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the ends of which are drawn out narrow and bent at right angles. The internal diameters of these two capillary tubes a and b are made unequal; in one, b, on which is placed a mark m, it measures about } millimetre; in the other it is less, not exceeding 1 millimetre at most. The filling of the apparatus is performed by the method shown in Fig. 52, the narrow tube a being fitted by means of a small cork to the glass bulb g, to the other limb of which is attached a piece of slender india-rubber tubing.

Dipping the wider tube b into the liquid and sucking at the india-rubber end, a sufficient vacuum may be produced if the bulb g be large enough, so that by keeping the tubing pinched with the finger enough liquid will enter to fill the apparatus.

The operation is complete when the liquid begins to drop out at a. The bulb is then removed, and the instrument placed nearly up to the level of the ends in a water-bath of the desired temperature. In the resulting changes of volume it will be seen that it is only in the wider capillary tube b that the level of liquid oscillates—that is to say, in the line of least resistance. In the narrower limb, it remains steady throughout at a. If at the desired temperature the liquid in the tube 6 stands outside the mark m, it can be adjusted by applying a piece of blotting-paper to the end a; if, on the other hand, it does not reach the mark, an additional drop of the solution may readily be introduced by applying it at a on the end of a glass rod; the capillary action of the tube sufficing to absorb it and carry forward the level of the liquid within 6.

This operation is capable of so much exactness that in successive experiments, assuming the temperature to continue perfectly uniform, the weight of the charged instrument will not vary by more than 0.1 to 0.2 milligramme. In removing the apparatus from the water-bath and wiping it previous to weighing, it is obviously requisite to avoid touching the point at a. The emptying is done by again attaching the glass bulb and blowing out the contents of the tube; then a little alcohol and ether sucked into it will serve to rinse it out and dry it.

Another form of Sprengel pycnometer is shown in Fig. 53.7 In this a thermometer is fused into the body of the instrument, whereby the temperature of the solution can be known with absolute certainty. The apparatus is furnished with capillary tubes as in the instrument already described ; but the end of the wider tube

May be obtained of Dr. Geissler, Bonn; or, Heintz, glassblower, Aachen.









is ground and fitted with a bend for immersion in the liquid to be aspirated.

Moreover, both ends can be closed with ground-glass caps to prevent loss by evaporation. This form of pycnometer is exceedingly convenient and accurate to work with, the specific gra

Fig. 53. vities determined from successive observations not varying more than two or three units in the fifth place of decimals.

If the specific gravity is to be determined accurately to the fourth decimal place, neglecting variations in the fifth, the temperature of the water-bath must not be allowed to vary by more than 0.2° Cent. With a pycnometer of 10 cubic centimetres capacity, filled with water at a temperature between 17o and 20° Cent., a variation of this amount will produce a difference of 0.4 milligramme in the weight; whilst in the case of other more expansible liquids the same amount of variation of temperature may cause a difference amounting to 2 milligrammes in the weight of 10 cubic centimetres, whereby the specific gravity will be altered by nearly 2 units in the fourth decimal place. In a pycnometer of 20 cubic centimetres capacity, the error will be half this amount.

As in observing the angles of rotation, a normal temperature of 20° Cent. is here also to be preferred. Cylindrical glass jars of several litres capacity, so as to maintain the temperature constant for some time, may be used as water-baths. The immersed thermometer should be graduated to at least fifths of a degree. In a pycnometer of 10 to 20 cubic centimetres capacity complete uniformity of temperature is generally attained in the course of ten minutes.

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§ 71. To determine the specific gravity or density we proceed as follows:- The pycnometer is filled at a temperature to, first with distilled water, from which the air has been previously expelled by boiling, and afterwards with the liquid under examination. If now we subtract from each of these weights the weight of the instrument empty, then putting

W for the weight of water,

F for the weight of liquid, F

will represent the specific gravity of the solution at a temW perature of to relative to that of water at the same temperature. Multiply this by the density of water at t° = Q (that of water at 4° Cent. being taken as 1), we get the specific gravity of the liquid at to relative to water at 4° Cent. Lastly, taking into account the influence on the weighings of the pressure of the atmosphere (density 0) we obtain the true specific weight, relative to water at 4° Cent., of the liquid at to in vacuo, which we may designated from the formula?

(Q - 0) + &

W The value so obtained expresses the weight in grammes of 1 cubic centimetre of the liquid at to weighed in vacuo.

At the normal temperature of 20° Cent. the density of water Q = 0.99826. Where some other temperature is employed the corresponding value of Q can be found in the table given in $ 73.

For the density ô of air—that is, the weight in grammes of 1 cubic centimetre, which varies with temperature and pressure, it will be sufficient to adopt the mean value 0.0012, or, reckoning to five places of decimals, 0.00119. ' If the specific gravity of the solution lies between 0.7 and 1:7, as is the case with nearly all solutions of optically active substances, the temperature of the air at the time of weighing being between 10° and 25°, and the barometric pressure between 720 and 770 millimetres, the above coefficient suffices to correct the influence of atmospheric pressure accurately to within at most 4 units in the fifth place of decimals. But in calculating specific rotations, it is sufficient to know the densities to the fourth decimal place.

Accordingly having ascertained the weight of the pycnometer 1 For the mode of deriving the formula, see F. Kohlrausch, Leitfaden d. prakt. Phys., 3 Aufl. S. 40. [The English reader may consult the translation already referred to on page 136.-D.C.R.]

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d" = ( 0-99707) + 0.00119,

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07). And

filled to the mark at 20° Cent. first with water and then with the liquid, the annexed formula will give the specific gravity :


log. 0.99707 = 0.998726 -1.

. Example: In determining the specific gravity of an aqueous solution of sugar, the pycnometer filled with water at 20° Cent. weighed W 13.6158 grammes, and filled with the solution F= 15:4015 grammes. Hence, by the formula above we get d = 1.1290.

= . Neglecting the reduction to vacuum-that is, taking the value simply F

0.99826—we get 1.1292, making the specific gravity 0.0002 W too high. Again, an alcoholic solution of camphor gave F= 11:4260 grammes, and, as before, W = 13•6158 grammes, whence d = 0·83863. By neglecting & the result would be 0.83763, or

0. 0.001 too small.

Having once determined the weight of water W, contained at the normal temperature by any particular pycnometer, we may Q – 0·00119

0.99707 reckon the quotient

= C (for 20°:
= C (°:


W with this constant the specific gravity of any liquid may be found from the value F by the forinula

d = F.C + 0.00119. If, as is not unusual, 17-5° Cent. is taken for normal temperature, then since at this temperature Q 0:99875, we get


W Lastly, if the specific gravity of a solution has to be determined at some temperature other than that at which the weight of water contained by the pycnometer has been ascertained, the change in capacity of the apparatus—that is, the coefficient of cubic expansion of glass—has to be taken into account. Let F represent the observed weight of liquid in the pycnometer at the

temperature to ; W the weight of water contained at temperature T°; Q the density of water at temperature T° (see table $ 73) ; ô the mean density of the air (0.0012); γ the coefficient of cubic expansion of glass, which may be taken at


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d* = (0-99756) + 0-00119.


then the specific gravity of a solution at the temperature to referred to water at 4° Cent. and reduced to its value in vacuo, may be obtained with sufficient accuracy from the formula

F die

[1 + (T t) »] (Q – 0) + d. W

E. Estimation of the Concentration of Solutions.

(Preparation of Solutions in Graduated Flasks.) $72. The concentrationby which term we mean the number of grammes of active substance in 100 cubic centimetres of solution—can be obtained by multiplying together the density and percentage weight determined as already described. It can, however, be ascertained directly by weighing a quantity of active substance in a measured flask and forming a solution of determinate volume. The latter method will suffice in cases where the object is simply to determine the specific rotation of some particular solution of the active substance. If, on the other hand, it be desired to know the variation of specific rotation consequent on changes in the proportion of inactive solvent present, and so to deduce the rotation-constant of the active substance itself, as described in SS 24 and 25, then it is essential to know the percentage composition of the solutions. The measuring flask may indeed also serve for determining this, for which purpose all that is necessary is Fig: 54.

simply to take the weight also of the contained volume of solution. The method is somewhat simpler, requiring fewer weighings than the process of preparing an indeterminate volume of solution, and then taking the specific gravity. On the other hand, it has the disadvantage that the volume cannot be nearly so accurately known with graduated flasks as with the pycnometer, and as we have to deal with larger volumes of the solutions, it requires longer time to bring the whole to the normal temperature. Moreover, it is not so easy a matter to prepare solutions exactly of the percentage desired. For exact observations,

the determination of specific gravity with the pycnometer is therefore far preferable.

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