Mass action equilibrium principle

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. 

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... 

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-... 

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... 

This step is catalyzed by a separate enzyme, malate dehydrogenase. It has a very unfavorable AG° of about +7 kcal/ mole. When this reaction is followed by reaction (17), the combined AG9 is about —1.3 kcal/mole, so the equilibrium constant for the overall sequence is favorable. You can view this simply as an illustration of the principle of mass action (17) pulls (18) along by removing one of the products. 

Besides, let us note the automatic observance (certainly with correctly set initial data) and, hence, needlessness of the formalized descriptions in equilibrium modeling of such important regularities of macroscopic system behavior as the Gibbs phase rule, the Le Chatelier-Brown principle, mass action laws, the Henry law, the Raoult law, etc. 

A mixture of electrons, ions, and atoms forms a system similar to that which we considered in Chap. X, dealing with chemical equilibrium in gases. Equilibrium is determined, as it was there, by the mass action law. This law can be derived by balancing the rates of direct and inverse collisions, but it can also be derived from thermodynamics, and the equilibrium constant can be found from the heat of reaction and the chemical constants of the various particles concerned. The heats of reaction can be found from the various ionization potentials, quantities susceptible of independent measurement, and the chemical constants are determined essentially as in Chap. VIII. Thus there are no new principles involved in studying the equilibrium of atoms, electrons, and ions, and we shall merely give a qualitative discussion in this section, the statements being equivalent to mathematical results which can be established immediately from the methods of Chap. X. 

In principle, any chemical equilibrium reaction can be described by the mass-action law. 

From basic principles of mass action, we know the relationship between these rate constants and the association (KA) and dissociation (KD) equilibrium constants ... 

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 specific examples in Section 14.5 illustrate how the law of mass action gives information about the nature of the equilibrium state. The law of mass action also explains and predicts the direction in which a reaction will proceed spontaneously when reactants and products are initially mixed together with arbitrary partial pressures or compositions. This requires a new concept, the reaction quotient Q, which is related to the equilibrium constant. Through the principle of Le Chatelier (described below), the mass action law also explains how a reaction in equilibrium responds to an external perturbation. 

The principle of electroneutrality in aqueous chemical systems states that the sum of the concentrations of all positively charged ions (expressed in equivalents) equals the sum of the concentrations of all negatively charged ions, so that the overall charge of the solution is zero. (If this were not true, we would be constantly bombarded with electrical shocks ) When an equation based on the principle of electroneutrality is combined with equations provided by conservation of mass, and by the mass action law, Eq. [1-12], the equilibrium chemical composition of a system can be calculated. 

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. 

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). 

Chemical equilibrium in homogeneous systems, from the thermodynamic standpoint—Gaseous systems—Deduction of the law of mass action—The van t Hoff isotherm—Principle of mobile equilibrium (Le Chateher and Braun)— Variation of the equilibrium constant with temperature—A special form of the equilibrium constant and its variation with pressure... 

In the stationary state produced by light we have a state of things diffenng in principle from the equilibrium point reached in the dark owing to ordinary chemical attractions acting according to the Law of Mass Action Thus in the dark the... 

To relate the concentrations of point and electronic defects to temperature and externally imposed thermodynamic conditions such as oxygen partial pressures, the defects are treated as chemical species and their equilibrium concentrations are calculated from mass action expressions. If the free-energy changes associated with all defect reactions were known, then in principle diagrams, known as Kroger-Vink diagrams, relating the defect concentrations to the externally imposed thermodynamic parameters, impurity levels, etc., can be constructed. 

Pressure. Pressure, like temperature, can affect the rate of reaction as well as the equilibrium position. The rate of reaction is generally increased by increasing pressure, because a gas phase is usually present, and increased pressure gives increased concentration. In general, increased concentration speeds up a reaction. Pressure increases the equilibrium yield in a hydrogenation reaction when there is a decrease in the volume of the reaction as it proceeds. This is the simple application of the mass-action law, or Le Chdtelier s principle. In hydrogenation reactions, there is usuaUy a decrease in volume. 

Equilibrium (1) represents the reaction between ethyl alcohol, sulfuric acid and water to form the intermediate product (2) the formation of the ethyl sulfuric acid (3) the formation of ethylene (4) the formation of ethylene and the simultaneous giving off of water (5) the formation of ethyl ether (6) the formation of a polymer of ethylene. All of these reactions have been observed experimentally, and the products actually obtained under given conditions, depend upon these conditions and the principles of the law of mass action. This list served to indicate the possibilities for the quantitative study of a common reaction presumably well-known. 

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