ρ_l_
whence α = [(_a_ - 1)_x_ + _p_] ----.
_V_
If now there be introduced into the calculation the final angle of
rotation αₙ, which can be determined with great exactness; we have
_p_ρ_l_ (_a_ - 1)_x_
αₙ = ------- and consequently α = αₙ[1 + ------------],
_V_ _p_
(_a_ - 1)_x_ α
whence ------------- = --- - 1.
_p_ αₙ
This equation gives the quantity _x_ of the unstable matter which is
transformed into the stable modification in the time θ.
It must be admitted that the quantity _dx_ which is changed during the
infinitely small time _d_θ is proportional to the mass _x_ which still
exists at the moment θ, whence _dx_ = -Cʹ_xd_θ where Cʹ represents a
constant positive factor. From this is derived the equation
_dx_
----- = -Cʹ_d_θ.
_x_
Integrating and calling _x_ the quantity of matter changed to the
stable form at the moment θ, corresponding to a rotation α₀, we have
1 _x_₀
Cʹ = ------- log. nap. ----, and taking into consideration
θ - θ₀ _x_
the equation given above, and substituting common for superior
logarithms we get
1 α₀ - αₙ
C = --------- log. ---------.
θ - θ₀ α - αₙ
Experience has shown that such a constant C really exists, and
its value can be easily calculated from the data of Parcus and
Tollens.[122] The mean value of C from these data is 0.0301 for
arabinose; 0.0201 for xylose; 0.0393 for rhamnose; 0.0202 for fucose;
0.00927 for galactose; 0.00405 for lactose; 0.00524 for maltose, and
for dextrose, 0.00348 at 11° to 13° and 0.00398 from 13° to 15°. The
constant C as is well known, increases as the temperature is raised.
The constant C, at a given temperature, measures the progress of the
phenomenon of the change from the unstable to the stable state. It will
be noticed that among the sugars possessing multirotation properties
the pentoses possess a much higher speed of transformation than the
others.
=150. Estimation of Pentose Sugars and Pentosans as Furfurol.=—The
production of furfurol by distilling carbohydrates with an acid has
already been mentioned. Tollens and his associates have shown that with
pentose sugars, and carbohydrate bodies yielding them, the production
of furfurol is quantitive.
The production and estimation of furfurol have been systematically
studied by Krug, to whose paper the reader is referred for the complete
literature of the subject.[123] The essential principles of the
operation are based on the conversion of the pentoses into furfurol by
distilling with a strong acid, and the subsequent precipitation and
estimation of the furfurol formed in the first part of the reaction.
The best method of conducting the distillation is as follows:
Five grams of the pentose substance are placed in a flask of about a
quarter liter capacity, with 100 cubic centimeters of hydrochloric acid
of 1.06 specific gravity. The arrangement of the apparatus is shown in
Fig. 46. The flame of the lamp is so regulated as to secure about two
cubic centimeters of distillate per minute.
[Illustration: FIGURE 46. DISTILLING APPARATUS FOR PENTOSES.]
The distillate is received in a graduated cylinder and as soon
as thirty cubic centimeters are collected, an equal quantity of
hydrochloric acid, of the strength noted, is added to the distilling
flask, allowing it to flow in slowly so as not to stop the ebullition.
The process is continued until a drop of the distillate gives no
sensible reaction for furfurol when tested with anilin acetate. The
test is applied as follows: Place a drop of the distillate on a piece
of filter paper moistened with anilin acetate. The presence of furfurol
will be disclosed by the production of a brilliant red color. Usually
about three hours are consumed in the distillation, during which time a
little less than 400 cubic centimeters of distillate is obtained. The
distillate is neutralized with solid sodium carbonate and, in order
to have always the same quantity of common salt present, 10.2 grams
of sodium chlorid are added for each fifty cubic centimeters of water
necessary to make the total volume to half a liter.[124]
The reactions with pentosans probably consist in first splitting up of
the molecule into a pentose and the subsequent conversion of the latter
into furfurol according to the following equations:
(C₅H₈O₄)ₙ + (H₂O)ₙ = (C₅H₁₀O₅)ₙ
Pentosan. Water. Pentose.
and
(C₅H₁₀O₅)ₙ = (C₅H₄O₂)ₙ + (3H₂O)ₙ.
Pentose. Furfurol. Water.
=151. Determination of Furfurol.=—The quantity of furfurol obtained by
the process mentioned above may be determined in several ways.
_As Furfuramid._—When ammonia is added to a saturated solution of
furfurol, furfuramid, (C₅H₄O)₃N₂, is formed. In order to secure the
precipitate it is necessary that the furfurol be highly concentrated
and this can only be accomplished by a tedious fractional distillation.
This method, therefore, has little practical value.
_As Furfurolhydrazone._—Furfurol is precipitated almost quantitively,
even from dilute solutions, by phenylhydrazin. The reaction is
represented by the equation:
C₆H₈N₂ + C₅H₄O₂ = C₁₁H₁₀N₂O + H₂O.
Phenylhydrazin. Furfurol. Furfurolhydrazone. Water.
=152. Volumetric Methods.=—Tollens and Günther have proposed
a volumetric method which is carried out as follows:[125] The
distillation is accomplished in the manner described. The distillate
is placed in a large beaker, neutralized with sodium carbonate and
acidified with a few drops of acetic. Phenylhydrazin solution of
known strength is run in until a drop of the liquid, after thorough
mixing, shows no reaction for furfurol with anilin acetate. The
reagent is prepared by dissolving five grams of pure phenylhydrazin and
three of glacial acetic acid in distilled water, and diluting to 100
cubic centimeters. The solution is set by dissolving from two-tenths
to three-tenths gram of pure furfurol in half a liter of water and
titrating with the phenylhydrazin as indicated above. The quantity of
the pentose used has a great influence on the result.
With nearly a gram of arabinose about fifty per cent of furfurol were
obtained while when nearly five grams were used only about forty-six
per cent of furfurol were found. With xylose a similar variation was
found, the percentage of furfurol, decreasing as the quantity of
pentose increased. The method, therefore, gives only approximately
accurate results.
=153. Method of Stone.=—Another volumetric method proposed by Stone
is based on the detection of an excess of phenylhydrazin by its
reducing action on the fehling reagent.[126] A standard solution of
phenylhydrazin is prepared by dissolving one gram of the hydrochlorate
and three grams of sodium acetate in water and completing the volume
of the liquor to 100 cubic centimeters. This solution contains 1.494
milligrams of phenylhydrazin in each cubic centimeter, theoretically
equivalent to 1.328 milligrams of furfurol. The reagent is set by
titrating against a known weight of furfurol. Pure furfurol may be
prepared by treating the crude article with sulfuric acid and potassium
dichromate, and subjecting the product to fractional distillation.
The distillate is treated with ammonia and the furfuramid formed is
purified by recrystallizing from alcohol and drying over sulfuric acid.
One gram of this furfuramid is dissolved in dilute acetic acid and
the volume completed to one liter with water.[127] The phenylhydrazin
solution being unstable, is to be prepared at the time of use.
The titration is conducted as follows: Twenty-five cubic centimeters of
the distillate obtained from a pentose body, by the method described
above, are diluted with an equal volume of water, a certain quantity
of the phenylhydrazin solution added to the mixture from a burette and
the whole heated quickly to boiling. The flask is rapidly cooled and a
portion of its contents poured on a filter. The filtrate should have
a pale yellow color and be perfectly clear. If it become turbid on
standing, it should be refiltered. Two cubic centimeters of the clear
filtrate are boiled with double the quantity of the fehling reagent.
If phenylhydrazin be present, the color of the mixture will change
from blue to green. By repeating the work, with varying quantities of
phenylhydrazin, a point will soon be reached showing the end of the
reaction in a manner entirely analogous to that observed in volumetric
sugar analysis.
In practice the volumetric methods have given place to the more exact
gravimetric methods described below.
=154. Gravimetric Methods.=—The distillation is carried on and the
volume of the distillate completed to half a liter as described above.
Chalmot and Tollens then proceed as follows:[128] Ten cubic centimeters
of a solution of phenylhydrazin acetate, containing in 100 cubic
centimeters twelve grams of the phenylhydrazin and seven and a half
grams of glacial acetic acid dissolved and filtered, are added to the
distillate and the mixture stirred with an appropriate mechanism for
half an hour. The furfurolhydrazone at the end of this time will have
separated as small reddish-brown crystals. The mixture is then thrown
onto an asbestos filter and the liquid separated with suction. The
suction should be very gradually applied so as not to clog the felt.
The precipitate adhering to the beaker is washed into the filter with
100 cubic centimeters of water. The precipitate is dried at about 60°
and weighed. As a check the hydrazone may be dissolved in hot alcohol,
the filter well washed, dried and again weighed. To obtain the weight
of furfurol the weight of hydrazone found is multiplied by 0.516 and
0.025 added to compensate for the amount which was held in solution
or removed by washing. Less than one per cent of pentose can not be
determined by this method since that amount is equalled by the known
losses during the manipulation.
_Factor._—To convert the furfurol found into pentoses, the following
factors are used:
Per cent furfurol Multiply for
obtained from Multiply for Multiply for penta-glucoses
five grams of arabinose by. xylose by. by.
pentoses.
2.5 per cent or less 1.90 1.70 1.67
5.0 ” ” ” more 2.04 1.90 1.92
=155. Method Of Krug.=—In conducting the determination of furfurol,
according to the method of Chalmont and Tollens just noticed, Krug
observed that the filtrate, after standing for some time, yielded a
second precipitate of furfurol hydrazone. Great difficulty was also
experienced in collecting the precipitate upon the filter on account
of the persistency with which it stuck to the sides of the vessel
in which the precipitation took place.[129] In order to avoid these
two objections, Krug modified the method as described below and this
modified method is now exclusively used in this laboratory.
After the precipitation of the furfurol hydrazone, it is stirred
vigorously, by means of an appropriate mechanical stirrer, for at
least half an hour and then allowed to rest for twenty-four hours. On
filtering after that length of time the filtrate remains perfectly
clear and no further precipitation takes place. After the filtration is
complete and the beaker and filtering tube well washed, no attempt is
made to detach the part of the filtrate adhering to the beaker but the
whole of the precipitate, both that upon the filter and that adhering
to the sides of the beaker, is dissolved in strong alcohol, from thirty
to forty cubic centimeters being used. The alcoholic solution is
collected in a small weighed flask, the alcohol evaporated at a gentle
heat and the last traces of water removed by heating to 60° and blowing
a current of dry air through the flask. After weighing the precipitate
of furfurol hydrazone, obtained as above, the calculation of the weight
of pentose bodies is accomplished by means of the usual factors.
=156. Precipitation of Furfurol with Pyrogalol.=—Furfurol is thrown
out of solution in combination with certain phenol bodies by heating
together in an acid solution. Hotter has proposed a method for the
determination of furfurol based on the above fact.[130] The furfurol
is obtained by distillation in the manner already described and
hydrochloric acid is added if necessary to secure twelve per cent of
that body in a given volume. The furfurol is thrown out of an aliquot
portion by heating with an excess of pyrogalol in closed tubes for
about two hours at 110°. The reaction takes place in two stages,
represented by the following equations: