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See also:SOLUTION (from See also:Lat. solvere, to loosen, dissolve)
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When a solid such as See also:salt or See also:sugar dissolves in contact with See also:water to See also:form a See also:uniform substance from which the components may be regained by evaporation the substance is called a See also:solution
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Gases too dissolve in liquids, while mixtures of various liquids show similar properties
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Certain solids also consist of two or more components which are See also:united so as to show similar effects
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All these cases of solution are to be distinguished from chemical compounds on the one See also:hand, and from See also:simple mixtures on the other
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When a substance contains its components in definite proportions which can only See also:change, if at all, by sudden steps, it may be classed as a chemical See also:compound
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When the relative quantities of the components can vary continuously within certain limits, the substance is either a solution or a mixture
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The distinction between these two classes is not See also:sharp; though when the properties of the resultant are sensibly the sum of those of the pure components, as is nearly the See also:case for a complex See also:gas such as See also:air, it is usual to class it as a mixture
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When the properties of the resultant substance are different from those of the components and it is not a chemical compound we define it as a solution
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See also:Historical.—Solutions were not distinguished from definite chemical compounds till See also: In 1867 botanical investigations by M . Traube, and in 1877 others by W . Pfeffer, made known the phenomena of the osmotic pressure which is set up by the passage of solvent through a membrane impermeable to the dissolved substance or solute . The importance of these experiments from the See also:physical point of view was recognized by J . H. See also:van't Hoff in 1885, who showed that Pfeffer's results indicated that osmotic pressure of a dilute solution conformed to the well-known laws of gas pressure, and had the same See also:absolute value as the same number of molecules would exert as a gas filling a space equal to the value of the solvent . The conception of a semi-permeable membrane, permeable to the solvent only, was used by van't Hoff as a means of applying the principles of See also:thermodynamics to the theory of solution . Another method of applying the same principles is due to J . See also:Willard See also:Gibbs, who considered the whole problem of physical and chemical etilibrium in papers published in 1877, though the application of his principles only began to make extensive progress about twenty years after the publication of his purely theoretical investigations . The phenomena of solution and of vapour pressure constitute cases of See also:equilibrium, and conform to the laws deduced by Gibbs, which thus yield a valuable method of investigating and classifying the equilibria of solutions . Solubility.—Some pairs of liquids are soluble in each other in all proportions, but, in See also:general, when dealing with solutions of solids or gases in liquids, a definite limit is reached to the amount which will go into solution when the liquid is in contact with excess of the solid or gas . This limit depends on the nature of the two components, on the temperature and on the pressure . When the limit is reached the solution is said to be saturated, and the See also:system is in equilibrium . If the solution of a solid more soluble when hot be cooled below the saturation point, the whole of the solid sometimes remains in solution . The liquid is then said to be supersaturated . But here the conditions are different owing to the See also:absence of solid . If a crystal of the solid be added, the See also:condition of supersaturation is destroyed, and the See also:ordinary equilibrium of saturation is reached by precipitation of solid from solution . The quantity of substance, or solute, which a given quantity of liquid or solvent will dissolve in presence of excess of the solute See also:measures the solubility of the solute in the given solvent in the conditions of temperature and pressure . The solubilities of solids may be expressed in terms of the See also:mass of solute which will dissolve in See also:loo grammes of water . The following may be taken as examples: Solute . Chemical Solubility Constitution of the Solid . at o° C. at 2o° C. at 1 oo°C . See also:Sodium chloride . NaCl 35'7 36•o 39'8 See also:Potassium nitrate KNO3 133 31.2 247.0 See also:Barium chloride . BaCl2 30'9 35.7 58'8 See also:Copper sulphate . CuSO4 22.0 73'5 See also:Calcium carbonate CaCO3 10.0018 227.3 0.0018 See also:Silver nitrate AgNO3 121.9 See also:IIII.0 (at 19°.5 (at IIO°) When dealing with gases it is usually more convenient to See also:express the solubility as the ratio of the See also:volume of the gas absorbed to the volume of the absorbing liquid . For gases such as See also:oxygen and See also:nitrogen dissolved in water the solubility as thus defined is See also:independent of the pressure, or the mass of gas dissolved is proportional to the pressure . This relation does not hold for very soluble gases, such as See also:ammonia, at See also:low temperatures . As a general See also:rule gases are less soluble at high than at low temperatures—unlike the See also:majority of solids . Thus oxygen, 4.89 volumes of which dissolve at atmospheric pressure in t volume of water at o° C., only dissolves to the extent of 3.10 volumes at 20° and 1.7o volumes at too° . Cause of Solubility.—At the outset of the subject we are met by a fundamental problem, to which no See also:complete See also:answer can be given: Why do certain substances dissolve in certain other substances and not in different substances ? Why are some pairs of liquids miscible in each other in all proportions, while other pairs do not mix at all, or only to a limited extent ? No satisfactory correlation of solubility with chemical or other properties has been made . It is possible to See also:state the conditions of solubility in terms of the theory of available See also:energy, but the result comes to little more than a re-statement of the problem in other terms . Nevertheless, such a re-statement is in itself sometimes an advance in knowledge . It is certain then that when See also:dissolution occurs the available energy of the whole system is decreased by the See also:process, while when equilibrium is reached and the solution is saturated the available. energy is a minimum . When a variable quantity is at a minimum a slight change in the system does not affect its value, and therefore, when a solution is saturated, the increase in the available energy of the liquid phase produced by dissolving in it some of the solid must be equal to the decrease in the available energy of the solid phase, causrd by the See also:abstraction from the bulk of that See also:part dissolved . The general theory of such equilibria will be studied later under the See also:head of the phase rule . It is possible that a correlation may be made between solubility and the energy of See also:surface tension . If a solid is immersed in a liquid a certain part of the energy of the system depends on, and is proportional to, the See also:area of contact between solid and liquid . Similarly with two liquids like oil and water, which do not mix, we have surface energy proportional to the area of contact . Equilibrium requires that the available energy and therefore the area of contact should be a minimum, as is demonstrated in See also:Plateau's beautiful experiment, where a large drop of oil is placed in a liquid of equal density and a perfect See also:sphere is formed . If, however, the energy of surface tension between the two substances were negative the surface would tend to a maximum, and complete mixture would follow . From this point of view the natural solubility of two substances involves a negative energy of surface tension between them . Gibbs's Phase Rule.—A saturated solution is a system in equilibrium, and exhibits the thermodynamic relations which hold for all such systems . Just as two electrified bodies are in equilibrium when their electric potentials are equal, so two parts of a chemical and physical system are in equilibrium when there is equality between the chemical potentials of each component See also:present in the two parts . Thus water and See also:steam are inequilibrium with each other when the chemical potential of water substance is the same in the liquid as in the vapour . The chemical potentials are clearly functions of the See also:composition of the system, and of its temperature and pressure . It is usual to See also:call each part of the system of uniform composition through-out a phase; in the example given, water substance, the only component is present in two phases—a liquid phase and a vapour phase, and when the potentials of the component are the same in each phase equilibrium exists . If in unit mass of any phase we have n components instead of one we must know the amount of n-I components present in that unit mass before we know the exact composition of it . Thus if in one gramme of a mixture of water, See also:alcohol and salt we are told the amount of water and salt, we can tell the amount of alcohol . If, instead of one phase, we have r phases, we must find out the values of r(n—I) quantities before we know the composition of the whole system . Thus, to investigate the composition of the system we must be able to calculate the value of r (n — t) unknown quantities . To these must be added the See also:external variables of temperature and pressure, and then as the See also:total number of variables, we have r (n+I) + 2 . To determine these variables we may form equations between the chemical potentials of the different components—quantities which are functions of the variables to be determined . If ,ul and µ2 denote the potentials of any one component in two phases in contact, when there is equilibrium, we know that AI =µ2 . If a third phase is in equilibrium with the other two we have also µ1=µa . These two equations involve the third relation µ2=µ3, which therefore is not an independent See also:equation . Hence with three phases we can form two independent equations for each component . With r phases we can form r—1 equations for each component, and with n components and r phases we obtain n(r—1) equations . Now by elementary See also:algebra we know that if the number of independent equations be equal to the number of unknown quantities all the unknown quantities can be determined,eand can possess each one value only . Thus we shall be able to specify the system completely when the number of variables, viz. r (n — t) + 2, is equal to the number of equations, viz. n(r—i); that is when r=n + 2 . Thus, when a system possesses two more phases than the number of its components, all the phases will be in equilibrium with each other at one definite composition, one definite temperature and one definite pressure, and in no other conditions . To take the simplest case of a one component system water substance has its three phases of solid See also:ice, liquid water and gaseous vapour in equilibrium with each other at the freezing point of water under the pressure of its own vapour . If we See also:attempt to change either the temperature or the pressure ice will melt, water will evaporate or vapour See also:con-dense until one or other of the phases has vanished . We then have in equilibrium two phases only, and the temperature and pressure may change . Thus, if we See also:supply See also:heat to the mixture of ice, water and steam ice will melt and eventually vanish . We then have water and vapour in equilibrium, and, as more heat enters, the temperature rises and the vapour-pressure rises with it . But, if we See also:fix arbitrarily the temperature the pressure of equilibrium can have one value only . Thus by fixing one variable we fix the state of the whole system . This condition is represented in the algebraic theory when we have one more unknown quantity than the number of equations; i.e. when r(n—t) + 2=n(r—i) + 1 or r=n-1-1, and the number of phases is one more than the number of components . Similarly if we have F more unknowns than we have equations to determine them, we must fix arbitrarily F co-ordinates before we fix the state of the whole system . The number F is called the number of degrees of freedom of the system, and is measured by the excess of the number of unknowns over the number of variables . Thus F = r(n — i) + 2 — n(r — i) = n — r + 2, a result which was deduced by J . Willard Gibbs (1839—1903) and is known as Gibbs's Phase-Rule (see See also:ENERGETICS) . The phenomena of equilibrium can be represented on diagrams . Thus, if we take our co-ordinates to represent pressure and temperature, the state of the systems p with ice, water and vapour in equilibrium is represented by the point 0 where the pressure is that of the vapour of water at the freezing point and the temperature is the freezing point under that pressure . If all the ice be melted, we pass along the vapour pressure See also:curve of water OA . If all the water be frozen, we have the vapour pressure curve of ice OB; while, if the pressure be raised, so that all the vapour vanishes, we get the curve OC of equilibrium between the pressure and the freezing point of water . The slope of these curves is determined by the so-called " latent heat equation " t FIG . I . (see THERMODYNAMICS), dp/dt=a/t(v2—v1), where p and t denote the pressure and temperature, X the heat required to change unit mass of the systems from one phase to the other, and v2—v1 the resulting change in volume . The phase rule combined with the latent heat equation contains the whole theory of chemical and physical equilibrium . Application to Solutions.—In a system containing a solution we have to See also:deal with two components at least . The simplest case is that of water and a salt, such as sodium chloride, which crystallizes without water . To obtain a non-variant system, we must assemble four phases—two more than the number of components . The four phases are (I) crystals of salt, (2) crystals of ice, (3) a saturated solution of the salt in water, and (4) the vapour, which is that practically of water alone, since the salt is non-volatile at the temperature in question . Equilibrium between these phases is obtained at the freezing point of the saturated solution under the pressure of the vapour . At that pressure and temperature the four phases can co-exist, and, as See also:long as all of them are present, the pressure and temperature will remain steady . Thus a mixture of ice, salt and the saturated solution has a See also:constant freezing point, and the composition of the solution is constant and the same as that of the mixed solids which freeze out on the abstraction of heat . This constancy both in freezing point and composition formerly was considered as a characteristic of a pure chemical compound', and hence these mixtures were described as components and given the name of " cryohydrates." In representing on a See also:diagram the phenomena of equilibrium in a two-component system we require a third See also:axis along which p to See also:plot the composition of a a variable phase . It is usual to take three axes at right j angles to each other to represent pressure, temperature and the composition of the variable phase . On a See also:plane figure this solid diagram must be See also:drawn in See also:perspective, the third axis C being imagined to See also:lie out of the plane of the See also:paper . The phase-rule diagram that we construct is then a See also:sketch of a solid See also:model, the lines of which do not really lie in the plane of the paper . Let us return to the case of the system of salt and water . At the cryohydric point 0 we have four phases in equilibrium at a definite pressure, temperature and composition of the liquid phase . The condition of the system is represented by a single point on the diagram . If heat be added to the mixture ice will melt and salt dissolve in the water so formed . If the supply of ice fails first the temperature will rise, and, since solid salt remains, we pass along a curve OA giving the relation between temperature and the vapour pressure of the saturated solution . If, on the other hand, the salt of the cryohydrate fails before the ice the water given by the continued See also:fusion dilutes the solution, and we pass along the curve OB which shows the freezing points of a See also:series of solutions of constantly increasing dilution . If the process be continued till a very large quantity of ice be melted the resulting solution is so dilute that its freezing point B is identical with that of the pure solvent . Again, starting from 0, by the abstraction of heat we can remove all the liquid and travel along the curve OD of equilibrium between the two solids (salt and ice) and the vapour . Or, by in-creasing the pressure, we eliminate the vapour and obtain the curve OF giving the relation between pressure, freezing point and composition when a saturated solution is in contact with ice and salt . If the salt crystallizes with a certain amount of water as well as with none, we get a second point of equilibrium between four phases . Sodium sulphate, for instance, crystallizes below 32.6° as Na2SO4•IoH2O, and above that temperature as the anhydrous solid Na2SO4 . Taking the point 0 to denote the state of equilibrium between ice, See also:hydrate, saturated solution and vapour, we pass along OA till a new solid phase, that of Na2SO4, appears at 32.6°; from this point arise four curves, analogous to those diverging from the point O . For the quantitative study of such systems in detail it is convenient to draw plane diagrams which are theoretically projections of the curves of the solid phase rule diagram on one or other of these planes . Experiments on the relation betweentemperature and concentration are illustrated by projecting the curve OA of fig . 2 on the tc-plane . The pressure at each point should be that of the vapour, but since the solubility of a solid does not change much with pressure, measurements under the constant atmospheric pressure give a curve practically identical with the theoretical one . Fig . 3 gives the equilibrium between sodium sulphate and water in this way . B is the freezing point of pure water, 0 that Molecular Percentage of See also:Hat S& i 2 3 4 5 FIG . 3 . of a saturated solution of Na2SO4•IoH2O . The curve OP represents the varying solubility of the hydrate as the temperature rises from the cryohydric point to 32.6° . At that temperature crystals of the anhydrous Na2SO4 appear, and a new fixed equilibrium exists between the four phases—hydrate, anhydrous salt, solution and vapour . As heat is supplied, the hydrate is transformed gradually into the anhydrous salt and water . When this process is complete the temperature rises, and we pass along a new curve giving the equilibrium between anhydrous crystals, solution and vapour . In this particular case the solubility decreases with rise of temperature . This behaviour is exceptional . Two Liquid Components.—The more complete phenomena of mutual solubility are illustrated by the case of phenol and water . In fig . 4 A represents the freezing point of pure water, and AB the freezing point curve showing the depression of the freezing point as phenol is added . At B is a non-variant system made up of ice, solid phenol, saturated solution and vapour . See also:BCD is the solubility curve of phenol in water . At C a new liquid phase appears—the solution of water in liquid phenol, the solubility of which is represented by the curve DE . At D the composition of the two liquids becomes identical, and at temperatures above D, 68°C the liquids are soluble in each other in all proportions, and only one liquid phase can exist . If the two substances are soluble in each other in all proportions at all temperatures above their melting points we get a diagram reduced to the two fusion curves cutting each other at a non-variant point . This behaviour is illustrated by the case of silver and copper (fig . 5) . 0 20 40 60 90 100% At the non-variant point A liquid in which the composition is nearly that of the eutectic shows the changes FIG . 5. in the See also:rate of fall of See also:tempera- See also:ture as it is allowed to cool . First a small quantity of one of the pure components begins to crystallize out, and the rate of cooling is thereby diminished owing to the latent heat liberated by the change of state . This process continues till the composition of the liquid phase reaches that of the eutectic, when the whole mass solidifies on the further loss of heat without change of temperature, giving a very definite freezing point . The process of cooling is thus represented by a path which runs vertically downwards till it cuts the the two metals freeze out together and the composition of the liquid is the same as that of the mixed solid which crystallizes from it . The solid is then known as a eutectic alloy . 1 L y~~4H das 0s . B freezing point curve, and then travels along it till the non-variant point is reached . In this way two temperature points are obtained in the investigation—the higher giving a point on the equilibrium curve, the See also:lower showing the non-variant point . Other pairs of See also:alloys, showing more complicated relations, are described in ALLOY . Experiments on alloys are, in some ways, easier to make than on pairs of non-metallic substances, partly owing to the possibility of polishing sections for microscopic examination, and the investigation of alloys has done much to elucidate the general phenomena of solution, of which metallic solution constitutes a See also:special case . When the two components form chemical compounds with each other, the phenomena of mutual solubility become more complex . a . For a simple case to serve as an introduction, let 1O°° us again turn to alloys . Copper and See also:antimony form a single compound SbCu2 . aoo If either copper or See also:anti- mony be added to this sa compound, the freezing soo C point is lowered just as it would be if a new sub- stance were added, to a 400 A solvent . Thus on each See also:side of the point B repre- so See also:ioo senting this compound, the FIG . 6. curve falls . Proceeding along the curve in either direction, we come to a non-variant or eutectic point . In one case (represented by the point A in the figure) the solid which freezes out is a See also:conglomerate of crystals of the compound with those of antimony, in the other case C with those of copper . Thus in interpreting complicated freezing point curves, we must look for chemical compounds where the curve shows a maximum, and for a eutectic or cryohydrate where two curves meet at a minimum point . We are now ready to study a case where several compounds are formed between the two components . A See also:good example is the to equilibrium of ferric chloride and water, studied by B . Roozeboom . The experi- See also:mental curve of solubility is shown in fig . 7 . At A we have the freezing point of pure water, which is lowered so by the See also:gradual addition of ferric chloride in the manner shown by the curve AB . At B we have the non-variant cryohydric point at which ice, the hydrate Fe2C16•I2H2O, 40 the saturated solution and the vapour are in equilibrium at 55° C . As the proportion of salt is increased, the melting point of the con-glomerate rises, till, at the maximum point C, we have the pure compound the hydrate with twelve molecules ro ra 20- 2s s0 of water . Beyond C, the -40 FIG . 7. addition of salt lowers the melting point again, till at D we obtain another non-variant point . This indicates the See also:appearance of a new compound, which should exist pure at E, the next maximum, and, led by these considerations, Roozeboom discovered and isolated a previously unknown hydrate, Fe2C167•See also:H2O . In a similar way the curve FGH, between 30° and 55°, shows the effect of the hydrate Fe2CI6.5H2O, and the curve HJK that of the hydrate Fe2C16.4H2O, which, when pure, melts at 73.5°—the point J on the diagram . At the point See also:wire, 66°, begins the solubility curve of the anhydrous salt, Fe2CI6, the fusion point of which when pure is beyond the limits of the diagram . Let us now trace the behaviour of a solution of ferric chloride which is evaporated to dryness at a constant temperature of 31 ° . The phenomena may be investigated by following a See also:horizontal See also:line across the diagram . When the curve BC is reached, Fe2Cl6•I2H2O separates out, and the solution solidifies . Further renewal of water will cause first liquefaction, as the curve CD is passed, and then resolidificatiori to Fe2Cl6.7H20 when DE is cut . Again the solid will liquefy and once more become solid as Fe2C16.5H2O . Still further evaporation causes these crystals to effloresce and pass into the anhydrous salt . As we have seen, the See also:maxima of the various curve-branches at C, E, G, and dJ correspond with the melting points of the various hydrates at 37 32.5°, 56° and 73.5° respectively; and at these points melting or solidification of the whole mass can occur at constant temperature . But we have also found this behaviour to be characteristic of the non-variant or transition points, which, in this case, are represented by the points B, D, F, H and K (-55°, 27.4°, 3o°, 55° and 66°) . Thus 60 20 0 0 -20 -60 See also:sin two ways at least a constant melting point can be obtained in a two-component system . Solid Solutions.—In all the cases hitherto considered, the liquid phase alone has been capable of continuous variation in composition . The solid phases each have been of one definite substance . Crystals of ice may lie side by side with crystals of See also:common salt, but each crystalline individual is either ice or salt; no one crystal contains both components in proportions which can be varied continuously . But, in other cases, crystals are known in which both components may enter . Such phenomena are well known in the alums—See also:double sulphates of See also:aluminium with another See also:metal . Here the other metal may be one, such as potassium, or two, such as potassium and sodium, and, in the latter case, the proportion between the two may vary continuously throughout wide limits . Such structures are known as mixed crystals or solid solutions .
The theoretical form of the freezing point diagrams when solid solutions are present depends on the relation between the available energy and the composition in the two phases
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This relation is known when the amount of either component present in the other is very small, for it is then the relation for a dilute system and can
A B A B A B A
be calculated
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But at intermediate compositions we can only guess at the form of the energy-composition curve, and the freezing point composition curve, deduced from it, will vary according to the supposition which we make
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With the most likely forms for the energy curves we get the accompanying diagrams for the relation between freezing point and concentration
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It will be noticed that in all these theoretical curves the points of initial fusion and solidification do not in general coincide; we reach a different curve first according as we approach the diagram from below, where all is solid, or from above, where all is liquid
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Again, it will be seen that the addition of a small quantity of one component, say B, to the other, A, does not necessarily lower the melting point, as it does with systems with no solid solutions; it is quite as likely to cause it to rise
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The second and third figures, too, show that the presence of solid solutions may simulate the phenomena of chemical See also:combination, where the curve reaches a maximum, and of non-variant systems where we get a minimum
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The See also:fourth figure shows that, in some cases, it should be possible for solid solutions to be present in a limited part of the See also: See also:hen the equilibria become more complex difficulties of See also:interpretation of the experimental results often arise . It is often very difficult to distinguish between a chemical compound, for example, and the case of solid solution represented by fig . 9 . All available See also:evidence, from the freezing point curve and from other See also:sources must be scrutinized before an See also:opinion is pronounced . But the elucidation of the complicated phenomena of solid solutions would have been impossible without the theoretical knowledge deduced from the principle of available energy . Supersaturation.—When a crystal of the solid phase is present the equilibrium of a solution is given by the solubility curves we have studied . If, however, a solution be cooled slowly past its saturation point with no solid present, See also:crystallization does not occur till some lower temperature is reached . Between the saturation point and this lower See also:temper.ture, the liquid holds in solution more of the solute than corresponds with equilibrium, and is said to be supersaturated . A See also:familiar example is to be found in solutions of sodium sulphate, which may be cooled much below their saturation point and kept in the liquid state till a crystal of the hydrate Na2SOa•roH2O is dropped in, when solidification occurs with a large See also:evolution of latent heat . These phenomena are explicable if we consider the energy relations, 372 for the See also:intrinsic energy of a system will contain terms depending on the area of contact between different phases, and, for a given mass of material, the area will be greater if the substance is finely divided . Hence the conditions necessary to secure equilibrium when the solid phase is present are not the same as those necessary to cause crystallization to start in a number of crystals at first excessively See also:minute in See also:size . The corresponding phenomenon in the case of vapours is well known . Dust-See also:free air will remain supersaturated with water-vapour in conditions where a dense See also:cloud would be formed in presence of solid dust-nuclei or electric ions which serve the same purpose . If a solution of a salt be stirred as it cools in an open See also:vessel, a thin shower of crystals appears at or about the saturation temperature . These crystals grow steadily, but do not increase in number . When the temperature has fallen about so° C. below this point of saturation, a dense shower of new crystals appear suddenly . This shower may be dense enough to make the liquid quite opaque . These phenomena have been studied by H . A . Miers and See also:Miss F . See also:Isaac . If the solution be confined in a sealed See also:glass See also:tube, the first thin shower is not formed, and the system remains liquid till the secondary dense shower comes down . From this and other evidence it has been shown that the first thin shower in open vessels is produced by the accidental presence of tiny crystals obtained from the dust of the air, while the second dense shower marks the point of spontaneous crystallization, where the decrease in total available energy caused by solidification becomes greater than the increase due to the large surface of contact between the liquid and the potentially existing multitudinous small crystals of the shower . If the temperature at which this dense spontaneous shower of crystals is found be determined for different concentrations of solution, we can plot a " supersolubility curve," which is found generally to run roughly parallel to the " solubility curve " of steady equilibrium between liquid and already existing solid . When two substances are soluble in each other in all proportions, we get solubility curves like those of copper and silver shown in fig . 5 . We should expect to find supersolubility curves lying below the solubility curves, and this result has been realized experimentally for the supersolubility curves of mixtures of salol (phenyl salicylate) and betol 0-naphthol salicylate) represented by the dotted lines of fig . 12 . In See also:practical cases of crystallization in nature, it is probable that these phenomena of supersaturation often occur . If a liquid mixture too' of A and B (fig . 12) were inocu- ~^~~^ lamed with crystals of A when its composition was as that t represented so' by x, cooled very slowly and those those d, of equilibrium tconditions throughout. would ^~'~~ When the temperature sank to a, on the freezing point curve, crystals of pure A would appear . ~1 The residual liquid would thus become richer in B, and the See also:tern- a, perature and composition would Mlllllliiiil pass along the curve till E, the eutectic point, was reached . The so 40 60 80 100 liquid then becomes saturated A Percentage of Salo: in Mixture B with B also, and, if inoculated FIG . 12. with B crystals, will See also:deposit B alongside of A, till the whole mass is solid . But, if no solid be present initially, or if the cooling be rapid, the liquid of composition x becomes supersaturated and may cool till the supersaturation curve is reached at b, and a cloud of A crystals comes down . The temperature may then rise and the concentration of B increase in the liquid in a manner represented by some such line as b f . The conditions may then remain those of equilibrium along the curve f E, but before reaching f the solution may become supersaturated with B and deposit B crystals spontaneously . The eutectic point may never be reached . The possibility of these phenomena should be See also:borne in mind when attempts are made to interpret the structure of crystalline bodies in terms of the theory of equilibrium . Osmotic Pressure.—The phase rule combined with the latent heat equation enables us to trace the general phenomena of equilibrium in solutions, and to elucidate and classify cases even of See also:great complexity . But other relations between the different properties of solutions have been investigated by another series of conceptions which we shall proceed to develop . Some botanical experiments made about 187o suggested the See also:idea of semi-permeable membranes, i.e. membranes which allow a solvent to pass freely but are impervious to a solute when dissolved in that solvent . It was found, for instance, that a film of insoluble copper ferrocyanide, deposited in the walls of aporous vessel by the inward diffusion and See also:meeting of solutions of copper sulphate and potassium ferrocyanide, would allow water to pass, but retained sugar dissolved in that liquid . It was found, too, when water was placed on one side of such a membrane, and a sugar solution in a confined space on the other, that water entered the solution till a certain pressure was set up when equilibrium resulted . The importance of these experiments from the point of view of the theory of solution, See also:lay in the fact that they suggested the conception of a perfect or ideal semi-permeable See also:partition, and that of an equilibrium pressure representing the excess of hydrostatic pressure required to keep a solution in equilibrium with its pure solvent through such a partition . Artificial membranes are seldom or never perfectly semi-permeable--some leakage of solute nearly always occurs, but the imperfections of actual membranes need no more prevent our use of the ideal conception than the faults of real engines invalidate the theory of ideal thermodynamics founded on the conception of a perfect, reversible, frictionless, heat See also:engine . Further, in the free surface the solutions of an involatile solute in a volatile solvent, through which surface the vapour of the solvent alone can pass, and in the boundary of a crystal of pure ice in a solution, we have actual surfaces which are in effect perfectly semi-permeable . Thus the results of our investigations based on ideal conceptions are applicable to the real phenomena of evaporation and freezing .
Dilute Solutions.—Before considering the more complicated case of a concentrated solution, we will deal with one which is very dilute, when the theoretical relations are much simplified
.
The vapour pressure of a solution may be measured experimentally by two methods
.
It may be
compared directly with that of the pure solvent, as the vapour-pressure of a pure liquid is determined, by placing solvent and solution respectively above the See also:mercury in two See also:barometer tubes, and comparing the depressions of the mercury with the height of a dry barometer at the same temperature
.
This method was used by See also:Raoult
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On the other hand, a current of dry air may be passed through the series of weighed bulbs containing solution and solvent respectively, and the loss in See also:weight of each determined
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The loss in the solution bulbs gives the mass of solvent absorbed from the solution, and the loss in the solvent bulbs the additional mass required to raise the vapour pressure in the air-current to equilibrium with the pure solvent
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The relative lowering of vapour pressure of the solution compared with that of the solvent is measured by the ratio of the extra mass absorbed from the solvent bulbs to the total mass absorbed from both series of bulbs
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Experiments by this method have been made by W
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Ostwald and J
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See also: See also:Hartley . The vapour pressure of the solution of a non-volatile solute is less than the vapour pressure of the pure solvent . Hence if two vessels, one filled with solvent and one with solution, be placed side by side in an exhausted chamber, vapour will evaporate from the solvent and condense on the solution . The solution will thus gain solvent,, and will grow more and more dilute . Its volume will also increase, and thus its upper surface will rise in the vessel . But as we ascend in an See also:atmosphere the pressure diminishes; hence the pressure of the vapour in the chamber is less the higher we go, and thus eventually we reach a state of equilibrium where the See also:column of vapour is in equilibrium at the appropriate level both with solvent and solution . Neglecting the very small buoyancy of the vapour, the hydrostatic pressure P at the See also:foot of the column of solution is h g p where h is the height of the column and p the mean density of the solution . If the height be not too great, we may assume the density of the vapour to be uniform, and write the difference in vapour pressure at the surfaces of the solvent and of the solution as p — p' = hgo . Hence we find that p — p' = Poip for a very dilute solution, where the difference p—p' is small and the height of the balancing column of solution small . In practice the See also:time required to reach these various conditions of equilibrium would be too great for experimental demonstration, but the theoretical See also:consideration of vapour pressures is of fundamental importance . Let us suppose that we possess a partition such as that described above, which is permeable to the solvent but not to the solute when dissolved in it, and let us connect the solution and solvent of fig . 13 with each other through such a partition . 
If solvent were to flow one way or the other through the partition, the Vapour Pressure . height of the column of solution would rise or fall and the equilibrium with the vapour be disturbed . A continual circulation might thus be set up in an isothermal enclosure and maintained with the performance of an unlimited supply of See also:work . This result would be contrary to all experience of the impossibility of " perpetual See also:motion," and hence we may conclude that through such a semi-permeable See also:wall, the solvent and the solution at the foot of the column would be in equilibrium under the excess of hydrostatic pressure represented when the solution is very dilute by P=(p—p')p/Q . But such a pressure represents the equilibrium osmotic pressure discussed above . Therefore the equilibrium osmotic pressure of a solution is connected with the vapour pressure, and, in a very dilute solution, is expressed by the simple relation just given . Another relation becomes evident if we use as a semi-permeable partition a " vapour See also:sieve " as suggested by G . F . See also:Fitzgerald . If a number of small enough holes be drilled through a solid substance which is not wetted by the liquid, our knowledge of the phenomena of capillarity shows us that it needs pressure to force the liquid into the holes . A See also:piston made of such a perforated substance, therefore, may be used to exert pressure on the liquid, while all the time the vapour is able to pass . By evaporation and condensation, then, the solvent can pass through this perforated partition, which thus acts as a perfect semi-permeable membrane . When the solution and solvent are in equilibrium across the partition, the vapour pressure of the solution has been increased by the application of pressure till it is equal to that of the solvent . In any solution, then, the osmotic pressure represents the excess of hydrostatic pressure which it is necessary to apply to the solution in See also:order to increase its vapour pressure to an equality with that of the solvent in the given conditions . Similar considerations show that, since at its freezing point the vapour pressure of a solution must be in equilibrium with that of ice, the depression of freezing point produced by dissolving a sub-stance in water can be calculated from a knowledge of the vapour pressure of ice and water below the freezing point of pure water . But another method of investigation will illustrate new ways of treating our subject . By imagining that a dilute solution is put through a thermodynamic See also:cycle we may deduce directly relations between its osmotic pressure and its freezing point . Let us freeze out unit mass of solvent from a solution at its freezing point T—dT and remove the ice, which is assumed to be the ice of the pure solvent . Then let us heat both ice and solution through the infinitesimal temperature range dT to the freezing point T of the solvent, melt the ice by the application of an amount of heat L, which measures its latent heat of fusion, and allow the solvent so formed to enter the solution reversibly through a semi-permeable wall into an engine See also:cylinder, doing an amount of work Pdv . By cooling the resultant solution through the range dT we recover the See also:original state of the system . The well-known expression for the efficiency of the cycle of reversible operation gives us Pdv'L = dT/T or dT = TPdv/L as a value for the depression of the freezing point of the solution compared with that of the pure solvent . The freezing point of a solution may be determined experimentally . The solution is contained in an inner tube, surrounding which is an air space . Then comes an See also:outer vessel, in which a freezing mixture can be placed .
This solution is stirred continuously and the temperature falls slowly below the freezing point, till the supersaturation point is reached, or until a crystal of ice is introduced
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The solution then freezes, until the heat liberated is enough to raise the tem.-perature to the point of equilibrium given by the tendency of the solution taken in contact with ice to approach the true freezing point on one side and the temperature of the enclosure on the other
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To get the true freezing point then, it is well to arrange that the temperature of the enclosure should finally be nearly that of the freezing point to be observed
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One way in which this has been secured is by obtaining the under cooling by temporary cooling of. the air space by a See also:spiral tube in which See also:ether may be evaporated, the outer vessel being filled with ice in contact with a solution of See also:equivalent concentration to that within
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Modifications of this method have been used by many observers, among others by Raoult, Loomis, H
.
C
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See also: On Absolute the fundamental hypotheses of the molecular theory, value of we must regard a solution as composed of a number osmotic of See also:separate particles of solute, scattered through- Pressure. out the solvent . Each particle may react in some way on the solvent in its neighbourhood, but if the solution be so dilute that each of these See also:spheres of See also:influence is unaffected by the See also:rest, no further addition of solvent will change the connexion between one particle of solute and its associated solvent . The only effect of adding solvent will be to separate further from each other the systems composed of solute particle as See also:nucleus and solvent as atmosphere; it will not affect the See also:action of each nucleus on its atmosphere . Thus the result will be the same whatever the nature of the inter-action may be . If solvent be allowed to enter through a semi-permeable wall into an engine cylinder, the work done when the solution within is already dilute will be the same whatever the nature of the interaction between solute and solvent, that is, whatever be the nature of the solvent itself . It will even be the same in those cases where, with a volatile solute, the presence of a solvent may be dispensed with, and the solute exist in the same volume as a gas . Now the work done by allowing a small quantity of solvent to enter reversibly into an osmotic cylinder is measured by the product of the osmotic pressure into the change in volume . Hence the osmotic pressure is measured by the work done per unit change of volume of the solution . The result of our consideration, therefore, is that the osmotic pressure of a dilute solution of a volatile solute must have the same value as the gaseous pressure the same number of solute particles would exert if they occupied as gas a volume equal to that of the solution . The reasoning given above is independent of the temperature, so that the variation with temperature of the osmotic pressure of a dilute solution must be the.same as that of a gas, while See also:Boyle's See also:law must equally apply to both systems . Experimental evidence confirms these results, and extends them to the cases of non-volatile solutes—as is, indeed, to be expected, since volatility is merely a See also:matter of degree . When the solution ceases to be dilute in the thermodynamic sense of the word, that is, when the spheres of influence of the solute particles intersect each other, this reasoning ceases to apply, and the resulting modification of the gas laws as applied to solutions becomes a matter for further investigation, theoretical or experimental . In the limit then, when the concentration of the solution becomes vanishingly small, theory shows that the osmotic pressure is equal to the pressure of a gas filling the same space . Experiments with membranes of copper ferrocyanide have verified this result for solutions of See also:cane-sugar of moderate dilutions . But the most accurate test of the theory depends on measurements of freezing points . A quantity of gas measured by its molecular weight in grammes when confined in a volume of one litre exerts a pressure of 22.2 atmospheres, and thus the osmotic pressure of a dilute solution divided by its concentration in gramme-molecules per litre has a corresponding value . But we have seen that the depression of dT of the freezing point of a dilute solution is measured by TPdv/L . Putting the absolute temperature of the freezing point of water as 273°, the osmotic pressure P as 22.2 atmospheres or 22.4X006, C.G.S. See also:units per unit concentration, L the latent heat as 79.4X 4.184X I& in the corresponding units, and dv the volume change Freezing Point . in the solution for unit mass of solvent added we get for the quantity dT/c, where c is the concentration of the solution, the value 1.857° C. per unit concentration . Experimental measurements of freezing points of various non-electrolytic solutions have been made by Raoult, Loomis, Griffiths, Bedford and others and See also:numbers ranging See also:round 1.85 found for this concentration . Equally good comparisons have been obtained for solutions in other solvents such as acetic See also:acid 3.88, formic acid 2.84, See also:benzene 5.30, and nitro-benzene 6.95 . Such a See also:concordance between theory and experiment not only verifies the accuracy of thermodynamic reasoning as applied to dilute solutions, but gives perhaps one of the most convincing experimental verifications of the general validity of thermodynamic theory which we possess . Another verification may be obtained from the phenomena of vapour pressure . Since, in dilute solutions, the osmotic pressure has the gas value, we may apply the gas equation PV =nRT =nevi to osmotic relations . Here n is the number of gramme-molecules of solute, T the absolute temperature, R the gas constant with its usual " gas " value, p the vapour pressure of the solvent and vl the volume in which one gramme-See also:molecule of the vapour is confined . In the vapour pressure equation p—p'=Pa/p, we have the vapour density a equal to M/v1, where M is the molecular weight of the solvent . The density of the liquid is MN/V, where N is the number of solvent molecules, and V the total volume of the liquid . Substituting these values, we find that the relative lowering of vapour pressure in a very dilute solution is equal to the ratio of the numbers of solute and solvent molecules, or (p — p')/p = n/N . The experiments of Raoult on solutions of organic bodies in water and on solutions of many substances in some dozen organic solvents have confirmed this result, and therefore the theoretical value of the osmotic pressure from which it was deduced . Although even good membranes of copper ferrocyanide are rarely perfectly semi-permeable, and in other membranes such as indiarubber, &c., which have been used, the defects from the theoretical values of the equilibrium pressure are very great, yet, in the See also:light of the exact verification of theory given by the experiments described above, it is evident that such failures to reach the limiting value in no See also:wise invalidate the theory of osmotic equilibrium . They merely show that, in the conditions of the particular experiments, the thermodynamic equilibrium value of the osmotic pressure cannot be reached—the thermodynamic or theoretical osmotic pressure (which must be independent of the nature of the membrane provided it is truly semi-permeable) is a different thing from the equilibrium pressure actually reached in a given experiment, which measures the See also:balance of See also:ingress and See also:egress of solvent through an imperfect semi-permeable membrane . Dilute solutions of substances such as cane-sugar, as we have seen, give experimental values for the connected osmotic properties—pressure, freezing point and vapour Solutions ec yt es. of pressure—in ressure—in conformity with the theoretical values . FJ All these solutions are non-conductors of See also:electricity . On the other hand, solution of See also:mineral acids and salts conduct the current with chemical decomposition—they are called electrolytes . In order to explain the See also:electrical properties of a solution, for instance of potassium chloride, we are driven to believe that each molecule of the salt is dissociated into two parts, potassium and See also:chlorine, each associated with an electric See also:charge equal in amount but opposite in sign . The See also:moveme |