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 a 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.
| Fig. 8. |
The determination of the density of a liquid by weighing a plummet in air, and in the standard and experimental liquids, has been put into a very convenient laboratory form by means of the apparatus known as a Westphal balance (fig. 8). It consists of a steelyard mounted on a fulcrum; one arm carries at its extremity a heavy bob and pointer, the latter moving along a scale affixed to the stand and serving to indicate when the beam is in its standard position. The other arm is graduated in ten divisions and carries riders—bent pieces of wire of determined weights—and at its extremity a hook from which the glass plummet is suspended. To complete the apparatus there is a glass jar which serves to hold the liquid experimented with. The apparatus is so designed that when the plummet is suspended in air, the index of the beam is at the zero of the scale; if this be not so, then it is adjusted by a levelling screw. The plummet is now placed in distilled water at 15°, and the beam brought to equilibrium by means of a rider, which we shall call 1, hung on a hook; other riders are provided, 1⁄10th and 1⁄100th respectively of 1. To determine the density of any liquid it is only necessary to suspend the plummet in the liquid, and to bring the beam to its normal position by means of the riders; the relative density is read off directly from the riders.
3. Methods depending on the free suspension of the solid in a liquid of the same density have been especially studied by Retgers and Gossner in view of their applicability to density determinations of crystals. Two typical forms are in use; in one a liquid is prepared in which the crystal freely swims, the density of the liquid being ascertained by the pycnometer or other methods; in the other a liquid of variable density, the so-called “diffusion column,” is prepared, and observation is made of the level at which the particle comes to rest. The first type is in commonest use; since both necessitate the use of dense liquids, a summary of the media of most value, with their essential properties, will be given.
Acetylene tetrabromide, C2H2Br4, which is very conveniently prepared by passing acetylene into cooled bromine, has a density of 3.001 at 6° C. It is highly convenient, since it is colourless, odourless, very stable and easily mobile. It may be diluted with benzene or toluene.
Methylene iodide, CH2I2, has a density of 3.33, and may be diluted with benzene. Introduced by Brauns in 1886, it was recommended by Retgers. Its advantages rest on its high density and mobility; its main disadvantages are its liability to decomposition, the originally colourless liquid becoming dark owing to the separation of iodine, and its high coefficient of expansion. Its density may be raised to 3.65 by dissolving iodoform and iodine in it.
Thoulet’s solution, an aqueous solution of potassium and mercuric iodides (potassium iodo-mercurate), introduced by Thoulet and subsequently investigated by V. Goldschmidt, has a density of 3.196 at 22.9°. It is almost colourless and has a small coefficient of expansion; its hygroscopic properties, its viscous character, and its action on the skin, however, militate against its use. A. Duboin (Compt. rend., 1905, p. 141) has investigated the solutions of mercuric iodide in other alkaline iodides; sodium iodo-mercurate solution has a density of 3.46 at 26°, and gives with an excess of water a dense precipitate of mercuric iodide, which dissolves without decomposition in alcohol; lithium iodo-mercurate solution has a density of 3.28 at 25.6°; and ammonium iodo-mercurate solution a density of 2.98 at 26°.