graduated tube. Solids may be directly admitted to the tube from a weighing bottle, while liquids are conveniently introduced by means of small stoppered bottles, or, in the case of exceptionally volatile liquids, by means of a bulb blown on a piece of thin capillary tube, the tube being sealed during the weighing operation, and the capillary broken just before transference to the apparatus. To prevent the bottom of the apparatus being knocked out by the impact of the substance, a layer of sand, asbestos or sometimes mercury is placed in the tube. To complete the experiment, the graduated tube containing the expelled air is brought to a constant and determinate temperature and pressure, and this volume is the volume which the given weight of the substance would occupy if it were a gas under the same temperature and pressure. The vapour density is calculated by the following formula:
in which W = weight of substance taken, V = volume of air expelled, α = 1/273 = .003665, t and p = temperature and pressure at which expelled air is measured, and s = vapour pressure of water at t°.
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Fig. 6. |
By varying the material of the bulb, this apparatus is rendered available for exceptionally high temperatures. Vapour baths of iron are used in connexion with boiling anthracene (335°), anthraquinone (368°), sulphur (444°), phosphorus pentasulphide (518°); molten lead may also be used. For higher temperatures the bulb of the vapour density tube is made of porcelain or platinum, and is heated in a gas furnace.
(4a) Hofmann’s Method.—Both the modus operandi and apparatus employed in this method particularly recommend its use for substances which do not react on mercury and which boil in a vacuum at below 310°. The apparatus (fig. 6) consists of a barometer tube, containing mercury and standing in a bath of the same metal, surrounded by a vapour jacket. The vapour is circulated through the jacket, and the height of the mercury read by a cathetometer or otherwise. The substance is weighed into a small stoppered bottle, which is then placed beneath the mouth of the barometer tube. It ascends the tube, the substance is rapidly volatilized, and the mercury column is depressed; this depression is read off. It is necessary to know the volume of the tube above the second level; this may most efficiently be determined by calibrating the tube prior to its use. Sir T. E. Thorpe employed a barometer tube 96 cm. long, and determined the volume from the closed end for a distance of about 35 mm. by weighing in mercury; below this mark it was calibrated in the ordinary way so that a scale reading gave the volume at once. The calculation is effected by the following formulae:—
in which w = weight of substance taken; t = temperature of vapour jacket; V = volume of vapour at t; h = height of barometer reduced to 0°; t1 = temperature of air; h1 = height of mercury column below vapour jacket; t2 = temperature of mercury column not heated by vapour; h2 = height of mercury column within vapour jacket; s = vapour tension of mercury at t°. The vapour tension of mercury need not be taken into account when water is used in the jacket.
(4b) Demuth and Meyer’s Method.—The principle of this method is as follows:—In the ordinary air expulsion method, the vapour always mixes to some extent with the air in the tube, and this involves a reduction of the pressure of the vapour. It is obvious that this reduction may be increased by accelerating the diffusion of the vapour. This may be accomplished by using a vessel with a somewhat wide bottom, and inserting the substance so that it may be volatilized very rapidly, as, for example, in tubes of Wood’s alloy, and by filling the tube with hydrogen. (For further details see Ber. 23, p. 311.)
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Fig. 7. |
We may here notice a modification of Meyer’s process in which the increase of pressure due to the volatilization of the substance, and not the volume of the expelled air, is measured. This method has been developed by J. S. Lumsden (Journ. Chem. Soc. 1903, 83, p. 342), whose apparatus is shown diagrammatically in fig. 7. The vaporizing bulb A has fused about it a jacket B, provided with a condenser c. Two side tubes are fused on to the neck of A: the lower one leads to a mercury manometer M, and to the air by means of a cock C; the upper tube is provided with a rubber stopper through which a glass rod passes—this rod serves to support the tube containing the substance to be experimented upon, and so avoids the objection to the practice of withdrawing the stopper of the tube, dropping the substance in, and reinserting the stopper. To use the apparatus, a liquid of suitable boiling-point is placed in the jacket and brought to the boiling-point. All parts of the apparatus are open to the air, and the mercury in the manometer is adjusted so as to come to a fixed mark a. The substance is now placed on the support already mentioned, and the apparatus closed to the air by inserting the cork at D and turning the cock C. By turning or withdrawing the support the substance enters the bulb; and during its vaporization the free limb of the manometer is raised so as to maintain the mercury at a. When the volatilization is quite complete, the level is accurately adjusted, and the difference of the levels of the mercury gives the pressure exerted by the vapour. To calculate the result it is necessary to know the capacity of the apparatus to the mark a, and the temperature of the jacket.
Methods depending on the Principles of Hydrostatics.—Hydrostatical principles can be applied to density determinations in four typical ways: (1) depending upon the fact that the heights of liquid columns supported by the same pressure vary inversely as the densities of the liquids; (2) depending upon the fact that a body which sinks in a liquid loses a weight equal to the weight of liquid which it displaces; (3) depending on the fact that a body remains suspended, neither floating nor sinking, in a liquid of exactly the same density; (4) depending on the fact that a floating body is immersed to such an extent that the weight of the fluid displaced equals the weight of the body.
1. The method of balancing columns is of limited use. Two forms are recognized. In one, applicable only to liquids which do not mix, the two liquids are poured into the limbs of a U tube. The heights of the columns above the surface of junction of the liquids are inversely proportional to the densities of the liquids. In the second form, named after Robert Hare (1781–1858), professor of chemistry at the university of Pennsylvania, the liquids are drawn or aspirated up vertical tubes which have their lower ends placed in reservoirs containing the different liquids, and their upper ends connected to a common tube which is in communication with an aspirator for decreasing the pressure within the vertical tubes. The heights to which the liquids rise, measured in each case by the distance between the surfaces in the reservoirs and in the tubes, are inversely proportional to the densities.
2. The method of “hydrostatic weighing” is one of the most important. The principle may be thus stated: the solid is weighed in air, and then in water. If W be the weight in air, and W1 the weight in water, then W1 is always less than W, the difference W − W11 representing the weight of the water displaced, i.e. the weight of a volume of water equal to that of the solid. Hence W/(W − W1) is the relative density or specific gravity of the body. The principle is readily adapted to the determination of the relative densities of two liquids, for it is obvious that if W be the weight of a solid body in air, W1 and W2 its weights when immersed in the liquids, then W − W1 and W − W2 are the weights of equal volumes of the liquids, and therefore the relative density is the quotient (W − W1)/(W − W2). The determination in the case of solids lighter than water is effected by the introduction of a sinker, i.e. a body which when affixed to the light solid causes it to sink. If W be the weight of the experimental solid in air, w the weight of the sinker in water, and W1 the weight of the solid plus sinker in water, then the relative density is given by W/(W + w − W1). In practice the solid or plummet is suspended from the balance arm by a fibre—silk, platinum, &c.—and carefully weighed. A small stool is then placed over the balance pan, and on this is placed a beaker of distilled water so that the solid is totally immersed. Some balances are provided with a “specific gravity pan,” i.e. a pan with short suspending arms, provided with a hook at the bottom to which the fibre may be attached; when this is so, the stool is unnecessary. Any air bubbles are removed from the surface of the body by brushing with a camel-hair brush; if the solid be of a porous nature it is desirable to boil it for some time in water, thus expelling the air from its interstices. The weighing is conducted in the usual way by vibrations, except when the weight be small; it is then advisable to bring the pointer to zero, an operation rendered necessary by the damping due to the adhesion of water to the fibre. The temperature and pressure of the air and water must also be taken.
There are several corrections of the formula Δ = W/(W − W1) necessary to the accurate expression of the density. Here we can only summarize the points of the investigation. It may be assumed that the weighing is made with brass weights in air at t° and p mm. pressure. To determine the true weight in vacuo at 0°, account must be taken of the different buoyancies, or losses of true weight, due to the different volumes of the solids and weights. Similarly in the case of the weighing in water, account must be taken of the buoyancy of the weights, and also, if absolute densities be required, of the density of water at the temperature of the experiment. In a form of great accuracy the absolute density Δ(0°/4°) is given by
Δ(0°/4°) = (ραW − δW1)/(W − W1),
in which W is the weight of the body in air at t° and p mm. pressure, W1 the weight in water, atmospheric conditions remaining very nearly the same; ρ is the density of the water in which the body is weighed, α is (1 + αt°) in which α is the coefficient of cubical expansion of the body, and δ is the density of the air at t°, p mm. Less accurate formulae are Δ = ρ W/(W − W1), the factor involving the density of the air, and the coefficient of the expansion of the solid being disregarded, and Δ = W/(W − W1), in which the density of water is taken as unity. Reference may be made to J. Wade and R. W. Merriman, Journ. Chem. Soc. 1909, 95, p. 2174.
