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 Δ = M/V; if now the temperature and pressure be changed to T1 and P1, the volume V1 under these conditions is VPT/P1T1, and the absolute density is MP1T/VPT1. It is customary to reduce gases to the so-called “normal temperature and pressure,” abbreviated to N.T.P., which is 0°C. and 760 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 0°C, the zero of the Centigrade scale and the freezing-point 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°/4°) means that the ratio of the weight of a definite volume of a substance at 0° to the weight of the same volume of water 4° is 1.093. 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 10 ℔ 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 10d represents the weight of a gallon in ℔. 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
| Fig. 1.—Say’s Stereometer. |
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. 1), 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 l. 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 section of the tube PC, and h the height of the 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 = 0, and the equation becomes (u + al1)(h - k1) = uh, whence u = al1(h - k1)/k1. 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 W1, 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)/(W1 - w).
| Fig. 2. |
Many forms of vessels have been devised. The commoner type of “specific gravity bottle” consists of a thin glass bottle (fig. 2) of a capacity varying from 10 to 100 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. 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 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.
| Fig. 3. |