Mass action expression

For other concentrations, we may employ the approximate Mass Action expression ... 

Many systems are not at equilibrium. The mass action expression, also called the reaction quotient, Q, is a measure of how far a system is from equilibrium and in what direction the system must go to get to equilibrium The reaction quotient has the same form as the equilibrium constant, K, but the concentration values put into Q are the actual values found in the system at that given moment. 

The term in square brackets provides a correction to the mass action expression which is clearly negligible in most circumstances. 

Kurbatov Plots. Kurbatov plots (6) are made by applying the linearization of a general overall mass action expression (e.g. Equation 4)... 

As a second example, consider the partitioning of Cd(II) between two adsorbents—a-TiC and (am)Fe20j.H20. Figure 11 shows Cd(II) fractional adsorption as a function of pH for binary mixtures of these adsorbents under experimental conditions such that Cddl) and SOUp are constant only the surface site mole fraction varies from one end-member to the next. As the site mole fraction shifts between the end-members, the fractional adsorption edges for the binary adsorbent mixtures varies between the limits defined by end-members. In the absence of particle-particle interactions, the adsorbents should act as independent ligands competing for complexa-tion of Cd(II). If this is the case, then the distribution of Cd(II) in such binary mixtures can be described by a composite mass-action expression (13) which includes a separate term for the interaction of Cd(II) with each adsorbent. 

The incorporation of Xn(pH 0 into macroscopic mass-action expressions for adsorption has shown not only that K is not a unique function of T at adsorption densities greater than i but that K is also not unique below T. In both cases it is due to the dependence of the macroscopic partitioning coefficient on pH (Figure 13). 

Physically, the solid and the fluid are linked by the mass transfer between them. The equilibrium concentrations in the solution are continually changing as the analytical concentrations change the adjustments are constrained to be such that the mass action expressions and balance equations are always... 

For each solution reaction, there is a mass action expression... 

The electrical transport properties of alkali metals dissolved in ammonia and primary amines in many ways resemble the properties of simple electrolytes except that the anionic species is apparently the solvated electron. The electrical conductance, the transference number, the temperature coefficient of conductance, and the thermoelectric effect all reflect the presence of the solvated electron species. Whenever possible the detailed nature of the interactions of the solvated electrons with solvent and solute species is interpreted by mass action expressions. 

Mass action equations. The first step in any calculation is to collate the mass action expressions that define the formation of the species. The way in which the formation constants can be used can be illustrated by considering a metal such as aluminium in an aqueous medium. Aluminium ions can undergo a number of hyrolysis reactions in water to form several hydroxy-metal complexes. The reactions can be written as the overall hydrolysis reactions and their associated equilibrium formation constants are shown below. 

Rearranging the above equations the following mass action expressions are obtained for the species... 

The equilibrium problem matrix. The information concerning components, stoichiometry and formation constants can be written in the form of a table which for the purposes of this chapter will be referred to as the equilibrium problem matrix (EPM). An example of an EPM table for the monomeric A1 species is shown in Table 5.6. The EPM is a logical and compact format for summarising all the information required for solving equilibrium problems. Reading across the rows of the table the information needed to formulate the mass action expressions is contained. Down each component column are the coefficients with which the concentration of each species should be multiplied to formulate the mass balance equation (MBE). Therefore, once given the chemical problem in an EPM format the nature of the mass action equations, formation constants and mass balances considered can all be deduced. 

The substitution of the mass action expressions for each species into the MBE for aluminium results in equation (5.42). In this example there is now only one unknown in the equation, Al3+, so the value Al3+ can be calculated for any given value of [Al]x. Once Al3+ has been determined the amounts of the hydroxy complexes can be determined by substitution of Al3+ into the formation equation of the relevant species ... 

By solving for Al3+ and SO4- and back substitution into the mass action expressions, the concentration of each species can be calculated. The proportion of each species as a proportion of the total aluminium is given in Fig. 5.3. The result shows the tendency of SO4 to form complexes in solution with aluminium in the pH range 3-5. 

If no acid or base is added to the system then PBE equals zero and the equation is solved for H+ by substituting in the appropriate mass action expressions for the aluminium species and KW[H+]-1 for OH-. 

The four mass action equations and the ENE give the five equations needed to solve the five unknowns. Substitution of the mass action expressions into the ENE yields... 

Complexation of cations and anions is achieved by introducing mass action expressions for the formation of the cation or anion surface complex into the mass balance for the total number of surface complexation sites and, if the new surface species is charged, into the charge balance equation, e.g. metal surface complexes, Cd2+. 

What is the mass-action expression for the following reaction at equilibrium ... 

The mass action expression for this slightly soluble salt is... 

It will be seen from Table 2 that with increasing concentration the activity-coefficient first falls more rapidly than the conductance-ratio, being about 10% smaller than the latter at concentrations 0.1 to 0.5 molal. This shows that at these concentrations there is an error of this magnitude in the common practice of employing in mass-action expressions the conductance-ratio as a measure of the activity of the ions of the add. The activity-coeffident, moreover, unlike the conductance-ratio, passes through a minimum at about 0.50 molal, and then increases rapidly with the concentration, becoming about equal to that... 

A quantity that characterizes the position of equilibrium for a reversible reaction its magnitude is equal to the mass action expression at equilibrium. K varies with temperature. 

For a reversible reaction, aA + bB cC + dD the product of the concentrations of the products (species on the right), each raised to the power that corresponds to its coefficient in the balanced chemical equation, divided by the product of the concentrations of reactants (species on the left), each raised to the power that corresponds to its coefficient in the balanced chemical equation. At equilibrium the mass action expression is equal to K at other times it is Q.[C]c[D]d [A]a[B]b = Q, or at equilibrium K Mass Deficiency... 

The mass action expression under any set of conditions (not necessarily equlibrium) its magnitude relative to K determines the direction in which the reaction must occur to establish equilibrium. 

A. Theoretical Considerations. The mass action expression for the combination of enzyme protein with a homogeneous population of binding sites on the carrier protein, collagen, may be treated in terms of a Langmuirian isotherm, where the isotherm is expressed in the following form (18, 23) ... 

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