The rate at which liquids diffuse is, however, extremely small, as compared with the rate at which gases diffuse. This fact confirms the molecular theory of the constitution of liquids and gases, for in gases it is supposed that the molecules travel about, only occasionally coming near enough to other molecules to influence their motion, the greater part of their path being traversed uninfluenced by other molecules. In a liquid, on the other hand, although the molecules move about, they never get far enough away from the adjacent molecules to escape from the influence of these molecules, so that although a liquid molecule may move relatively to neighbouring molecules, as soon as it passes out of the range of influence of one set of molecules it comes within the range of other molecules. Hence the molecular motion in liquids is much more constrained than in the case of gases, and we should expect the rate of diffusion to be slower.

B

The rates at which liquids (in most cases solutions of salts) diffuse into water were experimentally determined by Graham in the following manner. A small wide-mouthed bottle A (Fig. 139), filled with the liquid, was closed by a glass plate, and then placed in a larger vessel B containing water, so that the surface of the water was above the top of the bottle A. The glass plate was then carefully slid off the top of the bottle, and the liquids left to diffuse. After a certain time samples of the different layers of the mixed liquids were drawn off by a pipette, and the composition of the solution determined. With solutions of the same substance of different strengths, Graham found that the rates of diffusion were proportional to the strengths of the solution. The rates of diffusion of different substances are, however, very different.

A

FIG. 139.

If we consider a small cylinder, one centimetre long and one square centimetre in cross section, and if the concentrations of the solution of a salt in water, i.e. the mass of the salt contained in unit volume of the solution, at the two ends of the cylinder differ by unity, then the quantity of salt in grams which will diffuse through the cross section of the cylinder, i.e. through unit area, in a day is called the diffusion constant of the salt. The following table gives some values of the diffusion constant in grams per square centimetre per day :—

A consideration of the table of the diffusion constants given above shows that the rates of diffusion of different substances vary very considerably. Thus hydrochloric acid diffuses about one hundred times as fast as caramel. For this reason bodies have been subdivided into two classes, one containing such bodies as hydrochloric acid and the salts of the mineral acids, which are mostly crystalline, and diffuse comparatively rapidly. These are called crystalloids. The other, containing such bodies as gum, albumen, caramel, and the like, which are glue-like bodies of amorphous form that diffuse very slowly, and are called colloids.

A film of a colloid, such as paper coated with starch, if placed as a partition in a vessel, with pure water on one side and a solution of crystalloids and colloids on the other, will allow the crystalloids to diffuse through into the water, but entirely stops the passage of the colloids. Thus a colloid septum prevents the diffusion of other colloids, but allows the diffusion of crystalloids.

B

165. Osmosis.-If in a vessel A (Fig. 140), such as a thistle funnel with its larger end closed by a sheet of parchment, we place a solution of copper sulphate, filling the vessel up to about D, and then place it as shown in the figure, so that the parchment is below the surface of some pure water contained in a vessel C. Then it is found that the water makes its way through the parchment partition into A, the solution inside gradually rising up in the tube DB. Thus the water has been able to pass through the parchment in opposition to the hydrostatic pressure due to the column of liquid BD. After a time the water ceases to force its way through the partition, its tendency to do so being counterbalanced by the hydrostatic pressure. It will also be noticed that in time some of the copper sulphate travels out into the surrounding water. If, instead of placing the vessel A containing the copper sulphate solution in pure water, it is placed in a solution of copper sulphate of the same strength as that inside, no change in the quantity of liquid in the vessel takes place. If, however, it is placed in a stronger solution, water will pass out from the vessel A, so that the solution inside becomes more concentrated. These phenomena are called osmosis, and the pressure produced in the vessel containing the salt solution, when placed in water, is called the osmotic pressure.

C

FIG. 140.

By using as the separating membrane a substance which, while it readily permits the passage of pure water, is impervious to the passage of certain substances when dissolved in the water, Pfeffer was able to measure the osmotic pressure due to solutions of different substances at different concentrations. Thus in the case of cane sugar such a

semi-permeable membrane is prepared by depositing ferrocyanide of copper within the pores of a porous earthenware cylinder. The cylinder, filled with the sugar solution, is plunged into pure water, and the maximum pressure developed inside measured by means of a manometer.

The osmotic pressure may be explained by supposing that the semipermeable membrane is struck on both sides by the water molecules, but since there are fewer water molecules per unit volume inside, some of the space being occupied by sugar molecules which cannot traverse the membrane, more water molecules will in a given time strike the outside of the membrane than the inside, and hence, as the water molecules can pass through the membrane, more water molecules will enter than leave.

In the following table some of Pfeffer's results are given :-

It will be seen that, if we consider the sugar when in solution as occupying the volume occupied by the solution, then the product of the osmotic pressure (P) into the volume (V) occupied by a gram of sugar is constant. This result, as was first pointed out by Van 't Hoff, corresponds to Boyle's law for gases.

Measurements of the change of osmotic pressure with temperature have shown another remarkable relation between the behaviour of a dilute solution and of a gas. Thus the osmotic pressure (P) of a 1 per cent. solution of cane sugar at a temperature t is given by the formula

P=49.62(1+0.003677).

The coefficient 0.00367 will be found later on to be the same as that for the variation of the pressure of a gas with temperature (§ 196).

It is only for dilute solutions that the above resemblances of the behaviour of the dissolved body and a gas hold. It would, however, appear that in such a dilute solution the molecules of the dissolved body exist in a condition in some way resembling that which occurs in a gas. We shall see later, particularly when we come to consider the electrical properties of dilute solutions, what suppositions have been made to account for the fact that it is only when dilute that the solutions obey the above gaseous laws.

I

CHAPTER XIX

PROPERTIes of solIDS

166. Isotropic Bodies.-A body in which a spherical portion, when tested in different directions, exhibits no difference in its physical properties is said to be isotropic. Except under very special conditions, all liquids and gases are isotropic. Some solids, however (for instance, crystals), exhibit different physical properties in different directions, and are called ælotropic. In most of the following sections we shall deal exclusively with the properties of isotropic solid bodies.

167. A Perfect Solid. When discussing the distinction between solids and liquids, we pointed out that there was no clear line of demarcation, but that from a rigid solid, such as glass, there is a continuous series extending through soft solids such as lead and butter, very viscous liquids such as sealing-wax and pitch, to treacle and glycerine. Just as in considering the behaviour of liquids we dealt with a typical liquid such as water, so in the case of solids we shall consider one in which, after suffering a strain which alters its shape, on the removal of the stress it completely regains its former shape. Such a solid is called a perfect solid, and the above conditions are practically satisfied by many solid bodies so long as the deforming stress does not surpass a certain value.

168. Malleability and Ductility. By malleability is meant the property possessed by some solids of being beaten into thin sheets without losing their continuity. Of all materials pure gold possesses the property of malleability to the most marked degree. Thus, when preparing gold-leaf, a piece of gold is first rolled into a sheet somewhat thinner than foreign note-paper, next a portion is beaten out between two sheets of vellum till its surface has been increased, and therefore its thickness decreased about twenty-fold. This twenty-fold decrease of thickness, without rupturing the sheet, can be again twice repeated.

By ductility is meant the property of being drawn out into fine wires. A rod of the metal is passed in succession through a number of holes, each a little smaller than the last, the diameter of the rod continually decreasing, while its length is correspondingly increased.

169. Hardness.-When one body can be made to scratch a second, but cannot be scratched by it, we say that the former body is harder than the latter. Although some attempts have been made to devise a means of accurately measuring the hardness of bodies, they have not been

attended with much success. All that can be done at present is to give a body's position, as far as hardness is concerned, in a scale of hardness composed of various bodies. The scale usually adopted, and due to Mohs, is as follows, the first being the softest :-1. Talc; 2. Crystallised Gypsum; 3. Calcspar; 4. Fluorspar; 5. Apatite; 6. Felspar; 7. Quartz ; 8. Topaz; 9. Sapphire; 10. Diamond. A body having a hardness of 6.5 would be one which would scratch felspar, and be scratched with about the same ease by quartz.

170. Elasticity of Volume.-Solids, with few exceptions, are very slightly compressible, in this property resembling liquids. The volume elasticity of a solid is measured in the same way as that of a liquid. Thus if a uniform pressure of p dynes per square centimetre, acting everywhere normal to the surface of the solid, such as would be produced if the solid were immersed in a liquid under a pressure p, is applied, and the volume changes from V to V-v, then the coefficient of compressibility, or the volume elasticity, of the solid is p÷vV or pVv. The following table gives the value of the volume elasticity of some solids :— VOLUME ELASTICITY OF SOLIDS.

:

171. Elasticity of Shape (Rigidity).—The elasticity of shape or rigidity of a solid is measured by the ratio of the stress, i.e. the force producing the change of shape, to the strain, i.e. the change in shape, produced. The shape of a body may be altered in various ways: thus if weights are attached to one end of a wire, the other end being held fast, the wire stretches; on the removal of the weights, so long as the wire has not been too much deformed, it regains its original length. Another way of altering the shape of a body is to twist one end while the other end is held fast; or again, if one end of a rod is held in a vice, and the other end pulled on one side, the rod becomes bent; in each case the elasticity of the solid will resist the deformation, and when the stress is removed will cause the body to resume its unstrained position. We shall consider each of the above methods of straining a solid separately.

172. Elongation: Young's Modulus-Hooke's Law.-Suppose a wire of length L and radius r, when stretched by a force P in the direction of its length, increases in length by an amount 7, then the stress, or force per unit area, acting on the wire and tending to increase its length is P area of cross section, or Pπr2. The total elongation being, the strain, or elongation per unit length of the wire, is L. Hence the modulus of elasticity, Y, is given by