Law of mass-action

In the process of relaxation these components redistribute in proportions corresponding to their equilibrium stoichiometric coefficients imtil free enthalpy of products and reactants become equal, i.e., when 

In order to compare free enthalpy of the products and reactants we will use equation (1.57), which allows determining chemical potential of a component by values of its activities. Then, summing up chemical potentials of reactants (the left half of reaction equations), we will get 

For the products (the right half of reaction equations) the analogous sum is equal 

Summing up values of free enthalpy of the products and reactants, we will find the difference between them  

If we assrnne stoichiometric coefficients v, of reactions products positive and of reactants, negative, equation (1.91) maybe simplified. The first addend of the equation will assume the format 

Let the case of a simple reversible reaction, occurring under isothermal and isobaric conditions, be considered  

It was shown by Guldberg and Waage that when solids are present in a system, their active masses may be taken as constant and included in the equilibrium constant, K. For example, in the reaction  

It thus follows that in the general equation, A + B C + D, if, for example, B and D are pure solids, the equilibrium constant can be expressed as  

Proceeding further with the general solution in which no reactant or product is a pure solid, for the following reversible reaction, occurring at constant temperature and pressure, 

Chemical equilibrium is achieved between reactants and products when the amounts of the participants in the reaction remain constant. Forward and backward reactions still occur simultaneously. We write a chemical reaction in the following general way  

For practical reasons, we have chosen the stoichiometric coefficients for the reactants as negative (Va,Vb,.. ., 0). The amounts of the substances change linearly during the reaction according to 

Equation 5.86 is called the law of mass action. K is called the thermodynamic equilibrium constant. 

Equations of this type serve the bookkeeping and transfer of thermodynamic data between different measurements. 

7 Temperature Dependence of Equilibrium Constant If we apply the Gibbs-Helmholtz Equation 5.76 on AG, we obtain 

Historically, the state of reaction at chemical equilibrium was evaluated for fairly simple reactions, with only a few species, from the Law of Mass Action. 1 In recent years, high-temperature reactions, including many possible species (as many as 20 or more), have become of interest and newer techniques suitable for numerical solution on high-speed digital computers have been developed.2 Initially, we will discuss chemical equilibrium from the vantage point of the Law of Mass Action. It states that the rate at which a chemical reaction proceeds is proportional to the active masses of the reacting substances. The active mass for a mixture of ideal gases is the number density of each react- 

As a simple example of how this relation may be used to establish the equilibrium composition of reacting gases, consider the dissociation of nitrogen tetroxide when its temperature is increased from room temperature to some elevated value. 

For reactions in which the number of molecules do not change during the reaction, the amount of each reactant decomposed at equilibrium will be independent of the total pressure. Consider the reaction 

assume we start with A moles of N2 plus 02. We then heat this mixture to temperature T, at which point x molecules of each N2 and 02 have reacted to form NO. We can then write the partial pressure of NO formed as 

Comparing Equations (8) and (9), and recalling that Kp = Kp(T), we recognize that the extent of the reaction (x) is independent of the total pressure p, and depends only on the temperature through Kp. 

Three main methods allow an equilibrium to be calculated the direct application of the law of mass action, the minimization of the free enthalpy of the system and the simulation of a kinetic model. This last approach has the advantage of providing the time necessary to reach equilibrium. 

When the overall chemical equilibrium is reached, all the chemical reactions are themselves at equilibrium. The law of mass action can then be applied to them and the system of non-linear equations arising from it can be solved. 

Dividing both sides by the volume V of the reactor, which is assumed to be constant, gives  

The solution of this set of I non-linear equations with I unknowns 2 usually only possible using numerical methods. 

The pyrolysis of methane at temperatures of about 1200 °C leads mainly to the 

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Complex chemical mechanisms are written as sequences of elementary steps satisfying detailed balance where tire forward and reverse reaction rates are equal at equilibrium. The laws of mass action kinetics are applied to each reaction step to write tire overall rate law for tire reaction. The fonn of chemical kinetic rate laws constmcted in tliis manner ensures tliat tire system will relax to a unique equilibrium state which can be characterized using tire laws of tliennodynamics. 

In the early twentieth century, the law of mass action was appHed to the basic pathway of dmg—receptor interaction. Assuming that response, R, is proportional to the concentration of the dmg—receptor complex, ITT, and that maximum response, occurs when all receptors are occupied (2,6,10),... 

In an undoped, intrinsic semiconductor the equiHbrium concentrations of electrons, and holes,/), are described by a lever rule derived from the law of mass action (eq. 3) ... 

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). 

Law of Mass Action The effect of concentration on the rate is isolated as... 

The rates of many reactions are not represented by application of the law of mass action on the basis of their overall stoichiometric relations. They appear, rather, to proceed by a sequence of first- and second-order processes involving short-lived intermediates which may be new species or even unstable combinations of the reaclants for 2A -1- B C, the sequence could be A -1- B AB followed by A -1- AB C. 

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... 

Power law type, based directly on the law of mass action, say,... 

The interpretation of kinetic data is largely based on an empirical finding called the Law of Mass Action In dilute solution the rate of an elementary reaction 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... 

Guldberg and Waage (1867) clearly stated the Law of Mass Action (sometimes termed the Law of Chemical Equilibrium) in the form The velocity of a chemical reaction is proportional to the product of the active masses of the reacting substances . Active mass was interpreted as concentration and expressed in moles per litre. By applying the law to homogeneous systems, that is to systems in which all the reactants are present in one phase, for example in solution, we can arrive at a mathematical expression for the condition of equilibrium in a reversible reaction. 

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 ... 

This is the rigorously correct expression for the Law of Mass Action as applied to weak electrolytes. 

If the acid is a weak electrolyte, the Law of Mass Action may be applied, and the following expressions obtained ... 

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 ... 

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