Mass action indirect

When a small amount b of a foreign substance is dissolved in a liquid A, the chemical potential fi of this liquid will decrease at cmistant p and T. In fact, it decreases in proportion to the mole fraction Xb =Wb/(wa + Wb) of the foreign 

In order to describe the dependency of the chemical potential p of any substance upon composition (concentration c, partial pressure p, mole fraction x, etc.), chemists generally separate the potential p into two parts a basic component p independent of the composition and a residual that is dependent upon it (compare Sect. 6.2). In the sense explained here, p represents a particular basic value. Only when this needs to be emphasized will we use the notation / otherwise we will stay with p.  

Equation (12.2) for the lowering of potential is valid as long as the foreign substance B or foreign substances F (there can be several different ones, B, C, D,. .., since their kind does not matter) dissolve molecularly but do not associate or dissociate, meaning they may not decompose into smaller components or form aggregates of several molecules. This remarkable relation, which is valid for aU 

Note that this new equation holds only in the limit of a small amount of a foreign substance being added to the solvent. Admittedly, this change of potential is small. However, because substance A is highly concentrated, it can have significant effects, which we will look into in the next sections. 

For the mathematically inteiested In order to derive Eq. (12.2), we will refer back to the cross relation discussed in Sect. 9.3 known as n n coupling. When one substance tries to displace (or favor) another one, this happens reciprocally and with equal strength. The corresponding displacement coefficients are equal as can easily be shown by applying the flip rule (main equation dW = —pdV + TdS + ji drif + p dn )  

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On the right, all curves show the same slope RT in the vicinity of x= 1. On the left, they all approach negative infinity. The similar initial part of the curves on the right side is a consequence of indirect mass action which is the same for all substances (see Sect. 12.3). The similarities and differences for varying mixtures become even clearer when plotted logarithmically (Fig. 13.2). 

When we take the derivative of this function with respect to x at constant T, we obtain the value of RT at x = 1 as we should expect because of the indirect mass action ... 

This is the second of the two questions identified at the start of Section 1.2, where it was noted that the earliest pharmacologists had no choice but to use indirect methods in their attempts to account for the relationship between the concentration of a drug and the tissue response that it elicits. In the absence at that time of any means of obtaining direct evidence on the point, A. V. Hill and A. J. Clark explored the consequences of assuming (1) that the law of mass action applies, so that Eq. (1.2), derived above, holds and (2) that the response of the tissue is linearly related to receptor occupancy. Clark went further and made the tentative assumption that the relationship might be one of direct proportionality (though he was well aware that this was almost certainly an oversimplification, as we now know it usually is). 

In other words, for the forward reaction the rate at which an individual A molecule transforms into a B molecule in the reaction A B does not depend on NA or [A], This assumption is valid if each molecule of A does not interact with other A molecules (even indirectly) in transforming from A to B. Similarly for the reverse reaction, if j does not depend on [B] the reverse kinetics are governed by the law of mass action. (The mass-action assumption is not valid for the overall reaction, for example, if the reaction is catalyzed by an enzyme and the number of sites available for interaction with the enzyme depends on the total number of A and B molecules in the system competing for the enzyme. We shall see that when an enzyme catalyzes a reaction A = B, the overall reaction is typically modeled by a number of subreactions, each of which is governed by mass action.)... 

Therefore, each realisable reaction is comparable to a kind of scale which allows the comparison of chemical potentials or their sums, respectively. But the measurement is often impossible due to any inhibitions, i.e., the scale is jammed. If there is a decline in potential from the left to the right side, that only means that the process can proceed in this direction in principle however, it does not mean that the process will actually run. Therefore, a potential drop is a necessary but not sufficient condition for the reaction considered. The problem of inhibitions can be overcome if appropriate catalysts are available or indirect methods including chemical (using the mass action law), calorimetric, electrochemical and others can be used. Because we are interested in a first knowledge of the chemical potential, we assume for the moment that all these difficulties have been overcome and consider the values as given, just as we would consult a table when we are interested in the mass density or the electric conductivity of a substance. ... 

In addition to the direct methods for determining chemical drives and potentials, respectively, there are numerous indirect methods that are more sophisticated and therefore more difficult to grasp, yet more universally applicable. These include chemical (using the mass action law) (Sect. 6.4), calorimetric (Sect. 8.8), electrochemical (Sect. 23.2), spectroscopic, quanmm statistical, and other methods to which we owe almost all of the values that are available to us today. Just as every relatively easily measured property of a physical entity that depends upon temperature (such as its length, volume, electrical resistance, etc.) can be used to measure T, every property (every physical quantity) which depends upon fi can be used to deduce fi values. 

Law of Diffusion The flow of matter in a homogeneous environment at low concentration Cg represents an important special case. Here, the concentration, and indirectly the position dependency of the chemical potential, can be expressed by the mass action equation ... 

A number of chemicals with demonstrable suppression of immune function produce this action via indirect effects. By and large, the approach that has been most frequently used to support an indirect mechanism of action is to show immune suppression after in vivo exposure but no immune suppression after in vitro exposure to relevant concentrations. One of the most often cited mechanisms for an indirect action is centered around the limited metabolic capabilities of immunocompetent cells and tissues. A number of chemicals have caused immune suppression when administered to animals but were essentially devoid of any potency when added directly to suspensions of lymphocytes and macrophages. Many of these chemicals are capable of being metabolized to reactive metabolites, including dime-thylnitrosamine, aflatoxin Bi, and carbon tetrachloride. Interestingly, a similar profile of activity (i.e., suppression after in vivo exposure but no activity after in vitro exposure) has been demonstrated with the potent immunosuppressive drug cyclophosphamide. With the exception of the PAHs, few chemicals have been demonstrated to be metabolized when added directly to immunocompetent cells in culture. A primary role for a reactive intermediate in the immune suppression by dimethylnitrosamine, aflatoxin Bi, carbon tetrachloride, and cyclophosphamide has been confirmed in studies in which these xenobiotics were incubated with suspensions of immunocompetent cells in the presence of metabolic activation systems (MASs). Examples of MASs include primary hepatocytes, liver microsomes, and liver homogenates. In most cases, confirmation of a primary role for a reactive metabolite has been provided by in vivo studies in which the metabolic capability was either enhanced or suppressed by the administration of an enzyme inducer or a metabolic inhibitor, respectively. 

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