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DW (i+at)X587

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Originally appearing in Volume V08, Page 49 of the 1911 Encyclopedia Britannica.
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DW (i+at)X587,780 (p-s)V ' in which W=weight of substance taken, V=volume of air expelled, a = 11273 = •003665, t and p =temperature and pressure at which expelled air is measured, and s = vapour pressure of water at t°. 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°),phosphoruspentasulphide(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 sub-stance 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: 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: (I) 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 Wi the weight in water, then Wi is always less than W, the difference W-W1 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--Wi) 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, Wi and W2 its weights when immersed in the liquids, then W-Wi 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 W, the weight of the solid plus sinker in water, then the relative density is given by W/(W+w-WI). 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 =W/(W-W2) 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 vacua at o°, 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 0(o°/4°) is given by (0°/4°) = (paW-SW,)/(W-W ), in which W is the weight of the body in air at t° and p mm. pressure, WI the weight in water, atmospheric conditions remaining very nearly the same; p is the density of the water in which the body is weighed, a is (1 +at°) in which a is the coefficient of cubical expansion of the body, and S is the density of the air at t°, p mm. Less accurate formulae are 0=p W/(W-W1), the factor involving the density of the air, and the coefficient of the expansion of the solid being disregarded, and ,N=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. D _ 76ow (I +0.0036651) 0.0012934XVXB h h, _ h2 B __ I +o•000i 8tr – (I +o•o001812 I +o•000l8t--s l in which w=weight of substance taken; t=temperatureee of vapour jacket; V=volume of vapour at t; h=height of barometer reduced to o° ; t, =temperature of air; hi = 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 some-what wide bottom, and inserting the substance so that it may be volatilized very rapidly, as, for example, in tubes of Wood's alloy, D and by filling the tube with hydrogen. (For further details see Ber. 23, p. 311.) 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 mano- meter 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 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 steel-yard 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 I, hung on a hook; other riders are provided, ;ath and 10bth respectively of I. 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 pre-pared 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°. Rohrbach's solution, an aqueous solution of barium and mercuric iodides, introduced by Carl Rohrbach, has a density of 3.588. Klein's solution, an aqueous solution of cadmium borotungstate, 2Cd(OH)2 • B203.9WO3.16H2O, introduced by D. Klein, has a density up to 3.28. The salt melts in its water of crystallization at 75° and the liquid thus obtained goes up to a density of 3.6. Silver-thallium nitrate, TIAg(NOi)2, introduced by Retgers, melts at 75° to forma clear liquid of density 4.8; it may be diluted with water. The method of using these liquids is in all cases the same; a particle is dropped in; if it floats a diluent is added and the mixture well stirred. This is continued until the particle freely swims, and then the density of the mixture is determined by the ordinary methods (see MINERALOGY). In the " diffusion column " method, a liquid column uniformly varying in density from about 3.3 to I is prepared by pouring a little methylene iodide into a long test tube and adding five times as much benzene. The tube is tightly corked to prevent evaporation, and allowed to stand for some hours. The density of the column at any level is determined by means of the areometrical beads proposed by Alexander Wilson (1714-1786), professor of astronomy at Glasgow University. These are hollow glass beads of variable density;they may be prepared by melting off pieces of very thin capillary tubing, and determining the density in each case by the method just previously described. To use the column, the experimental fragment is introduced, when it takes up a definite position. By successive trials two beads, of known density, say d2, are obtained, one of which floats above, and the other below, the test crystal; the distances separating the beads from the crystal are determined by means of a scale placed behind the tube. If the bead of density d1 be at the distance 11 above the crystal, and that of d2 at 12 below, it is obvious that if the density of the column varies uniformly, then the density of the test crystal is (dill-f-d2l,)/(li+l2). Acting on a principle quite different from any previously discussed is the capillary hydrometer or staktometer of Brewster, which is based upon the difference in the surface tension and density of pure water, and of mixtures of alcohol and water in varying proportions. If a drop of water be allowed to form at the extremity of a fine tube, it will go on increasing until its weight overcomes the surface tension by which it clings to the tube, and then it will fall. Hence any impurity which diminishes the surface tension of the water will diminish the size of the drop (unless the density is proportionately diminished). According to Quincke, the surface tension of pure water in contact with air at 2o° C. is 81 dynes per linear centimetre, while that of alcohol is only 25.5 dynes; and a small percentage of alcohol produces much more than a proportional decrease in the surface tension when added to pure water. The capillary hydrometer consists simply of a small pipette with a bulb in the middle of the stem, the pipette terminating in a very fine capillary point. The instrument being filled with distilled water, the number of drops required to empty the bulb and portions of the stem between two marks m and n (fig. 9) on the latter is carefully counted, and the experiments repeated at different temperatures. The pipette having been carefully dried, the process is repeated with pure alcohol or with proof spirits, and the strength of any admixture of water and spirits is determined from the corresponding number of drops, but the formula generally given is not based upon sound data. Sir David Brewster found with one of these instruments that the number of drops of pure water was 734, while of proof spirit, sp. gr. 920, the number was 2117.
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