Relation Between Activity and Concentration

Although a full discussion of the concept of activity is given in Chapter 3, some remarks about the relation between activity and concentration are relevant now. In general, the activity of a substance in solution may be related to its concentration. Thus, 

In extremely dilute solutions of most solutes, the value of each y, and therefore, the activity coefficient quotient, approaches unity and K = K. Hence, for solutes in very dilute solutions, we may write Equation 2-9 as follows  

In applying equilibrium calculations to problems of chemical composition, that is, what species are present and in what concentrations, it is vital to be clear about the respective roles of the concentration of a species, [A], and its activity, a. For example, let us take 0.01 M HCl. In this solution of 

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Use of equation 1.5 for the relation between activity and concentration makes it possible to express these activities as concentrations. Except for high ionic strength solutions such as brines (ionic strength > 1), it is usually sufficient to approximate the activity of water as unity, thus eliminating the an2o term. The resulting equations for concentrations are ... 

The advantage of this standard state is that it provides a very simple relat between activity and concentration for cases in which Henry s law is at Ic approximately valid. Its range does not commonly extend to a concentratioii 1 m. In the rare case where it does, the standard state is a real state of the soh This standard state is useful only where AG data are available for the ideal the sense of Henry s law) 1-molal standard state, for otherwise the equilibril constant cannot be evaluated by Eq. (15.14). 

To enable the application of the law of mass action to actual problems the activities appearing in equation (V-14) have to be substituted by directly measurable quantities (such as pressures or concentrations). To achieve this we use different suitable standard states according to the character of the process in order to obtain a simple relation between activity and pressure (or concentration). In the following chapter the selection of the most suitable standard states in individual cases will be discussed. 

Most liquid solutions, also called liquid mixtures, are non-ideal. This follows from the fact that the components are in intimate contact with one another, and that the forces between the various species are usually not the same. As a result, the physical properties of the solution, for example, the vapor pressure of a given component, are usually not simply related to its concentration. This non-ideality leads to the concept of the activity of a solution component. As far as the analytical chemist is concerned, only concentration is ultimately of interest. Thus, if an analysis is based on the measurement of a physical property which in turn depends on the activity of a component, it is very important that the relationship between activity and concentration be understood for the system in question. 

I showed that equation (1 -8) is a correct description of inhibition by measuring the ratio of inactive to active carbonic anhydrase at several concentrations of thiocyanate (Fig. 1-18, left) and the relation between active and inactive concentrations of carbonic anhydrase at several total concentrations of the enzyme in the presence of a constant concentration of thiocyanate (Fig. 1-18, center). 

The overall strategy for finding the relation between K and Kc is to replace the partial pressures that appear in K by the molar concentrations and thereby generate Kc. For this calculation, we write activities as Pj/P° and [J]/c° and track the units by keeping P° and c° in our expressions. 

In this expression, the square brackets refer to the activity of the component although it is more convenient to use its concentration. This approximation is generally satisfactory, except at very high concentrations, and is particularly suitable for analytical use. Where it is necessary to distinguish between the constant obtained using concentrations and the true thermodynamic equilibrium constant Ka the former may be termed the equilibrium quotient and assigned the symbol Q. The exact relation between Ke and Q has been the subject of much investigation and speculation. In this... 

The theory of equilibrium is treated on the basis of thermodynamics considering only the initial and final states. Time or intermediate states have no concern. However, there is a close relationship between the theory of rates and the theory of equilibria, in spite of there being no general relation between equilibrium and rate of reaction. A good approximation of equilibrium can be regarded between the reactants and activated state and the concentration of activated complex can, therefore, be calculated by ordinary equilibrium theory and probability of decomposition of activated complex and hence the rate of reaction can be known. 

Fig. 2. Example of rough activity landscape. This figure shows the activity landscape for a series of related antibacterial compounds plotted in using the 2D BCUT descriptors to arrange the compounds. (A) Shows how the compounds are arrayed in a 2D representation of the chemistry space with the height of the marker being proportional to the minimum inhibitor concentration of the compounds [the smaller the minimum inhibitory concentration (MIC) the more potent the compound]. (B) This second panel presents the upper figure as a 2D figure to enhance the sharp cutoff between active and inactive compounds, emphasizing the point that activity landscapes are rarely smooth continuous functions.

The nonlinear relation between k2 and catalyst concentration can be understood by assuming a mechanism with fast dissociation of the catalyst into a catalytically active species. 

It is appropriate at this point to discuss the "apparent" pH, which results from the sad fact that electrodes do not truly measure hydrogen ion activity. Influences such as the surface chemistry of the glass electrode and liquid junction potential between the reference electrode filling solution and seawater contribute to this complexity (see for example Bates, 1973). Also, commonly used NBS buffer standards have a much lower ionic strength than seawater, which further complicates the problem. One way in which this last problem has been attacked is to make up buffered artificial seawater solutions and very carefully determine the relation between measurements and actual hydrogen ion activities or concentrations. The most widely accepted approach is based on the work of Hansson (1973). pH values measured in seawater on his scale are generally close to 0.15 pH units lower than those based on NBS standards. These two different pH scales also demand their own sets of apparent constants. It is now clear that for very precise work in seawater the Hansson approach is best. 

Up to now it has been assumed that the concentration of the bulk of the solution remains practically constant with increasing current density. Actually the concentration of the active substance drops during the course of every electrolytical reduction and oxidation. It is, therefore, advantageous to study the electrochemical process at a constant current density and to follow the relation between potentials and current efficiencies and quantities of eleotric-... 

Interaction seen only with phenytoin and mediated by displacement from plasma protein binding sites no reduction in methotrexate activity is expected the relation between total methotrexate concentration and effect can be altered. 

Plasma protein binding interactions are usually clinically unimportant, but they should be recognized, because they alter the relation between serum drug concentration and the clinical response if displacement occurs, therapeutic and toxic effects are reached at a total drug concentration lower than usual. For example, valproic acid and salicylate displace phenytoin from plasma proteins this usually results in a fall in total phenytoin concentration without any change in the concentration of unbound (pharmacologically active) phenytoin. 

An electron transfer reaction, Eq. (1), is characterized thermodynamically by the standard potential E°, that is, the value of E at which the activities of the oxidized form A and the reduced form B of the redox couple are the same. Thus, the second term in the Nernst equation, Eq. (2), cancels. Here, R is the molar gas constant (8.314 JK mol ), T is the temperature (K), n is the number of electrons, and F is Faraday s constant (96,485 C). Parentheses are used for activities, brackets for concentrations, and fA and fe are the activity coefficients. However, what may be measured directly is the formal potential E° defined in Eq. (3). It follows that the relation between E and E° is given by Eq. (4). In this chapter we assume that activity coefficients are unity and therefore that E° = E°... 

The results of enzymatic determinations of ceruloplasmin are often expressed in arbitrary units, and the values judged in the light of a series of results obtained in normal subjects by the same method. Expression of the enzyme activity in milligrams of ceruloplasmin per unit volume of serum is also possible. The relation between oxidase activity and the amount of ceruloplasmin in serum can be determined by measuring in parallel samples of sera both the oxidase activity and the change of optical density at 610 mix before and after the addition of ascorbic acid or cyanide. On the basis of the known absorbancy index, the ceruloplasmin concentration can be calculated (see Section 2.2.1) and the relation between it and the enzyme activity determined. Alternatively, purified human ceruloplasmin can be used for standardization of the enzymatic method. The ceruloplasmin content of the purified preparation can be determined colorimetrically or, in the case of a highly purified preparation, by nitrogen analysis. Predetermined increments of ceruloplasmin can then be added to aliquots of a selected serum. It is convenient to select a serum with relatively low ceruloplasmin level to start with. Serum of a patient with Wilson s disease, some of whom have no measurable amount of enzyme activity, would be ideal for the purpose however, Walshe (W5) has recently found an inhibitor in these sera. 

Rea HM, Thomson CD, Campbell DR, et al. 1979. Relation between erythrocyte selenium concentrations and glutathione peroxidase (EC 1.11.1.9) activities of New Zealand residents and visitors to New Zealand. Br J Nutr 42 201-208. 

Relation (7.83) holds only for the activity coefficient as defined in equation (7.82), i.e., based on the number density scale. However, it is quite a simple matter to use any other activity coefficient to extract the same information. Let Cs be any other concentration units (e.g., molality, mole fraction, etc). We write the general conversion relation between Cs and ps symbolically as... 

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