Mass action, principle

Most gases dissolve monatomically in liquid metals. For example, the solution reactions may be written as H2 -> 2H, N2 —> 2N, O2 —> 20, where the underlining signifies the element is in solution. Sievert s law for diatomic gases is an application of the mass action principle. It states that the solubility is proportional to the square root of the partial pressure of the gas. For example,... 

Thus, for a toxicant (ligand) interacting with a single (or homogeneous population) of receptor(s), mass-action principles require ... 

The relevant kinetic model for competition experiments with a radiolabeled drug [D] and an unlabeled competitor [I] is shown in the two equations in (19.15). When both sets of reactions have proceeded to equilibrium, the net rate of formation of both (DR) and (IR) are zero, and the following Eq. (19.16) can be derived from mass-action principles. 

The basic principles of ion exchange have been discussed by Walton [78]. However, this discussion was mainly limited to the case of small inorganic ions. For the separation of biomolecules, e stoichiometric displacement model (SDM, next subsection) is of particular interest. This model is based on the assumption that ion exchange is the only mechanism of retention of the components studied and that the ion-exchange process can be modeled as a stoichiometric "reaction" described by the mass action principle. 

Although ninhydrin is typically used as an indicator for terminal amines, it has been used for the protection of A-terminal cysteine peptides. The derivative is readily formed under aqueous conditions at neutral to acidic pH. It is cleaved by reaction with an excess of cysteine using the mass action principle, 3-mercaptopropiosulfonic acid at pH 7.7, or Zn in 10% aqueous TFA. ... 

Because equation 10.4 describes an equilibrium state, it stands to reason that it should be possible to derive the equation from arguments that are not based on reaction kinetics. In fact, this is the case, and a more general derivation of equation 10.4 from statistical mechanics, or more simply from the mass-action principle, is possible. 

Graham s, 159, 722 Hess s, 244 Hooke s, 92 ideal gas, 147 integrated rate, 540 Kirchhoff s, 256 Newton s second, 10 of mass action, 360 of radioactive decay, 712 periodic, 38 Raoult s, 330 rate, 535, 537 second, 267 Stefan-Boltzmann, 9 third, 276 Wien s, 9 LCAO-MO, 117 Le Chatelier, H., 377 Le Chatelier s principle, 377, 468... 

For reversible reactions one normally assumes that the observed rate can be expressed as a difference of two terms, one pertaining to the forward reaction and the other to the reverse reaction. Thermodynamics does not require that the rate expression be restricted to two terms or that one associate individual terms with intrinsic rates for forward and reverse reactions. This section is devoted to a discussion of the limitations that thermodynamics places on reaction rate expressions. The analysis is based on the idea that at equilibrium the net rate of reaction becomes zero, a concept that dates back to the historic studies of Guldberg and Waage (2) on the law of mass action. We will consider only cases where the net rate expression consists of two terms, one for the forward direction and one for the reverse direction. Cases where the net rate expression consists of a summation of several terms are usually viewed as corresponding to reactions with two or more parallel paths linking reactants and products. One may associate a pair of terms with each parallel path and use the technique outlined below to determine the thermodynamic restrictions on the form of the concentration dependence within each pair. This type of analysis is based on the principle of detailed balancing discussed in Section 4.1.5.4. 

The principle of mass action explains the relationship between concentration and complexation. The abundance of ion pairs in aqueous solution is controlled by... 

Words that can be used as topics in essays 5% rale buffer common ion effect equilibrium expression equivalence point Henderson-Hasselbalch equation heterogeneous equilibria homogeneous equilibria indicator ion product, P Ka Kb Kc Keq KP Ksp Kw law of mass action Le Chatelier s principle limiting reactant method of successive approximation net ionic equation percent dissociation pH P Ka P Kb pOH reaction quotient, Q reciprocal rule rule of multiple equilibria solubility spectator ions strong acid strong base van t Hoff equation weak acid weak base... 

Similar to generalized mass-action models, lin-log kinetics provide a concise description of biochemical networks and are amenable to an analytic solution, albeit without sacrificing the interpretability of parameters. Note that lin-log kinetics are already written in term of a reference state v° and S°. To obtain an approximate kinetic model, it is thus sometimes suggested to choose the reference elasticities according to simple heuristic principles [85, 89]. For example, Visser et al. [85] report acceptable result also for the power-law formalism when setting the elasticities (kinetic orders) equal to the stoichiometric coefficients and fitting the values for allosteric effectors to experimental data. 

The kinetic behavior of the reductive dissolution mechanisms given in Figure 2 can be found by applying the Principle of Mass Action to the elementary reaction steps. The rate expression for precursor complex formation via an inner-sphere mechanism is given by ... 

The underlying principles and theories of gravimetric analysis are as stated below (/) Law of mass action and reversible reactions,... 

From the chemist s point of view as a user, these simulation techniques require him to provide computer code for the time derivative of each chemical species in the mechanism. According to the principle of mass-action, the derivative of the r-th species concentration in a mechanism of M reactions involving P chemical species is given by... 

TNC. 11. I. Prigogine, Steady states and variational principles, in The Law of Mass Action, Universitetsforlaget, Oslo, 1964, pp. 95-116. 

Many different types of reversible reactions exist in chemistry, and for each of these an equilibrium constant can be defined. The basic principles of this chapter apply to all equilibrium constants. The different types of equilibrium are generally denoted using an appropriate subscript. The equilibrium constant for general solution reactions is signified as or K, where the c indicates equilibrium concentrations are used in the law of mass action. When reactions involve gases, partial pressures are often used instead of concentrations, and the equilibrium constant is reported as (p indicates that the constant is based on partial pressures). and are used for equilibria associated with acids and bases, respectively. The equilibrium of water with the hydrogen and hydroxide ions is expressed as K. The equilibrium constant used with the solubility of ionic compounds is K p. Several of these different K expres-... 

It has been shown in Section 1.3.7 that in semiconductors or insulators the lattice defects and electronic defects (electrons and holes), derived from non-stoichiometry, can be regarded as chemical species, and that the creation of non-stoichiometry can be treated as a chemical reaction to which the law of mass action can be applied. This method was demonstrated for Nii O, Zr Cai Oiand Cuz- O in Sections 1.4.5, 1.4.6, and 1.4.9, as typical examples. We shall now introduce a general method based on the above-mentioned principle after Kroger, and then discuss the impurity effect on the electrical properties of PbS as an example. This method is very useful in investigating the relation between non-stoichiometry and electrical properties of semiconductive compounds. 

The forward rate constants are k/ = 1 and kf2 = 1000, the equilibrium constants are K — 0.01 and K2 =, and the reverse rate constants are krt = kjJK and kn = kfr/Ki- The rate constants and species concentrations used here are taken to be unitless. Based on the principles of mass-action kinetics, the transient behavior of the system can be represented in differential-equation form as... 

Based on the principles of mass-action kinetics the transient behavior of the system can be represented in differential-equation form as... 

Specific examples illustrate that similar principles affect the absorption spectra. For example, as we have pointed out above, the neutral form of the C-2 benzyl ester is red in MeOH and orange in methylene chloride. Thus it has the spectrum of the ionized form in the polar, protic solvent and of the nonionized form in the nonpolar solvent methylene chloride [248]. The tributyl ammonium salt of the C-2 octyl ester is soluble in solvents ranging from ethanol-water to toluene. Its spectrum in an essentially nonionizing solvent such as toluene is that of the ionized xanthene [249], The spectrum of the pyrillium salt in ethanol is concentration dependent. In dilute solution the compound is totally ionized and is red, whereas in concentrated solution the compound is not fully ionized and the orange form predominates, as predicted by the law of mass action. 

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