Part 28

With organic compounds in water the value of K is almost constant.

Brown and Morris report results of their work in extending Raoult’s investigations of the molecular weight of the carbohydrates. The process is carried on as follows:

A solution of the carbohydrate is prepared containing a known weight of the substance in 100 cubic centimeters of water. About 120 cubic centimeters of the solution are introduced into a thin beaker of about 400 capacity. This beaker is closed with a stopper with three holes. Through one of these a glass rod for stirring the solution is inserted. The second perforation carries a delicate thermometer graduated to 0°.05. The temperature is read with a telescope. The beaker is placed in a mixture of ice and brine at a temperature from 2° to 3° below the freezing point of the solution. The solution is cooled until its temperature is from 0°.5 to 1° below the point of congelation. Through the third aperture in the stopper a small lump of ice taken from a frozen portion of the same solution, is dropped, causing at once the freezing process to begin. The liquid is briskly stirred and as the congelation goes on the temperature rises and finally becomes constant. The reading is then taken. The depression in the freezing point, controlled by the strength of the solution, should never be more than from 1° to 2°.

The molecular weights may also be determined by the boiling points of their solutions as indicated by the author, Beckmann, Hite, Orndorff and Cameron.

The method applied to some of the more important carbohydrates gave the following results:

DEXTROSE.

Calculated for C₆H₁₂O₆. Found. M = 180 M = 180.2

SUCROSE.

Calculated for C₁₂H₂₂O₁₁. Found. M = 342 M = 337.5

INVERTOSE (DEXTROSE AND LEVULOSE).

Calculated for C₆H₁₂O₆. Found. M = 180 M = 174.3

MALTOSE.

Calculated for C₁₂H₂₂O₁₁. Found. M = 342 M = 322

LACTOSE.

Calculated for C₁₂H₂₂O₁₁. Found. M = 342 M = 345

ARABINOSE.

Calculated for C₅H₁₀O₅. Found. M = 150 M = 150.3

RAFFINOSE. Calculated for C₁₈H₃₂O₁₆.5H₂O. Found. M = 594 M = 528

=149. Birotation.=—As is well known, dextrose exhibits in fresh solutions the phenomenon of birotation. The authors supposed that this phenomenon might have some relation to the size of the molecule. They, therefore, determined the molecular volume of freshly dissolved dextrose by the method of Raoult and found M = 180. The high rotatory power of recently dissolved dextrose is therefore not due to any variation in the size of its molecule.

The mathematical theory of birotation is given by Müller as follows. In proportion as the unstable modification A is transformed into the stable modification B, the rotation will vary. Let ρ = the specific rotatory power of B and aρ = that of A, both in the anhydrous state. Let now p grams of the substance be dissolved in V cubic centimeters of solvent and observed in a tube l decimeters in length. The time from making the solution is represented by θ. The angle of rotation α is read at the time θ. Let x = the mass of A, and y = that of B, and the equation is derived.

aρxl ρyl α = --------- + ------: V V

But x + y = p

ρl 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

pρl (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 dθ is proportional to the mass x which still exists at the moment θ, whence dx = -Cʹxdθ where Cʹ represents a constant positive factor. From this is derived the equation