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Originally appearing in Volume V08, Page 48 of the 1911 Encyclopedia Britannica.
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PRACTICAL DETERMINATION OF DENSITIES The methods for determining densities may be divided into two groups according as hydrostatic principles are employed or not. In the group where the principles of hydrostatics are not employed the method consists in determining the weight and volume of a certain quantity of the substance, or the weights of equal volumes of the substance and of the standard. In the case of solids we may determine the volume in some cases by direct measurement—this gives at the best a very rough and ready value; a better method is to immerse the body in a fluid (in which it must sink and be insoluble) contained in a graduated glass, and to deduce its volume from the height to which the liquid rises. The weight may be directly determined by the balance. The ratio " weight to volume " is the absolute density. The separate determination of the volume and mass of such substances as gunpowder, cotton-wool, soluble sub-stances, &c., supplies the only means of determining their densities. The stereometer of Say, which was greatly improved by Regnault and further modified by Kopp, permits an accurate determination of the volume of a given mass of any such substance. In its simplest form the instrument consists of a glass tube PC (fig. 1), of uniform bore, terminating in a cup PE, the mouth of which can be rendered air-tight by the plate of glass E. The substance whose volume is to be determined is placed in the cup PE, and the tube PC is immersed in the vessel of mercury D, until the mercury reaches the mark P. The plate E is then placed on the cup, and the tube PC raised until the surface of the mercury in the tube stands at M, that in the vessel D being at C, and the height MC is measured. Let k denote this height, and let PM be denoted by 1. Let u represent the n volume of air in the cup before the body was inserted, v the volume of the body, a the area of the horizontal FIG. 1.—Say's section of the tube PC, and h the height of the Stereometer. mercurial barometer. Then, by Boyle's law (u—v+al) (h—k) = (u—v)h, and therefore v=u—al(h—k)/k. The volume u may be determined by repeating the experiment when only air is in the cup. In this case v=o, and the equation becomes (u+al') (h—k') =uh, whence u=al'(h—k')/k'. Substituting this value in the expression for v, the volume of the body inserted in the cup becomes known. The chief errors to which the stereometer is liable are (1) variation of temperature and atmospheric pressure during the experiment, and (2) the presence of moisture which disturbs Boyle's law. The method of weighing equal volumes is particularly applicable to the determination of the relative densities of liquids. It consists in weighing a glass vessel (1) empty, (2) filled with the liquid, (3) filled with the standard substance. Calling the weight of the empty vessel w, when filled with the liquid W, and when filled with the standard substance W,, it is obvious that W —w, and W, —w, are the weights of equal volumes of the liquid and standard, and hence the relative density is (W —w)/(W, —w). Many forms of vessels have been devised. The corn moner type of " specific gravity bottle " consists of a thin glass bottle (fig. 2) of a capacity varying from to to too cc., /too fitted with an accurately ground stopper, which is vertically. aperforated by a fine hole. The bottle is carefully cleansed by washing with soda, hydrochloric acid and distilled \150c water, and then dried by heating in an air bath or by blow- - ing in warm air. It is allowed to cool and then weighed. FIG. 2. The bottle is then filled with distilled water, and brought to a definite temperature by immersion in a thermostat, and the stopper inserted. ' It is removed from the thermostat, and carefully E s wiped. After cooling it is weighed. The bottle is again cleaned and dried, and the operations repeated with the liquid under examination instead of water. Numerous modifications of this bottle are in use. For volatile liquids, a flask provided with a long neck which carries a graduation and is fitted with a well-ground stopper is recommended. The bringing of the liquid to the mark is effected by removing the excess by means of a capillary. In many forms a thermometer forms part of the apparatus. Another type of vessel, named the Sprengel tube or pycnometer (Gr. av uos, dense), is shown in fig. 3. It consists of a cylindrical tube of a capacity ranging from to to 50 cc., provided at the upper end with a thick-walled capillary bent as shown on the left of the figure. From the bottom there leads another fine tube, bent upwards, and then at right angles so as to be at the same level as the capillary branch. This tube bears a graduation. A loop of platinum wire passed under these tubes serves to suspend the vessel from the balance arm. The manner of cleansing, &c., is the same as in the ordinary form. The vessel is filled by placing the capillary in a vessel containing the liquid and gently aspirating. Care must be taken withdrawing any excess from the capillary end by a strip of bibulous paper or by a capillary tube. Many variations of this apparatus are in use; in one of the commonest there are two cylindrical chambers, joined at the bottom, and each provided at the top with fine tubes bent at right angles; sometimes the inlet and outlet tubes are provided with caps. The specific gravity bottle may be used to determine the relative density of a solid which is available in small fragments, and is insoluble in the standard liquid. The method involves three operations:—(1) weighing the solid'in air (W), (2) weighing the specific gravity bottle full of liquid (WI), (3) weighing the bottle containing the solid and filled up with liquid (W2). It is readily seen that W+Wi–W2 is the weight of the liquid displaced by the solid, and therefore is the weight of an equal volume of liquid; hence the relative density is W/(W+WI–W2). The determination of the absolute densities of gases can only be effected with any high degree of accuracy by a development of this method. As originated by Regnault, it consisted in filling a large glass globe with the gas by alternately exhausting with an air-pump and admitting the pure and dry gas. The flask was then brought to 0° by immersion in melting ice, the pressure of the gas taken, and the stop-cock closed. The flask is removed from the ice, allowed to attain the temperature of the room, and then weighed. The flask is now partially exhausted, transferred to the cooling bath, and after standing the pressure of the residual gas is taken by a manometer. The flask is again brought to room-temperature, and re-weighed. The difference in the weights corresponds to the volume of gas at a pressure equal to the difference of the recorded pressures. The volume of the flask is determined by weighing empty and filled with water. This method has been refined by many experimenters, among whom we may notice Morley and Lord Rayleigh. Morley determined the densities of hydrogen and oxygen in the course of his classical investigation of the composition of water. The method differed from Regnault's inasmuch as the flask was exhausted to an almost complete vacuum,a performance rendered possible by the high efficiency of the modern air-pump. The actual experiment necessitates the most elaborate precautions, for which reference must be made to Morley's original papers in the Smithsonian Contributions to Knowledge (1895), or to M. Travers, The Study of Gases. Lord Rayleigh has made many investigations of the absolute densities of gases, one of which, namely on atmospheric and artificial nitrogen, undertaken in conjunction with Sir William Ramsay, culminated in the discovery of argon (q.v.). He pointed out in 1888 (Prot. Roy. Soc. 43, p. 361) an important correction which had been overlooked by previous experimenters with Regnault's method, viz. the change in volume of the experimental globe due to shrinkage under diminished pressure; this may be experimentally determined and amounts to between 0.04 and o.16 % of the volume of the globe. Related to the determination of the density of a gas is the determination of the density of a vapour, i.e. matter which at ordinary temperatures exists as a solid or liquid. This subject owes its importance in modern chemistry to the fact that the vapour density, when hydrogen is taken as the standard, gives perfectly definite information as to the molecular condition of the compound, since twice the vapour density equals the molecular weight of the compound. Many methods have been devised. In historical order we may briefly enumerate the following:—in 1811, Gay-Lussac volatilized a weighed quantity of liquid, which must be readily volatile, by letting it rise up a short tube containing mercury and standing inverted in a vessel holding the same metal. This method was developed by Hofmann in 1868, who replaced the short tube of Gay-Lussac by an ordinary barometer tube, thus effecting the volatilization in a Torricellian vacuum. In 1826 Dumas devised a method suitable for substances of high boiling-point; this consistedin its essential point in vaporizing the substance in a flask made of suitable material, sealing it when full of vapour, and weighing. This method is very tedious in detail. H. Sainte-Claire Deville and L. Troost made it available for specially high temperatures by employing porcelain vessels, sealing them with the oxyhydrogen blow-pipe, and maintaining a constant temperature by a vapour bath of mercury (3500), sulphur (4400), cadmium (86o°) and zinc (1040°). In 1878 Victor Meyer devised his air-expulsion method. Before discussing the methods now used in detail, a summary of the conclusions reached by Victor Meyer in his classical investigations in this field as to the applicability of the different methods will be given: (I) For substances which do not boil higher than 26o° and have vapours stable for 30° above the boiling-point and which do not react on mercury, use Victor Meyer's " mercury expulsion method." (2) For substances boiling between 26o° and 420°, and which do not react on metals, use Meyer's " Wood's alloy expulsion method." (3) For substances boiling at higher temperatures, or for any substance which reacts on mercury, Meyer's " air expulsion method " must be used. It is to be noted, however, that this method is applicable to substances of any boiling-point (see below). (4) For substances which can be vaporized only under diminished pressure, several methods may be used. (a) Hofmann's is the best if the substance volatilizes at below 31o°, and does not react on mercury; otherwise (b) Demuth and Meyer's, Eykman's, Schall's, or other methods may be used. I. Meyer's " Mercury Expulsion" Method.—A small quantity of the substance is weighed into a tube, of the form shown in fig. 4, which has a capacity of about 35 cc., provided with a capillary tube at the top, and a bent tube about 6 mm. in diameter at the bottom. The vessel is completely filled with mercury, the capillary sealed, and the vessel weighed. The vessel is then lowered - into a jacket containing vapour at a known temperature which is sufficient to volatilize the substance. Mercury is expelled, and when this expulsion ceases, the vessel is removed, allowed to cool, and weighed. It is necessary to determine the pressure exerted on the vapour by the mercury in the narrow limb; this is effected by opening the capillary and inclining the tube until the mercury just reaches the top of the narrow tube; the difference between FIG. 4. the height of the mercury in the wide tube and the top of the narrow tube represents the pressure due to the mercury column, and this must be added to the barometric pressure in order to deduce the total pressure on the vapour. The result is calculated by means of the formula: WO +at) X7,980,000 D = (p+pi—s) [m 1 i +l3(t—to) }—mi 1 I +7(t—to) } ] (1 +70' in which W=weight of substance taken; t=temperature of vapour bath; a=0.00366=temperature coefficient of gases; p=baro." metric pressure; pi=height of mercury column in vessel; s= vapour tension of mercury at t°; m= weight of mercury contained in the vessel ; m1=weight of mercury left in vessel after heating ; 15' =coefficient of expansion of glass = *0000303; y =coefficient of expansion of mercury=o•000t8 (0.00019 above 240°) (see Ber. 1897, to, p. 2068; 1886, 19, p. 1862). 2. Meyer's Wood's Alloy Expulsion Method.—This method is a modification of the one just described. The alloy used is composed of 15 parts of bismuth, 8 of lead, 4 of tin and 3 of cadmium; it melts at 70°, and can be experimented with as readily as mercury. The cylindrical vessel is replaced by a globular one, and the pressure on the vapour due to the column of alloy in the side tube is readily reduced to millimetres of mercury since the specific gravity of the alloy at the temperature of boiling sulphur, 444° (at which the apparatus is most frequently used), is two-thirds of that of mercury (see Ber. 1876, 9, p. 1220). 3. Meyer's Air Expulsion Method.—The simplicity, moderate accuracy, and adaptability of this method to every class of substance which can be vaporized entitles it to rank as one of the most potent methods in analytical chemistry; its invention is indissolubly connected with the name of Victor Meyer, being termed " Meyer's method " to the exclusion of his other original methods. It consists in determining the air expelled from a vessel by the vapour of a given quantity of the substance. The apparatus is shown in fig. 5. A long tube (a) terminates at the bottom in a cylindrical chamber of about 100-150 cc. capacity. The top is fitted with a rubber stopper, or in some forms with a stop-cock, while a little way down there is a bent delivery tube (b). To use the apparatus, the long tube is placed in a vapour bath (c) of the requisite temperature, and after the air within the tube is in equilibrium, the delivery tube is placed beneath the surface of the water in a pneumatic trough, the rubber stopper pushed home, and observation made as to FIG. 5. whether any more air is being expelled. If this be not so, a graduated tube (d) is filled with water, and inverted over the delivery tube. The rubber stopper is removed and the experimental substance introduced, and the stopper quickly replaced to the same extent as before. Bubbles are quickly disengaged and collect in the 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:

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