Equilibrium Law of Mass Action

The concept of equilibrium is really dynamic and not static, in the sense that when equilibrium is attained the reaction proceeds both in forward and backward directions at equal rates, so that the amount of reactants disappearing per unit time is reproduced from the action in opposite direction. The reactions proceeding in both directions are called reversible reactions which is indicated with double arrows in opposite direction. It is very likely that all chemical reactions are reversible, but in some cases the extent of backward reaction is so small as to be negligible and such reactions are said to proceed to completion in one direction. Under such condition the equilibrium is attained at an extreme end of the concentrations of the resultants, the concentration of unreacted materials being extremely small to be detected. 

A quantitative relation between the amoimts of reactants and the resultants of equilibrium was developed from a basic principle, called the law of Mass Action emmtiated by two Norweigian chemists, Gulberg and Waage (1867). 

The law states Temperature remaining constant, the rate of a chemical reactions is proportional to the active masses of the reacting substances. The expression active mass in the statement requires serious consideration. For solids and pure liquids, the active masses or concentrations are taken as unity since the rate of reaction is independent of their amounts present. Let us consider the simple reversible reaction at constant temperature  

Let C -terms denote the concentrations of the components at a given instant during the progress of reaction. According to the law, the rate of the forward reaction (R ) between A and B at that moment will be 

With progress of reaction, the concentrations of C and D would increase and hence the 

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To shift this reaction as far to the right as possible, the hydrogen ions produced must be removed from the equilibrium (law of mass action). This can be done with a suitable pH buffer system (acetate, hydrogen phosphate, citrate, etc.). Unfortunately, these added buffer systems sometimes also form weak complexes with the metal ion to be measured. This can easily be confirmed with the corresponding metal cation-, indicating ion-selective electrode. In this case the electrode potential in the pH buffer system-metal ion solution will be more negative than that in a pure metal ion solution of the same concentration. 

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. 

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 ... 

The equilibrium concentration of defects is obtained by applying the law of mass action to Eq. (7) or (8). This leads in the case of Frenkel disorder to... 

The deduction adopted is due to M. Planck (Thermodynamik, 3 Aufl., Kap. 5), and depends fundamentally on the separation of the gas mixture, resulting from continuous evaporation of the solution, into its constituents by means of semipermeable membranes. Another method, depending on such a separation applied directly to the solution, i.e., an osmotic process, is due to van t Hoff, who arrived at the laws of equilibrium in dilute solution from the standpoint of osmotic pressure. The applications of the law of mass-action belong to treatises on chemical statics (cf. Mel lor, Chemical Statics and Dynamics) we shall here consider only one or two cases which serve to illustrate some fundamental aspects of the theory. 

Within experimental error, Guldberg and Waage obtained the same value of K whatever the initial composition of the reaction mixture. This remarkable result shows that K is characteristic of the composition of the reaction mixture at equilibrium at a given temperature. It is known as the equilibrium constant for the reaction. The law of mass action summarizes this result it states that, at equilibrium, the composition of the reaction mixture can be expressed in terms of an equilibrium constant where, for any reaction between gases that can be treated as ideal,... 

The law of mass action states that the rate of a reaction is proportional to the product of the concentrations of the reactants. Thus the rate of the forward reaction is proportional to [A][R] = k+i[A][R], where k+ is the association rate constant (with units of M s ). Likewise, the rate of the backward reaction is proportional to [AR] = k i[AR], where k- is the dissociation rate constant (with units of s ). At equilibrium, the rates of the forward and backward reactions will be equal so... 

Immunoassays are based on the reaction of an analyte or antigen (Ag) with a selective antibody (Ab) to give a product (Ag-Ab) that can be measured. The reactants are in a state of equilibrium that is characterized by the law of mass action (Figure 1). 

The method of representing the equilibrium state The value of the equilibrium constant changes if the reversible reaction is considered to proceed in the reverse direction. For example, the reaction A + B C + D can also be written asC + D A+Bso that [A] [B]/[C] [D] = kr/kf = K. In this case the value of the equilibrium constant for the reverse reaction is given by K = 1/K. To avoid such confusion while applying the law of mass action, the concentrations of the products are always placed in the numerator and those of the reactants in the denominator. 

The system, therefore, is at equilibrium at a given temperature when the partial pressure of carbon dioxide present has the required fixed value. This result is confirmed by experiment which shows that there is a certain fixed dissociation pressure of carbon dioxide for each temperature. The same conclusion can be deduced from the application of phase rule. In this case, there are two components occurring in three phases hence F=2-3 + 2 = l, or the system has one degree of freedom. It may thus legitimately be concluded that the assumption made in applying the law of mass action to a heterogeneous system is justified, and hence that in such systems the active mass of a solid is constant. 

According to the law of mass action, the equilibrium constant (K) is given by... 

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 ... 

Listed after the reactions are the corresponding equilibrium quotients. The law of mass action sets the concentration relations of the reactants and products in a reversible chemical reaction. The negative log (logarithm, base 10) of the quotients in Eqs. (3.1)—(3.4) yields the familiar Henderson-Hasselbalch equations, where p represents the operator -log ... 

For other electrolytes, now termed weak, factor i has non-integral values depending on the overall electrolyte concentration. This fact was explained by Arrhenius in terms of a reversible dissociation reaction, whose equilibrium state is described by the law of mass action. 

This is the important Hill-Langmuir equation. A. V. Hill was the first (in 1909) to apply the law of mass action to the relationship between ligand concentration and receptor occupancy at equilibrium and to the rate at which this equilibrium is approached. The physical chemist I. Langmuir showed a few years later that a similar equation (the Langmuir adsorption isotherm) applies to the adsorption of gases at a surface (e g., of a metal or of charcoal). 

Our first task is to apply the law of mass action to derive a relationship between the concentration of agonist and the proportion of receptors that are in the active form at equilibrium. This proportion will be denoted by pAR. ... 

The law of mass action was first applied to competitive antagonism by Clark, Gaddum, and Schild at a time before the importance of receptor activation by isomerization was established. It was assumed, therefore, that the equilibrium among agonist, antagonist, and their common binding site could be represented quite simply by the reactions ... 

Our task is to work out how the proportion of receptors occupied by the agonist varies with the concentrations of the agonist and the antagonist. Equilibrium is assumed. Applying the law of mass action gives ... 

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