DENSITY. The density of a substance is the mass of unit volume of the substance.
Density determinations are comparatively simple to carry out and a high degree of precision is often attainable. A knowledge of the density of a material is of considerable interest both from a theoretical and a practical standpoint. A few examples will in dicate the wide range of problems and operations into which considerations of density enter. Accurate density determinations form a means of determining the molecular weight of gases. A knowledge of the density of the crystals examined is extremely valuable in the X-ray analysis of the structure of crystals. Density determinations have been used in the study of the constitution of liquids, of the dissociation of gases, and of the effects of cold work on metals. Lord Rayleigh's determination of the density of "atmospheric nitrogen" led to the discovery of argon. The very considerable revenue resulting from the duty on beer is assessed during the process of manufac ture on the basis of determina tions of the density of the worts.
It is often specified in contracts for the supply of material that its density must be within prescribed limits, and density determina tions are frequently necessary in industrial operations.
These examples suffice to show in how many directions a knowl edge of the density of materials is of service. The widespread recurrence of density throughout the whole range of science and technology is not fortuitous, but a direct consequence of the fact that density is a fundamental physical property.
Different materials and condi tions and the varying degrees of accuracy required for different purposes necessitate a number of different methods of determining density.
The most generally convenient unit is grammes per millilitre.
The litre is defined as the volume at its temperature of maximum density (4° C) of one kilogram of pure water and the millilitre is the one-thousandth part of a litre or one cubic centimetre. It follows, therefore, that the density of water at 4° C expressed in terms of grammes per millimetre is unity.
Temperature and Pressure Effects.—In general, a rise in tem perature causes a decrease in density and a rise in pressure causes an increase in density. With gases the changes are large and it is necessary to take both pressure and temperature into account when considering the density of gases. This is dealt with in detail later. Liquids are only slightly compressible but their density changes appreciably with change in temperature. It is therefore necessary, to secure precision, to specify the temperature at which a liquid has a stated density, but the pressure may usually be omitted. The variation in the density of solids with changes in temperature and pressure is comparatively small.
A pyknometer is simply a vessel which can be filled with pre cision. In addition it should be easy to clean and weigh and suitable for allowing its contents to be brought to a uniform temperature.
There are numerous kinds of pyknometers, and five forms of interest in their relation to each other are shown in figs. z to 5.
Fig. z shows a small bottle having a well fitting ground glass stopper with a small hole drilled vertically through it, and in use the bottle is filled flush to the top of this hole. In fig. 2 is a type of pyknometer due to Sprengel which is finally filled by with drawing liquid from the jet A with the aid of blotting paper until the liquid surface in the other horizontal tube is at a mark B. This form avoids errors which might arise in the preceding one if the stopper is not always pushed precisely the same amount inside the neck at each filling. Fig. 3 shows a more robust form of Sprengel tube which is provided with a small bulb above the graduation mark B. This bulb will accommodate any liquid which might expand from the main part of the pyknometer should the temper ature rise after it has been filled, a happening which would be in convenient in the two preceding forms. A pyknometer due to Bousfield (fig. 4) is still more robust, but retains all the advan tages of the one shown in fig. 3 and has a glass hook D, by which it can be hung from a balance hook, thus getting rid of the wire suspensions, liable to alter in weight, required for the Sprengel type. The last pyknometer, due to Dr. C. Barr of the National Physical Laboratory, and not hitherto published, retains the advantages of the Sprengel method of filling but reverts to the bottle type of fig. z for the body of the instrument, and so se cures the advantages of a pyknometer which will stand on its own base and not require suspension for weighing.
When using a pyknometer it is important to ensure that the contents of the pyknometer have attained a constant temperature before completing the filling, and to observe- this temperature accurately. This is generally done by immersing the bulk of the pyknometer in liquid contained in a thermostat, keeping it there for a sufficient time to ensure uniformity of temperature, and then taking the temperature of the outer liquid at the time the final filling of the pyknometer is carried out as that of the liquid inside the pyknometer.
The operations in determining the density of a liquid by means of a pyknometer are to weigh the pyknometer (a) when empty (Wp grammes), (b) when filled with water gms.), and (c) when filled with liquid (W a gms.). We will assume that the same temperature t° C obtains during each filling of the pyknometer and that the air density has the same value a gms./ml. during each weighing.
We must now consider how to determine the density mass per unit volume—of the liquid from the weights TV,,, and W 1.
Weights are adjusted so that their mass is equal to the nominal value marked on them. When used on a balance they are subject to the buoyancy effect of the surrounding air, which is equivalent to a reduction in mass equal to the mass of air displaced by the weights. The equilibrium obtained in the operation of weighing may therefore be represented by the equation:—(Mass of weights minus mass of air displaced by weights = Mass of body weighed minus mass of air displaced by body weighed).
If, contrary to our initial assumptions, the air density varied from weighing to weighing and the pyknometer was filled at different temperatures, the calculations are a little more compli cated but involve no new principle. It is merely necessary to introduce individual values for the air density instead of a com mon value u and to make due allowance for changes in the volume of the pyknometer with changes in temperature.
Sinker Method.—A hollow glass cylinder with closed hemispher ical ends and provided with a glass ring by which it can be suspended, forms a convenient sinker for density determinations.
It is necessary to load the sinker so that it will sink in any liquid whose density is to be determined by its aid.
When a sinker is weighed suspended in a liquid the buoyancy effect of the surrounding liquid is equivalent to an upward force on the sinker equal to the weight of liquid which it displaces. If this upward force is determined and the volume of the sinker is known, the weight of a known volume of the liquid is determined and hence its density also. To determine the density of a liquid the sinker is weighed (a) in air gms.), (b) suspended in water (W. gms.), and (c) suspended in the liquid (W t gms.). The first and second weighings serve to determine the volume of the sinker and the first and third the mass of an equal volume of liquid. By considering these weighings in precisely the same manner as the pyknometer weighings were considered it can be shown that if the water and liquid are at the same temperature which is of precisely the same form as equation (7) and may be simplified to an equation which is subject to the same limitations as equation (9).
The sinker method is much more convenient than the pyknom eter method for determining the density of a liquid at a sequence of different temperatures, and if the sinker has not quite attained the temperature of the surrounding liquid, the resulting error is of much less consequence than if the liquid inside a pyknometer has not attained the temperature measured outside.
Osborne, McKelvy and Pearce carried out an extensive series of determinations of the densities of mixtures of ethyl alcohol and water, using both the pyknometer and sinker methods, and their work might be consulted for details of both methods.
The Westphal balance is an application of the sinker method in which the upward force on a sinker is directly measured on a balance of the steel-yard type. The balance is shown diagram matically in fig. 6. With the sinker hanging in air the balance arm is adjusted so that the pointer P is at the middle of the scale S. If, now, a vessel containing a liquid of density i gm./ml. is placed so that the sinker hangs in the liquid there will be an upward force on the sinker amounting to i o gms. weight, assuming the sinker to have a volume of i o ml., and the balance arm will no longer be in equilibrium. A io gm. weight placed on the balance arm at the point on the scale marked i .o, i.e., immediately above the point from which the sinker is suspended, would restore the equilibrium of the balance arm and bring the pointer P back to the middle of the scale S. If the density of the liquid were i • 5 gms./ml. then a i o gm. weight placed at i.o on the balance arm and a second io gm. weight placed at o•5 on the balance arm would counter-balance the i 5 gms. weight upward force on the sinker. If the density of the liquid were i•56 gms./ml. the second io gm. weight would have to be placed at a point corresponding to 0•56 on the balance arm to restore equilibrium. Alternatively the second i o gm. weight could be placed at o• 5 on the balance arm and r gm. weight at o.6 on the scale, and the three weights together would then balance the i 5.6 gms. buoyancy effect on the sinker. The balances are usually provided with three sizes of weights, the largest having a value in grammes numerically equal to the volume of the sinker in millilitres, the next size having one tenth this weight and the third one-hundredth. The positions of the heaviest weights on the balance arm give the units and first decimal place of the density, the position of the next smaller weight gives the second decimal place and that of the smallest the third decimal place.
Westphal balances are convenient when densities are required to an accuracy of about one part in a thousand, but a hydrometer (see HYDROMETERS) provides a more rapid and convenient means of attaining this degree of accuracy, and is replacing the Westphal balance in industry.
The principle of the Westphal balance has been applied to chainomatic balances, which can be obtained with scales indicat ing densities directly. In chainomatic balances the use of frac tional weights is avoided by using a fine chain AB (see fig. 7) for the final adjustment. The end A of the chain is fixed to one end of the balance beam and the end B is attached to a hook on the Vernier V which slides along the scale CD. By lowering or raising V a greater or less fraction of the total weight of the chain is supported by the balance beam and this affords a deli cate means of bringing the beam into its position of equilibrium, i.e., with the pointer P central on the scale S. Such a balance obviously lends itself to adaptation for density determinations. A sinker is suspended from the end of the balance arm remote from A and hangs immersed in the liquid whose density is required. It is balanced by placing a movable weight in an appropriate notch on the beam and moving the vernier V to obtain the final adjustment. The notched beam is graduated from o to 2.0 and the position of the movable weight gives the unit and first decimal place of the density the subsequent decimal places being read off on the scale CD by means of the vernier V.
The sinker method is used as the basis of recording densimeters variations in the buoyancy effect on a sinker being used to operate recording mechanism.
If a sinker has precisely the same density as a liquid in which it is placed—no suspension wire being used, it will tend neither to sink nor to float but will remain in suspension in the body of the liquid. The equilibrium is a very delicate one and has been made the basis of accurate density determinations.
Prof. A. Pollard has devised a total immersion instrument for density determinations, the essential portion of which is shown in fig. 8. This is a specially designed glass float A which is sup ported on a flat surface BC by a small sphere D fused on the float. When wholly immersed in a liquid the float is free to rotate in a vertical plane about D and takes up a position of rest in which its inclination to the horizontal is dependent on the density of the liquid which is read off on a circular scale placed behind E.
Hare's Method. A long inverted U tube is held with one limb (A) dipping into a liquid and the other limb (B) dipping into a second liquid. By applying suction to a branch tube at the top of the U each of the limbs is partially filled with liquid. If di is the density and hi the height of the liquid in A, (12 and h2 similarly referring to B, p is the pressure of the air enclosed in the U and P is the atmospheric pressure then p = P P —h2d2 and so hi = di X n2 Hence if di is known the measurement of hi and h2 suffices to determine d2.
The method of balancing the pressure due to columns of liquids of different densities has been made use of in accurate density determinations.
The method is convenient for solids available in small frag ments or powders and a pyknometer such as that shown in fig. 1, into which such solids can be easily introduced is necessary. Pow ders are liable to entrap a quantity of air which remains in the pyknometer when filled with liquid. This is avoided by filling the pyknometer under reduced pressure.
By Weighing the Solid in Air and also Suspended in a Liquid. —If Ms. gms. is the mass of solid, Vs. ml. its volume, Wagms. the observed weight in air and W gms. the observed weight when suspended in a liquid of density p gms./m1., then for the two weighings we have Wa( — a/A) = Ms— Vs and Wi(r — °IA) = Ms— Vs • p the density of the solid d is given by W.
d= — = (p a)+a or approximately d= .P.
W.—Wi Wa—W If the solid has a density greater than that of the liquid in which it is weighed all that is necessary for the weighing is to suspend the solid by means of a fine wire from one arm of a balance so that it hangs suspended in a vessel of the liquid placed on a stand bridging the scale pan. The weight of the suspension wire is allowed for.
If the solid has a density less than the liquid then for the weighing in the liquid a heavier body is attached to the same suspension wire so that the two together sink in the liquid. The heavier body must also be weighed alone in the liquid and if W3 gms. is this weight W2 gms. the weight observed when both bodies are suspended in the liquid, and WI gms. the weight of the lighter solid in air then from the usual equations for each weighing it follows that— d gms./ml. being the required density of the solid, p gms./ml. that of the liquid in which it is weighed and a gms./ml. the density of the air.
Flotation Method.—The flotation method consists in ad justing the density of a liquid, e.g., by mixing two liquids of dif ferent density in appropriate proportions, until it is equal to that of the solid. The criterion of equality is that the solid remains suspended in the liquid, neither sinking nor rising. The method is chiefly used for minerals available only in small frag ments and in limited amounts. Methylene iodide (density 3.3 gms./ml.) and benzol (density 0.98 gms./ml.) are convenient liquids for mixing together to obtain intermediate densities.
Direct Displacement Methods.—If a solid is added to a vessel partially filled with liquid the level of the liquid surface will be raised and the volume of liquid between the original and final levels of the liquid will be equal to the volume of the solid. This affords a means of obtaining the volume of a previously determined weight of solid, and so the density of the solid. Flasks with graduated necks having scales on which the volume corresponding to the rise in the liquid surface can be read directly are used for determining the density of fine materials such as sand and cement. Sometimes a flask with a single mark is used and the volumes required to fill it to the mark (a) when initially empty, (b) when containing a known weight of solid, are measured by means of a burette.
In Regnault's volumenometer the solid displaces air in a chamber connected to a manometer. By observing pressure changes on expanding or contracting the air by a definite amount (a) when the chamber contains air only, (b) when it contains the solid also, the volume of the solid can be determined.
Methods of Determining the Density of Gases.—By Weighing a Globe Filled with the Gas.—The determination of the mass of gas required to fill a globe of known volume affords an accurate means of determining the density of gases. The method is the counterpart of the pyknometer method for determining the density of liquids, and in principle is equally simple. The volume of the globe is determined from its water content and then the globe is weighed first evacuated and secondly filled with gas at a measured temperature and pressure.
Owing, however, to the large volume occupied by a small mass of gas the mass of the globe must inevitably be large compared with that of the enclosed gas. Hence small percentage errors in the weighings involve large percentage errors in the mass of the gas. This coupled with the necessity for accurate control and measurement of both temperature and pressure render the accu rate determination of the densities of gases by this method a matter calling for the utmost refinement of experimental pro cedure.
By Measuring the Volume of a Known Mass of Gas. This method is the reverse of the preceding one and consists in using one or more globes, or other suitable measuring apparatus, merely to determine the volume of the gas whose mass is determined separately. For example, one of the methods used by Morley in his determination of the density of hydrogen was to weigh the hydrogen absorbed in palladium and to measure the volume of the hydrogen in three globes having a total capacity of 42 litres.
Perman and Davies absorbed a measured volume of ammonia in concentrated sulphuric acid in order to obtain its mass.
By Means of the Micro-Bal ance.—The principle of the mi cro-balance may be readily seen from the diagrammatic representation in fig. 9. A very light quartz balance beam represented by AB is delicately pivoted at its centre C. At one end of the beam is a small solid sphere of quartz and at the other a larger hollow quartz sphere filled with air. The whole balance is enclosed in a vessel which can be filled with gas under any desired pressure and the pressure can be measured by a manometer M.
Suppose the balance beam is an equilibrium (i.e., with the point D opposite the fixed point P) in one gas at a pressure and in a second gas at a pressure the temperature remaining con stant. Since the beam is asymmetrical as regards volume, it follows that to produce equilibrium the first gas at the pressure must exert the same buoyancy effect on the beam as the second gas at the pressure p2. The first gas must therefore have the same density at the pressure that the second gas has at the temperature and from this it follows directly that the density d of the second gas at N.T.P. is given by P2 where p is the density of the first gas at N.T.P.
The micro-balance affords an extremely accurate means of comparing the densities of two gases and can be operated with exceedingly minute quantities of gas. It has been developed considerably in recent years and in addition to the delicate quartz micro-balances robust instruments based on the same principle have been designed for the commercial determination of gas densities.
In determining the density of a vapour one usually starts with the substance in its liquid form, and the vaporization of the liquid is an integral part of the density determination.
Dumas' Method.—This consists in vaporizing the liquid in a globe having a neck drawn down to a capillary. So long as any liquid remains in the globe, vapour may be seen issuing from the capillary, but ceases abruptly when the supply of liquid is ex hausted. At this instant the capillary is sealed. By weighing the globe the mass of the contained vapour may be determined and its volume may be obtained by weighing the globe both when full of air and when filled with water. The resulting density is that of the vapour at the temperature and pressure prevailing when the bulb was sealed.
Schulze has recently introduced an ingenious modification of the method in which the vapour is liquefied into a small subsidiary bulb before weighing, and so the errors incident to weighing a large globe containing only a comparatively small mass of vapour are avoided.
Gay-Lussac's Method.—This consists in volatilizing a known mass of liquid over a mercury column and measuring the volume of vapour produced. By using a long vertical tube to contain the mercury the liquid can be volatilized under low pressure. A number of modifications of the method have been introduced from time to time, two recent ones being those of Young and of Egerton.
Victor Meyer's Method. —A simple arrangement of apparatus for Victor Meyer's method of determining the density of a vapour is shown in fig. 1o. The liquid in A is heated until air ceases to issue from the tube B. A jar C, filled with water, is then placed over B and a small bottle containing a known weight of liquid is dropped into the inner bulb B. The tem perature in A is arranged to be high enough to ensure rapid volatilization of the liquid when introduced into D. The vapour so produced displaces air from the apparatus, and this is collected and measured in C.
The volume of this air reduced to N.T.P.
is equal to that of the vapour reduced to N.T.P. since before displacement from D the air was at the same temperature and pressure as the vapour.
The Victor Meyer method has been widely used, and details of a modern form of the apparatus having an improved method for introducing the liquid to be vaporized is described by McInnes and Kreiling.