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• Density
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1911 Encyclopedia Britannica
• Density

(Lat. densus, thick), in physics, the mass or quantity of matter contained in unit volume of any substance: this is the absolute density; the term relative density or specific gravity denotes the ratio of the mass of a certain volume of a substance to the mass of the same volume of some standard substance. Since the weights used in conjunction with a balance are really standard masses, the word "weight" may be substituted for the word "mass" in the preceding definitions; and we may symbolically express the relations thus: - If M be the weight of substance occupying a volume V, then the absolute density O = M/V; and if m, m 1 be the weights of the substance and of the standard substance which occupy the same volume, the relative density or specific gravity S = m/m l ; or more generally if m i be the weight of a volume v of the substance, and m l the weight of a volume v l of the standard, then S = mv l /m l v. In the numerical expression of absolute densities it is necessary to specify the units of mass and volume employed; while in the case of relative densities, it is only necessary to specify the standard substance, since the result is a mere number. Absolute densities are generally stated in the C.G.S. system, i.e. as grammes per cubic centimetre. In commerce, however, other expressions are met with, as, for example, "pounds per cubic foot" (used for woods, metals, &c.), "pounds per gallon," &c. The standard substances employed to determine relative densities are: water for liquids and solids, and hydrogen or atmospheric air for gases; oxygen (as 16) is sometimes used in this last case. Other standards of reference may be used in special connexions; for example, the Earth is the usual unit for expressing the relative density of the other members of the solar system. Reference should be made to the article Gravitation for an account of the methods employed to determine the "mean density of the earth." In expressing the absolute or relative density of any substance, it is necessary to specify the conditions for which the relation holds: in the case of gases, the temperature and pressure of the experimental gas (and of the standard, in the case of relative density); and in the case of solids and liquids, the temperature. The reason for this is readily seen; if a mass M of any gas occupies a volume V at a temperature T (on the absolute scale) and a pressure P, then its absolute density under these conditions is O = M/V; if now the temperature and pressure be changed to l and P,, the volume V l under these conditions is VPT/PIT1, and the absolute density is MP,T/VPT I. It is customary to reduce gases to the so-called "normal temperature and pressure," abbreviated to N.T.P., which is o° C. and 769 mm.

The relative densities of gases are usually expressed in terms of the standard gas under the same conditions. The density gives very important information as to the molecular weight, since by the law of Avogadro it is seen that the relative density is the ratio of the molecular weights of the experimental and standard gases. In the case of liquids and solids, comparison with water at 4° C., the temperature of the maximum density of water; at o C., the zero of the Centigrade scale and the freezingpoint of water; at 15° and 18°, ordinary room-temperatures; and at 25°, the temperature at which a thermostat may be conveniently maintained, are common in laboratory practice. The temperature of the experimental substance may or may not be the temperature of the standard. In such cases a bracketed fraction is appended to the specific gravity, of which the numerator and denominator are respectively the temperatures of the substance and of the standard; thus 1.093 (0 0 14°) means that the ratio of the weight of a definite volume of a substance at o to the weight of the same volume of water 4° is I093. It may be noted that if comparison be made with water at 4°, the relative density is the same as the absolute density, since the unit of mass in the C.G.S. system is the weight of a cubic centimetre of water at this temperature. In British units, especially in connexion with the statement of relative densities of alcoholic liquors for Inland Revenue purposes, comparison is made with water at 62° F. (16.6 C.); a reason for this is that the gallon of water is defined by statute as weighing Io lb at 62° F., and hence the densities so expressed admit of the ready conversion of volumes to weights. Thus if d be the relative density, then Iod represents the weight of a gallon in lb. The brewer has gone a step further in simplifying his expressions by multiplying the density by 1000, and speaking of the difference between the density so expressed and 1000 as "degrees of gravity" (see Beer).

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 substances, &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. I), of uniform bore, terminating in a cup PE, the mouth of which can be rendered airtight 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 volume of air in the cup before the body was inserted, v the volume of the body, a the area of the horizontal FIG. I. - Say's section of the tube PC, and h the height of the Stereo'meter. 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 l) (h - k') =uh, whence u = al' (h - k l) /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 (I) 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 (I) 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 l, it is obvious that W - w, and W1 - w, are the weights of equal volumes of the liquid and standard, and hence the relative density is (W - w)/(Wi - 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., fitted with an accurately ground stopper, which is vertically perforated by a fine hole. The bottle is carefully cleansed by washing with soda, hydrochloric acid and distilled water, and then dried by heating in an air bath or by blowing 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 F. 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. iruicubs, dense), is shown in fig. 3. It consists of a cylindrical tube of a capacity ranging from 10 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 P 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 plati num 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 6 gently aspirating. Care must be taken that no air bubbles are enclosed. The liquid is adjusted to the mark by 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 (W 1), (3) weighing the bottle containing the solid and filled up with liquid (W2). It is readily seen that W+W i - W 2 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 o° 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. He pointed out in 1888 (Proc. 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 o04 and o16% 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 consisted in 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 (860°) 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 260° 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 260° 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 310°, and does not react on mercury; otherwise (b) Demuth and Meyer's, Eykman's, Schall's, or other methods may be used.