PROPERTIES OF MIXTURES The term mixture is applied to a system in which the con stituent particles are directly or indirectly distinguishable from one another. When the difference can be recognized directly or by the use of some optical magnifying device, it is customary to speak of mechanical mixtures, whilst the term solution is reserved for mixtures in which the constituent particles are of molecular dimensions. There is no funda mental difference between the two classes of mixtures for they can all be resolved by the application of mechanical forces, for example, by a process of centrifuging. Gases are all completely miscible with one another, but miscibility in the liquid and solid states is much less general. Some pairs of liquids are miscible in all propor tions and complete series of mixed crystals are formed by certain pairs of crystalline solids. Other pairs of liquids and solid sub stances are practically immiscible. A third group is formed by pairs which are miscible in limited proportions. Miscibility de pends upon the temperature and in gen eral is favoured by the chemical simi larity of the substances concerned. Water does not mix with hydrocarbons, is completely miscible with methyl and ethyl alcohols, partially miscible with butyl and amyl alcohols, but practically immiscible with higher members of the alcohol series.
When two partially miscible liquid substances A and B are brought together, then, in general, two layers are formed which contain different proportions of A and B. The composition of these layers (so-called conjugate pairs) depends on the tem perature. As a rule, the difference between the conjugates diminishes with rise of temperature and in some cases may ulti mately disappear. The temperature at which this occurs is the "critical solution temperature" and above this the two substances are miscible in all proportions. Increased miscibility is sometimes produced by a fall of temperature and a few pairs of substances are known for which both upper and lower critical temperatures can be observed. Nicotine and water, for example, are completely miscible below 61° C and above 21o° C ; between these limits they are only partially miscible. Fig. 4 shows these relations : conjugate pairs are connected by horizontal lines.
In gaseous mixtures at the ordinary pressure, the molecules are so widely separated that the effects of intermolecular forces can be almost entirely ignored. In the absence of chemical inter action between them, the independence of the molecules would lead us to expect that the properties peculiar to the molecules of a substance A will not be affected by admixture with the molecules of B. In these circumstances, the properties of a gaseous mixture which contains A and B in the molecular ratio (I —x) : x should be given by the simple mixture rule, which may be written (I where PA, PB and represent the values of the property for A, B and the mixture respectively. Dalton's law of partial pressures affords an example of this relation.
In the interpretation of such curves, two different points of view have been adopted. On the one hand, the changes in physical properties have been attributed to variations in the molecular attractive forces. If the attractive forces between the unlike molecules and between the two sets of like molecules are denoted respectively by and then if is much greater than and it may be anticipated that the substances in question will mix readily, whilst if a AB is much smaller than a A and a there are reasonable grounds for the anticipation that most will be only partially miscible. In the former case, pro nounced changes in the physical properties may be expected to accompany the mixing of the two substances, whereas if the attractive forces between the unlike molecules are of the same order of magnitude as the forces between the two sets of like molecules, it may be supposed that admixture will not be accom panied by any pronounced change in the general physical proper ties.
In contrast with the above view, some authors maintain that well-marked changes in physical properties afford evidence that the mixing of the two substances in question has resulted in chemical interaction. It may be that these two views are not so widely different as would be suggested by the arguments of the respective protagonists, for the action of molecular forces of sufficient magnitude between the molecules of A and B may lead to a form of physical association which is by no means easy to distinguish from what would be described as the chemical com bination of molecules of A and B. In any case it is probable that deviations from the simple mixture rule may be due in part to differences in the acting molecular forces, whilst the formation of definite chemical compounds may sometimes be the chief cause of the departure.
Theoretical considerations based on the law of mass action (see CHEMICAL ACTION) indicate that if the two components of a liquid mixture combine together to form a compound, the pro portion of this in the mixture will be greatest when the corn position of the mixture, as a whole, is the same as that of the compound. If such compound formation is the cause of the deviation in the physical properties from what would be expected according to the simple mixture rule, the determination of the composition of that liquid mixture for which the deviation has a maximum value should give the composition of the compound. In support of this and of the chemical theory, it is frequently found that maximum deviation occurs at a point which corre sponds with a simple molecular ratio of the components. For example, the volume and viscosity curves indicate the existence of the compound in ethyl alcohol–water mixtures and the formation of in mixtures of pyridine and water. The viscosity curve for methyl alcohol–water mixtures suggests the formation of the compound and the maximum deviation is independent of the temperature between 1o° and 6o° C.
If the curves for different properties show a maximum deviation at the same composition and if this composition is not affected appreciably by change of temperature, there would seem to be strong evidence for the formation of a compound represented by the corresponding formula. When a single stable compound is formed, its presence should be clearly indicated, but if the com pound is relatively unstable and therefore present in small quan tity the evidence may be much less conclusive. Furthermore, when more than one compound is formed, the property–composi tion curves may easily lead to erroneous conclusions, for if the compounds and are actually present, the maximum deviation of the experimental curve from the simple mixture line will probably occur at a point which falls between and and may indeed suggest the formation of the compound AB.
The properties of binary liquid mixtures which have been sys tematically examined include volume, viscosity, vapour pressure, dielectric capacity, heat capacity, heat of mixing, etc. In the graphic representation of the results it is necessary to correlate the units in terms of which the property is measured with those which are used to represent the composition of the mixture. If the composition is expressed in molecular percentages, in which case the abscissa corresponds directly with the relative numbers of molecules of A and B in the various mixtures, the property should also be evaluated on a molecular basis. The plot of the specific value of a property against the molecular composition would obviously have much less justification. In actual practice, the importance of such matters has not received adequate atten tion and to this fact must be attributed some of the difficulties which have been met with in the interpretation of property– composition curves.
Freezing-point curves and boil ing-point curves are somewhat different from other property composition curves in that they correspond with conditions which permit of the coexistence of the liquid with a solid or a vapour phase. In accordance with the fact that vapours are completely miscible, the boiling-point curves are nevertheless c on t i n u o u s, whereas the freezing-point curves are generally discontinuous. This is due to the circumstance that miscibility of substances in the solid state is very limited and that the freezing-point depends on the nature of the solid substance which separates out. Many cases are known in which the same liquid mixture has two or more freezing-points, the temperature varying with the product of crystallization.
When the components of a binary liquid mixture are completely miscible in the solid state, the two types of freezing-point curves which are obtained are closely similar to the boiling-point curves already described. For mixtures of the first type the freezing points lie between those of the pure components. In general, the composition of the mixed crystals which separate out differs from that of the mother-liquor, and the relation between the two can be represented on the freezing-point diagram by two curves— the so-called liquidus and solidus (see fig. 6) . Corresponding points L and S on these curves, i.e., points on the same horizontal line, are conjugate in the sense in which this term is applied to two coexisting liquid phases. Binary mixtures of the second type show either a maximum or a minimum freezing-point, at which the liquidus and solidus meet (cf. fig. 7). If the proportions of the components in the mixture correspond with this point, the liquid freezes at a constant tem perature and then behaves like a pure substance. A vertical line drawn through the maximum (or minimum) point divides the complete series of mixtures into two subgroups, the behaviour of which is exactly similar to that of mixtures of the first type.
If the components of a binary liquid mixture are immiscible in the solid state, the freezing point curve is discontinuous. In the simplest case, it consists of two descending branches which intersect at the eutectic point (cf. fig. 8; curve I). The eu tectic mixture is that mixture which has the lowest freezing point, and is further distinguished by the circumstance that the two components crystallize out simul taneously in the proportions in which they are present in the eu tectic liquid. The freezing temperature therefore remains con stant. Mixtures which contain an excess of A (or B) in com parison with the eutectic mixture deposit A (or B) on freezing. This alters the composition of the residual liquid and the freezing point falls continuously until the eutectic point is reached. The solidification is then completed at constant temperature.
If one or more compounds separate out on freezing, the dia gram is of a more complicated type. Fig. 8, curve II, illustrates the relations when a compound of the type AB crystallizes out. There are now four freezing point curves and two eutectic points. The two intermediate curves intersect in a point which corresponds with the freezing point of the compound AB. In spite of the increased complexity of the diagram, the relations are very similar to those which char acterize the simpler form, and complex diagrams of this kind can be resolved into a series of simple diagrams by drawing verti cal lines through the points which correspond with the several corn pounds formed. If three such compounds A,B, AB and AB, are formed, this process leads to four separate freezing-point diagrams, for which the components are - - A and A,B and AB, AB and AB,, and AB, and B respectively. Fig. 9 shows the relations for water and sulphur trioxide where five compounds are formed. It frequently happens that a solid compound decomposes into its components below its melting point. This is the case for Glauber's salt, which decomposes at 32.38° C. When such changes occur, the freezing point diagram shows one curve only for the compound.
Changes, very similar to those which characterize the equilibria between solid and liquid phases, also occur in systems which arc entirely solid, and these are largely responsible for the variations which are found in the properties of solid mixtures such as the alloys (q.v.). An exact knowledge of the equilibrium relations of the greatest importance, for the properties of such solids depend not only on the composition but on the constitution as represented by the phase equilibria. The changes produced in the physical properties of alloys by thermal and mechanical treatment are often directly due to changes in the phase equilibria.