Systems containing more than one component

In solutions containing more than one electroactive species, various voltammetric waves appear. The same can happen if there is a second 

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When the system contains more than one component it is important to be able to explore the distribution of the different components both locally and at long range. One way in which this can be achieved is to evaluate the distribution function for the different species. For example in a binary mixture of components A and B there are four radial distribution functions, g (r), g (r), g (r) and g (r) which are independent under certain conditions. More importantly they would, with the usual definition, be concentration dependent even in the absence of correlations between the particles. It is convenient to remove this concentration dependence by normalising the distribution function via the concentrations of the components [26]. Thus the radial distribution function of g (r) which gives the probability of finding a molecule of type B given one of type A at the origin is obtained from... 

In the next two chapters, we use thermodynamic relationships summarized in Chapter 1 la to delve further into the world of phase equilibria, using examples to describe some interesting effects. As we do so, we must keep in mind that our discussion still describes only relatively simple systems, with a much broader world available to those who study such subjects as critical phenomena, ceramics, metal alloys, purification processes, and geologic systems. In this chapter, we will limit our discussion to phase equilibria of pure substances. In Chapter 14, we will expand the discussion to describe systems containing more than one component. 

Partial molar quantities are very commonly used to describe solutions, or systems containing more than one component. Mathematically, a partial molar quantity Zi is defined as the partial derivative... 

We have so far described a statistical mechanics of molecular liquids, implying that a system includes only one chemical species. However, in ordinary chemistry, a system contains more than one component, and major and minor components in the mixture are conventionally called solvent and solute , respectively. The vanishing limit of solute concentration, or infinite dilution, is of particular interest because it purely reflects the nature of solute-solvent interactions. The word solvation is most commonly used for describing properties concerning solute-solvent interactions at the infinite dilution limit. Here, we provide a brief outline of the way to obtain solvation properties, solvation structure and thermodynamics, from the RISM theory described in the previous sections [3]. It is straightforward to generalize the RISM equation to a mixture of different molecular species. The equation for a mixture can be written in a matrix notation as... 

However, if the system contains more than one component, the situation is no longer so simple. For illustration, we shall considera binary stem consisting of ni moles of component 1 and n2 moles of component 2. Protein solutions usually contain at least three components (water, protein, and salt) and the equations are easily extended to three-component systems. The volume of a binary solution at fixed temperature and pressure is... 

Most chemical engmeermg systems contain more than one component. In contrast to the total mass, the components or species are not always conserved they may be generated or consumed due to chemical reactions. In this case, the net generation rate within the system must be quantified by reaction rate equations. 

A number of recent studies consider more complex systems, such as freezing vesicles [246] (freezing can be induced by reducing the tether length) or mixed membranes which contain more than one component [247,248]. The possibility that a membrane may break up and form pores has also been considered [249]. 

In your laboratory work you will deal mostly with liquid solutions. Liquid solutions can be made by mixing two liquids (for example, alcohol and water), by dissolving a gas in a liquid (for example, carbon dioxide and water), or by dissolving a solid in a liquid (for example, sugar and water). The result is a homogeneous system containing more than one substance—a solution. In such a liquid, each component is diluted by the other component. In salt water, the salt... 

Steam distillation is a process whereby organic liquids may be separated at temperatures sufficiently low to prevent their thermal decomposition or whereby azeotropes may be broken. Fats or perfume production are examples of applications of this technique. The vapour-liquid equilibria of the three-phase system is simplified by the usual assumption of complete immiscibility of the liquid phases and the validity of the Raoult and Dalton laws. Systems containing more than one volatile component are characterised by complex dynamics (e.g., boiling point is not constant). 

Having considered single component systems, multicomponent systems need to be addressed now. If a closed system contains more than one phase, the equilibrium condition can be written as ... 

When the catalyst contains more than one component, selective gas chemisorption methods are normally used for analysing the surface area associated with a particular component. In this procedure, a gas (H2 or CO for Group VIII metals) is adsorbed on only the component of interest. The method is also particularly useful for studying the dispersion state and surface areas in highly dispersed metallic systems. 

The setting up of the constitutive relation for a binary system is a relatively easy task because, as pointed out earlier, there is only one independent diffusion flux, only one independent composition gradient (driving force) and, therefore, only one independent constant of proportionality (diffusion coefficient). The situation gets quite a bit more complicated when we turn our attention to systems containing more than two components. The simplest multicomponent mixture is one containing three components, a ternary mixture. In a three component mixture the molecules of species 1 collide, not only with the molecules of species 2, but also with the molecules of species 3. The result is that species 1 transfers momentum to species 2 in 1-2 collisions and to species 3 in 1-3 collisions as well. We already know how much momentum is transferred in the 1-2 collisions and all we have to do to complete the force-momentum balance is to add on a term for the transfer of momentum in the 1-3 collisions. Thus,... 

In most cases, little or no difficulty will be experienced in deciding as to the number of the components, if the rules given on pp. 8 and 9 are borne in mind. If the composition of all the phases, each regarded as a whole, is the same, the system is to be regarded as of the first order, or a one-component system if the composition of the different phases varies, the system must contain more than one component. If, in order to express the composition of all the phases present when the system is in equilibrium, two of the constituents participating in the equilibrium are necessary and sufficient, the system is one of two components. Which two of the possible substances are to be regarded as components will, however, be to a certain extent a matter of arbitrary choice. 

In practical experiments, it is hard to obtain a perfect semi-circle. More often two semi-circles are obtained, meaning an electrochemical system contains more than one RC circuit, corresponding to a more complex electrolytic system. Moreover, when the electrochemical system contains a component which is under diffusion control, an oblique line with a slope of -1/2 appears on Niquist s plot and the equivalent circuit is modified adding a diffusion component, W, known as Warburg impedance (Figure 10.11). 

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