CHAPTER 1 INTRODUCTION 1.1 GENERAL: The science of solution chemistry is very complex. It requires for its clarification, the help of many branches such as mechanics, electrostatics, and hydrodynamics. In 1887 an organized theoretical and experimental investigation of conducting solution was begun, van't Hoff[l], predicted that solutions which readily conduct electric current possess freezing points, boiling points, osmotic pressures and vapor pressures, characteristics of a special class of a system, and the simultaneous and even more important discovery of Arrhenius[2] that such systems contain electrically charged particles or ions. The powerful methods of thermodynamics were for the first time applied by van't Hoff to solutions in a systematic manner. His treatment, however, lacked the generality, which might have been achieved at that time if the system of thermodynamics developed by by Gibbs [3], ten years earlier had been employed. Gibbs great treatise provided all the essential basic principles required for the thermodynamics of solutions. The most important contribution of thermodynamics has been to reduce all measurements of system in equilibrium to the determination of a single thermodynamic function. Traditional theories of solutions well exclusively on two aspects of liquid mixtures. One of these is the entropy associated with dispersion of the two molecular species, or of their constituent elements in the case of complex molecules among one another. A lattice model often serves as the device for estimating this "combinational" entropy. The other aspect relates to the interactions between neighboring molecules and, in particular, to the difference in the interactions between unlike and like neighbor pairs. Treatment of l the properties of the liquid mixtures has progressed little beyond the level of interpretation possible within the framework supported by these two considerations alone [4,5]. The equilibrium properties of a liquid are strongly dependent on what may be loosely called its local structure, often expressed in terms such as packing density, free volume or more exactly in terms of the radial distribution function. In as much as this local structure depends on the forces between molecules and on the forms and volumes of the molecules, in general, it will change with the composition. This change in turn will be reflected in the thermodynamic properties of the mixture. Contributions of this nature have either been ignored altogether, or correction to a state of null volume change on mixing has been adopted as a means of compensating for the effects referred to [5]. This device alters the various properties of the mixtures altered by the changes they would sustain if the volumes were adjusted to the value linearly interpolated between the volumes of the pure components. It will be apparent, however, that adjustments of one thermodynamic quantity (e.g. volume) in this manner will not, in general, effect a simultaneous correction of others (e.g. the free energy or that part of it relating to the local structure) to their linearly interpolated values. The choice of volume as the property to be "conserved" is arbitrary, and there is no assurance that nullifying volume change obviates consideration of other characteristic properties of the liquid. Interest in the thermodynamic properties of binary liquid mixtures extended over most of the 19th century. Binary liquid mixtures are often used as solvents for chemical equilibria and for media in which to carry out chemical reactions. Binary liquid mixtures can be broadly classified into simple mixtures and 2 associated mixtures. Simple mixtures are defined as those in which the nominal components are identical with the actual species in the pure liquids as well as in the mixtures. The associated mixtures are defined as those in which there is an evidence for the association of at least one of the components either with each other (self association) or with those of another component. It is possible to approach the description of such mixtures in terms of the properties of the components in a formal thermodynamic manner or with respect to the molecular interactions, such as dipole-interactions, hydrogen bonding, and coordinative bond formation etc. 1.2 DENSITY: The density of a material is defined as its mass per unit volume. The symbol of density is p (the Greek letter rho). In some countries (for instance, in the United States), density is also defined as its weight per unit volume [6]. Mathematically: Density = Mass / Volume m p"v Where, p (rho) is the density, m is the mass, V is the volume. Different materials usually have different densities, so density is an important concept regarding buoyancy, metal purity and packaging. In some cases density is expressed as the dimensionless quantities specific gravity (SG) or relative density (RD), in which case it is expressed in multiples of the density of some other standard material, usually water or air/gas. For a homogeneous object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate scale or balance; the volume may be measured directly (from the geometry of the object) or by the 3 displacement of a fluid. Hydrostatic weighing is a method that combines these two[7]. The density of a solution is the sum of mass (massic) concentrations of the components of that solution. Mass (massic) concentration of a given component p; in a solution can be called partial density of that component. The SI unit for density is: • kilograms per cubic metre (kg/m3) Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m3). Liquid water has a density of about 1 kg/dm3, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm3[8]. • kilograms per cubic decimeter (kg/dm3) • grams per cubic centimeter (g/cc, gm/cc or g/cm3) • mega grams per cubic meter (Mg/m3) Liters and metric tons are not part of the SI, but are acceptable for use with it. Since 1 L = 1 dm3, we also have these of the same size: • kilograms per liter (kg/L) • grams per milliliter (g/mL) • metric tons per cubic meter (t/m3) 1.2.1 Changes of density: In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure will always increase the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behaviour is observed in silicon at low temperatures. 4 The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10~6 bar-1 (1 bar=0.1 MPa) and a typical thermal expansivity is 1CT5 K"1. In contrast, the density of gases is strongly affected by pressure. 1.3 EXCESS VOLUMES OF BINARY LIQUID MIXTURES: "Of the various thermodynamic functions for the mixing process, the volume change on mixing at constant pressure is one of the most interesting, yet certainly still one of the least understood." Hildebrand and Scott[5] wrote this in 1962 at a time when the subject of excess volumes of binary liquid mixtures was entering a phase of renewed interest and development. This renewed interest is closely tied to the advances in the theories of solutions which were made in the 1960's. For a long time the precision attainable on measuring volume changes on mixing was several orders of magnitude better than theory could calculate. The first breakthrough in the corresponding states theories was in predicting accurately the sign of the volume change on mixing. Current theories of solution are much more accurate with respect to sign and magnitude, and this has spawned a vigorous expansion in techniques and measurement. Volume changes on mixing have been determined mainly by two principle methods, a) by directly mixing the liquids and observing volume changes in dilatometer and b) indirectly by measuring the density of liquid mixtures. The volume change on mixing at constant pressure for the binary liquid mixtures is one of the most interesting thermodynamic functions of mixing. This property remains to be of interest because the experimental procedures are relatively easy to perform with great precision and 5 because the volume change on mixing is a sensitive indicator to the accuracy of theories of solution. 1.4 VISCOSITY : Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress. In everyday terms (and for fluids only), viscosity is "thickness". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement (fluidity)[9]. Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction. All real fluids have some resistance to stress and therefore are viscous, but a fluid which has no resistance to shear stress is known as an ideal fluid or inviscid fluid. In general, in any flow, layers move at different velocities and the fluid's viscosity arises from the shear stress between the layers that ultimately opposes any applied force. 1.4.1 Viscosity coefficients: Viscosity coefficients can be defined in two ways: • Dynamic viscosity, also absolute viscosity, the more usual one; • Kinematic viscosity is the dynamic viscosity divided by the density. Viscosity is a tensorial quantity that can be decomposed in different ways into two independent components. The most usual decomposition yields the following viscosity coefficients: • Shear viscosity, the most important one, often referred to as simply viscosity, describing the reaction to applied shear stress; simply put, it is the ratio between the pressure exerted on the surface of a fluid, in the lateral or horizontal direction, to the 6 change in velocity of the fluid as you move down in the fluid (this is what is referred to as a velocity gradient).