of dextrose in 100 grams of the solution. In a ten per cent solution
the gyrodynat of dextrose is therefore nearly exactly [_a_]_{D}20° =
53°. As calculated by Tollens the gyrodynats corresponding to several
degrees of concentration are shown in the following table:
_p_ = grams in 100 [_a_]_{D}20° calculated for
grams of solution. anhydrous dextrose.
7.6819 52°.89
9.2994 52°.94
9.3712 52°.94
10.0614 52°.96
10.6279 52°.98
12.9508 53°.05
18.6211 53°.25
31.6139 53°.83
40.7432 54°.34
43.9883 54°.54
53.0231 55°.17
82.6111 57°.80
=107. Gyrodynats of Other Sugars.=—Of the other sugars it will be
sufficient to mention only levulose, maltose, lactose, and raffinose.
For complete tables of gyrodynatic powers the standard books on
carbohydrates may be consulted.[69]
The gyrodynat of levulose is not definitely established. At 14° the
number is nearly expressed by [_a_]_{D}14° = -93°.7.
Invert sugar, which should consist of exactly equal molecules of
dextrose and levulose, has a gyrodynat expressed by the formula
[_a_]_{D}0° = -27°.9, with a concentration equivalent to 17.21 grams of
sugar in 100 cubic centimeters. The gyrodynat decreases with increase
of temperature, according to the formula [_a_]_{D}_t_° = -(27°.9
- 0.32_t_°). According to this formula the solution is neutral to
polarized light at 87°.2, and this corresponds closely to the data of
experiment.
Maltose, in a ten per cent solution at 20°, shows a gyrodynat of
[_a_]_{D}20° = 138°.3.
The general formula for other degrees of concentration is [_a_]_{D} =
140°.375 - 0.01837_p_ - 0.095_t_, in which _p_ represents the number
of grams in 100 grams of the solution and _t_ the temperature of
observation.
In the case of lactose [_a_]_{D} = 52°.53, and this number does not
appear to be greatly influenced by the degree of concentration; but is
somewhat diminished by a rising temperature.
The gyrodynat of raffinose in a ten per cent solution is [_a_]_{D} =
104°.5.