Law of mass action equation

From the above scheme we may easily write down the law of mass action equations for the rates of change of the concentrations p, a, and b ... 

The law of mass action (Equation 15-2) is always stated as applying to a given temperature, and it appears not to have temperature involved in its statement. Yet the rates of chemical reaction invariably increase markedly with increase in temperature. Because concentrations will be negligibly affected by temperature, the temperature-sensitive factor in the law of mass action must be the rate constant, 1. As a good approximation, we say that k is proportional to the fraction of molecules (or collisions) that have the required enthalpy of activation ... 

Mutarotation has been shown to be a first-order reaction, the velocity constant being independent of reaction time and concentration of reactants. The rate of mutarotation increases 2.8 times with a 10°C rise in temperature. By applying the law of mass action, equations have been developed to measure the rate of the reversible reaction between the a and (3 forms of lactose. If a dilute lactose solution at constant temperature contain a moles of a and b moles of /3, then the amount of (3 formed (x) per unit of time is... 

At equilibrium the number of holes may then be computed from the law of mass action (equation 8), because both electrons and holes are always present in a semiconductor. The Fermi level can be determined from equation 4. 

When a heterogeneous reaction is considered, the partial pressures included in the "Law of Mass Action," Equation (1), are only those for the gaseous reactants. For example, when silicon is deposited on a surface due to silane pyrolysis, we have... 

To use equilibrium constants, we must express them in terms of the reactant and product concentrations. Our only guide is the law of mass action [Equation (14.2)], which is the general formula for finding equilibrium concentrations. However, because the concentrations of the reactants and products can be expressed in different units and because the reacting species are not always in the same phase, there may be more than one way to express the equilibrium constant for the same reaction. To begin with, we will consider reactions in which the reactants and products are in the same phase. 

Thermodynamic equilibrium in a system with a binary solid-solution Bx.xCxA can be defined by the law-of-mass-action equations ... 

We can write a law of mass action equation relating the fractional molar concentration of the vacancy pairs. At equilibrium... 

This equation emphasizes that four sites are required on each sublattice. We can write the law of mass action equation for the precipitation reaction... 

It is assumed in the above and following discussions that the activities occurring in the law of mass action equation can be replaced by molar concentrations. The assumption is exact when a polymer melt is polymerized to a polymer soluble in the monomer without interaction between the components, that is, when the activities are equal to unity. Nonideal behavior is treated in Section 16.2.5. 

Strategy The concentrations given are equilibrium concentrations. They have units of mol/L, so we can calculate the equilibrium constant K using the law of mass action [Equation (14.2)]. 

The law of mass action (equation [11.3]) shows that the electron holes are in the minority if the electrons are in the majority. This is why their contribution has not been considered in the previous development. Some dopants or defects are associated with levels close to the valence band and are susceptible to acquire electrons, creating electron holes in the valence band. These are referred to as acceptor levels. If the electron holes are in the majority, we refer to them as p-type semi-conductors. 

The law of mass action, the laws of kinetics, and the laws of distillation all operate simultaneously in a process of this type. Esterification can occur only when the concentrations of the acid and alcohol are in excess of equiUbrium values otherwise, hydrolysis must occur. The equations governing the rate of the reaction and the variation of the rate constant (as a function of such variables as temperature, catalyst strength, and proportion of reactants) describe the kinetics of the Hquid-phase reaction. The usual distillation laws must be modified, since most esterifications are somewhat exothermic and reaction is occurring on each plate. Since these kinetic considerations are superimposed on distillation operations, each plate must be treated separately by successive calculations after the extent of conversion has been deterrnined (see Distillation). 

The two basic laws of kinetics are the law of mass action for the rate of a reac tion and the Arrhenius equation for its dependence on temperature. Both of these are strictly empirical. They depend on the structures of the molecules, but at present the constants of the equations cannot be derived from the structures of reac ting molecules. For a reaction, aA + hE Products, the combined law is... 

Note the rate constant symbolism denoting the forward (fc,) and backward (/c i) steps.] The differential rate equation is written, according to the law of mass action, as... 

According to the law of mass action the differential rate equation is... 

From the law of mass action it is straighforward to show that the concentrations satisfy the following three equations ... 

The subscript i labels the six concentrations and energies defined previously. It is straightforward to show that by minimising G with respect to the c, subject to the three constraints, we recover the three equations for the q predicted by the law of mass action. 

If n is the concentration of defects (cation vacancies or positive holes) at equilibrium, then, applying the law of mass action to equation 1.157... 

In the deduction of the Law of Mass Action it was assumed that the effective concentrations or active masses of the components could be expressed by the stoichiometric concentrations. According to thermodynamics, this is not strictly true. The rigorous equilibrium equation for, say, a binary electrolyte ... 

Applying the Law of Mass Action to this equation, we obtain, for any given temperature ... 

By applying the Law of Mass Action along the lines of Case 1, the following equations are obtained ... 

In these equations the independent variable x is the distance normal to the disk surface. The dependent variables are the velocities, the temperature T, and the species mass fractions Tit. The axial velocity is u, and the radial and circumferential velocities are scaled by the radius as F = vjr and W = wjr. The viscosity and thermal conductivity are given by /x and A. The chemical production rate cOjt is presumed to result from a system of elementary chemical reactions that proceed according to the law of mass action, and Kg is the number of gas-phase species. Equation (10) is not solved for the carrier gas mass fraction, which is determined by ensuring that the mass fractions sum to one. An Arrhenius rate expression is presumed for each of the elementary reaction steps. 

The law of mass action has been successfully applied to many drug dose-response relationships since the early work of Clark. The systematic relation between the dose of a drug and the magnitude of its response is based on three assumptions (1) response is proportional to the level of receptor occupancy (occupancy theory), (2) one drug molecule combines with one receptor site, and (3) a negligible fraction of total drug is combined with the receptors. These assumptions must also apply to Beidler s equation. 

Consideration thus far has been on only balanced reactions which occur in one phase, that is, homogeneous reactions. There are, of course, a great many reactions which occur between substances in different phases, and these are known as heterogeneous reactions. Numerous reversible, heterogeneous reactions are known, and it is pertinent now to bestow consideration on how far the law of mass action can be applied to such cases. The familiar reaction of the decomposition of calcium carbonate thermally - a well-known example of a reversible reaction represented by the equation... 

The rate or the kinetic equations actually result from the law of mass action which states that, at a constant temperature, the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants. In order to elaborate, by way of illustration the reaction between hydrogen and chlorine, represented in the following manner, is considered ... 

A molecule HA of a weak electrolyte is now considered. It is assumed to dissociate in its aqueous solution according to the equation HA =f H+ + AT The application of the law of mass action to the above equation gives... 

When deriving material balance equations the rate of each component transformation in the reactor obeys the law of mass action. However, as distinct from the reactions with participation of exclusively low molecular weight substances, the... 

Secondary Ion Yields. The most successful calculations of secondary in yields are based on the local thermal equilibrium (LTE) model of Andersen and Hinthorne (1973), which assumes that a plasma in thermodynamic equilibrium is generated locally in the solid by ion bombardment. Assuming equilibrium, the law of mass action can be applied to find the ratio of ions, neutrals and electrons, and the Saha-Eggert equation is derived ... 

For the simple reaction we have looked at so far, we are dealing with one reactant, S, and we require only one mole of S to produce one mole of product P. Hence the law of mass action dictates that the reaction rate will be directly proportional to [S]1. Such a reaction is referred to as a first-order reaction because there is only one reactant concentration term in the rate equation (Equation A1.2). 

From the general form of the law of mass action, we require the concentration of A to appear twice in the rate equation ... 

Here k, is the rate constant for this dissociation. By the law of mass action, we know that the rate of dissociation will be directly proportional to the concentration of El complex, with -k, being the constant of proportionality (the minus sign denotes the fact that the concentration of El is diminishing over time). Thus the rate equation for this dissociation reaction is given by... 

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