The Concept of Activity

For this reaction neither K nor Kp has units, and K is equal to Kp. Because there are identical powers in the numerator and denominator, the units cancel. For equilibrium expressions in which the powers in the numerator and denominator are not the same, the equilibrium constants will have (apparent) units and K will not equal Kp. 

Note that in the above discussion we used the term apparent units when referring to equilibrium constants. This term was used because the theoretical foundation for the concept of equilibrium based on thermodynamics includes a reference state for each substance, which always causes the units of concentration or pressure to cancel. We will explore this situation thoroughly in Chapter 10, but we will introduce this concept in Section 6.4. 

As we will see in Chapter 10, the true equilibrium constant expression does not simply involve the observed equilibrium pressure or the concentration for a substance but involves the ratio of the equilibrium pressure (or concentration) for a given substance to a reference pressure (or concentration) for that substance. This ratio is defined as the activity of the substance, which in terms of pressures is defined as 

In 1982 the International Union of Pure and Applied Chemists (IUPAC) set the standard pressure as 1 bar (exactly). Both conventions are now used, although most thermodynamic data are now referenced to l bar instead of 1 atm. 

Using the concept of activities, the equilibrium expression for the reaction 

For many real solutions the equation - /if ( ) 4- RTlnXi (Section 6.1) does not hold for the solvent, and the expression which corresponds to Henry s Law (Section 6.10), pt = f(l) + R7Tnx( also fails to hold for the solute. In such circumstances it is convenient to introduce the concept of activity. We may write 

This equation defines the activity af of component i in terms of its chemical potential in the solution and in the standard state. This activity may be regarded as the effective concentration of component i relative to its standard state. (Activity is defined only in so far as the standard state to which it refers is also specified.) The effective concentration may, in a real solution, differ greatly from the true concentration as a result of the interactions between the molecules. The extent to which this is so is measured by the activity coefficient 7c 

This can be illustrated by consideration of a real liquid mixture. 

This is in keeping with our definition of activity as the effective concentration. In the example we have taken Pt P, (ideal). The concentration of i in the vapour phase is less than would have been expected for a solution of such a concentration on the basis of ideal behaviour, and at x(. The effective concentration is less than the real concentration and the activity coefficient Vi( is less than one. (In an ideal solution a = x and yt = 1.) We can think of this result, yf 1, as indicating that the component under investigation finds the solution a more congenial environment than that of an ideal solution under the same conditions. Thus it shows less tendency to escape into the vapour phase. 

Earlier we considered a system in which the components deviated positively from Raoult s Law, and had vapour pressures greater than the law would predict. In such a solution at xh and y( 1. For most normal liquid mixtures in which the components do not interact specifically (as in hydrogen-bond formation) this is the most common behaviour. The components show a greater tendency to escape into the vapour phase than in the corresponding ideal solution. In extreme cases the dislike of the components for each other in the solution may cause the solution to separate into two phases at sufficiently low temperatures. The phenol-water system deviates 

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Polarization can be divided into activation polarization and concentration polarization , Activation polarization is an electrochemical reaction that is controlled by the reaction occurring on the metal-electrolyte interface. Figure 4-418 illustrates the concept of activation polarization where hydrogen is being reduced over a zinc surface. Hydrogen ions are adsorbed on the metal surface they pick up electrons from the metal and are reduced to atoms. The atoms combine to... 

It is important to realise that whilst complete dissociation occurs with strong electrolytes in aqueous solution, this does not mean that the effective concentrations of the ions are identical with their molar concentrations in any solution of the electrolyte if this were the case the variation of the osmotic properties of the solution with dilution could not be accounted for. The variation of colligative, e.g. osmotic, properties with dilution is ascribed to changes in the activity of the ions these are dependent upon the electrical forces between the ions. Expressions for the variations of the activity or of related quantities, applicable to dilute solutions, have also been deduced by the Debye-Hiickel theory. Further consideration of the concept of activity follows in Section 2.5. 

On his return to Princeton after the war, Hugh Taylor organized catalytic research at the Frick Chemical Laboratory. He applied high vacuum technique, liquid air cryoscopy to the study of adsorptive characteristics of catalysts, correlating rates of catalytic reactions and rates of adsorption. He introduced the concept of activated adsorption and defended it against all comers. ... 

His researches and those of his pupils led to his formulation in the twenties of the concept of active catalytic centers and the heterogeneity of catalytic and adsorptive surfaces. His catalytic studies were supplemented by researches carried out simultaneously on kinetics of homogeneous gas reactions and photochemistry. The thirties saw Hugh Taylor utilizing more and more of the techniques developed by physicists. Thermal conductivity for ortho-para hydrogen analysis resulted in his use of these species for surface characterization. The discovery of deuterium prompted him to set up production of this isotope by electrolysis on a large scale of several cubic centimeters. This gave him and others a supply of this valuable tracer for catalytic studies. For analysis he invoked not only thermal conductivity, but infrared spectroscopy and mass spectrometry. To ex-... 

Of great importance for the development of solution theory was the work of Gilbert N. Lewis, who introduced the concept of activity in thermodynamics (1907) and in this way greatly eased the analysis of phenomena in nonideal solutions. Substantial information on solution structure was also gathered when the conductivity and activity coefficients (Section 7.3) were analyzed as functions of solution concentration. 

Here, the a s refer to the activities in the chosen arbitrary state. The concept of activity is presented separately in a later section. For the present, the activity of a species in a system may just be considered to be a function of its concentration in the system, and when the species is in a pure form (or in its standard state), its activity is taken to be unity. The activities ac, aD, aA, aB given above correspond to the actual conditions of the reaction, and these may or may not correspond to the state of equilibrium. Two special situations can be considered. In the first, the arbitrary states are taken to correspond to those for the system at equilibrium. Q would then become identical to the equilibrium constant K and, according to the Van t Hoff isotherm, AG would then be zero. In the second situation, all the reactants and the products are considered to be present as pure species or in their standard states, and aA, aB, ac, and aD are all equal to 1. Then (7=1 and the free energy change is given by... 

Consideration of a variety of other systems leads to the conclusion that very rarely does the collision theory predict rate( constants that will be comparable in magnitude to experimental values. Although it is not adequate for predictions of reaction rate constants, it nonetheless provides a convenient physical picture of the reaction act and a useful interpretation of the concept of activation energy. The major short-... 

The concept of activity was introduced in the early 20th century by one of the giants of American chemistry, G. N. Lewis. 

The concept of activity is extremely important in soil. Protons or hydro-nium ions attracted to exchange sites or other components in the system will not be measured as part of the solution composition. 

So far, we have defined the Nemst equation in terms of activities (a) rather than concentrations (c). This representation is rather false, so we need to remedy the situation. The concept of activity was introduced because the Nemst equation cannot adequately describe the relationship between an electrode potential Eq.r... 

More than anything else it was the curious meta-activation found in the photosubstitution of nitrophenyl esters and ethers by various nucleophiles that stimulated closer investigation of this class of reactions (Section 1). In order to avoid misunderstanding, it should be stressed that the concept of activation at the meta-position vwth respect to the nitro-group does not exclude reactions taking place at other positions in the excited molecule. It merely means that, other things being equal, substitution is preferred at the meta-position over the ortho- and para-positions. 

In theory, one can use statistical thermod3mamics to calculate the partition functions of all the species from first principles, AS, AH, and hence k. For simple systems, the calculation results are in good agreement with experimental data (e.g.. Chapter 3 in Laidler, 1987). For complicated geological systems, however, it is not possible to calculate k from first principles, but the concept of activated complexes is very useful for a microscopic understanding of the reaction... 

Relative humidity and temperature are two variables which have influence on the chromatographic behavior of the solutes [2] but which can not always be set at desired levels. The relative humidity is expected to have a large influence, while temperature has a small influence. In reference [2] it is stated that a temperature change of 5 degrees seldom exceeds reproducibility limits of the standard working techniques. It is most feasible to discuss the effect of variation in relative humidity and temperature in terms of activity. Therefore in the following paragraphs first the concept of activity will be introduced. Then the concept will be applied in a short examination of the effect of relative humidity and temperature on the retention. 

The concept of activated adsorption explains why the heat of adsorption is often small at low temperatures and large at higher temperatures. This is because at low temperature the heat is due to physical adsorption... 

This important piece of work had four main facets first, it showed that structure could be quantitatively related to biological activity secondly, it introduced the concept of activity being described by more than one parameter thirdly, the two-stage variation of activity wim the water-octanol partition coefficioit, denot by logP, was quantified using a quadratic equation and fourthly, it introduced the concept of the... 

We understand very well that any book inavoidably reflects authors interests and scientific taste this fact is, first of all, usually seen in the selection of material which in our case is very plentiful and diverse. For instance, Chapter 2 gives examples of different general approaches used in chemical kinetics (macroscopic, mesoscopic and microscopic) and numerous methods for solving particular problems. We focus here on the microscopic approach based on the concept of active particles (structure elements, reactants, defects) whose spatial redistribution arises due to their diffusion affected by... 

Although it is not really needed at this point, we introduce the concept of activity coefficients, which are very common for chemical engineers, but much less for theoretical and computational chemists. In the standard definition, the activity coefficients make reference to the pure liquid compound, i, at the same temperature and pressure. Hence, the activity coefficient yt of species i is defined by... 

Chemical kinetics had originated in the classical studies by Van t Hoff and Arrhenius in the 1880s. Then the physical sense of reaction orders was interpreted and the concept of activation energy was suggested. The main ideas in Van t Hoff s book [4] are still appropriate. 

Explain the concept of activity-based budgeting and the benefits it brings to the budgeting process. 

C) which he derived from the ionic product of water (Kw = 10 14 mol x dm 3). Some years later, Lewis introduced the concept of activity, and in 1923 Debye and Hiickel published their theory for strong electrolyte solutions. On the basis of this knowledge, Soerensen and Linderstroem-Lang [2] suggested a new pH definition in terms of the relative activity of hydrogen ions in solution ... 

The question as to why bromobenzene gives rise to more ester sulfate than does bromophenol is not fully answered by the above reactions.127 The phenomenon can be explained by the concept of activation during... 

Vol kenshtem 294) treated chemisorption phenomena on solids with surfaces that are provided with such sorts of microdefects 295). These microdefects possess a mobility which is characterized by an energy of activation. They have the ability of interacting with one another and they give rise to new microdefects when chemisorption takes place on them. Instead of the concept of active centra, therefore, which are bound... 

Of central importance in the chemistry of nitrogen fixation is the concept of activation (4f). This involves a transfer of electronic charge from the transition metal to the coordinated N2 by metal — ligand back donation, making this very inert molecule susceptible... 

The concept of activity cliffs and the landscape paradigm have also been applied to R-groups, where an R-cliff occurs when a pair of compounds differs in a single R-group. This is clearly a specialization of the activity cliff concept, placing this type of analysis in the context of analogue series derived via R-group decompositions (43, 44). 

In the context of RTILs the criterion (3) raises considerable problems since the concept of activity and activity coefficients of ions is largely unexplored in such media. Accordingly, validation of the applicability of the Nernst equation in such media is a non-simple exercise, given that RTILs are likely to exhibit gross non-ideality. Rather, electrochemical measurements based on otherwise validated reference electrodes, may likely in the future provide a methodology for the study of RTIL non-ideality. 

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