Equilibrium constant in terms

These data can be used to obtain the value of the equilibrium constant at any temperature and this in turn can be used to calculate the degree of dissociation through the equation for the conceiiuation dependence of the constant on the two species for a single element, die monomer and the dimer, which coexist. Considering one mole of the diatomic species which dissociates to produce 2x moles of the monatomic gas, leaving (1 — jc) moles of the diatomic gas and producing a resultant total number of moles of (1 +jc) at a total pressure of P atmos, the equation for the equilibrium constant in terms of these conceiiU ations is... 

The formulation of transition state theory has been in terms of reactant and transition state concentrations let us now define an equilibrium constant in terms of activities. 

The Equilibrium Constant in Terms of Molar Concentrations of Gases... 

K is the equilibrium constant in terms of molar concentrations of gases (Section 9.6). 

We have seen that the value of an equilibrium constant tells us whether we can expect a high or low concentration of product at equilibrium. The constant also allows us to predict the spontaneous direction of reaction in a reaction mixture of any composition. In the following three sections, we see how to express the equilibrium constant in terms of molar concentrations of gases as well as partial pressures and how to predict the equilibrium composition of a reaction mixture, given the value of the equilibrium constant for the reaction. Such information is critical to the success of many industrial processes and is fundamental to the discussion of acids and bases in the following chapters. 

To calculate the equilibrium composition of a reaction mixture, set up an equilibrium table in terms of changes in the concentrations of reactants and products, express the equilibrium constant in terms of those changes, and solve the resulting equation. 

We will see functions like the one occurring under the logarithm operator quite often. For efficiency, this is generally written as In(Products)/(Reactants), where (Products) and (Reactants) denote the partial pressures of the species relative to the standard state pressure raised to a power that is equal to the stoichiometric coefficients. Kp is the equilibrium constant in terms of pressures. Since all pressures are in the same units, Rp is dimensionless. Note that in some literature there may be a combination of some power of P with Kp to obtain an equilibrium constant with pressure units. In this case. 

We have in Eq. (77) expressed the equilibrium constant in terms of the relevant partition functions, which must be calculated ... 

We express the equilibrium constant in terms of the partition functions of both the reactant and the transition state, and we take the partition function of the reaction coordinate separately ... 

Note that we have also specified these equilibrium constants in terms of the activity of the associated defects. We can also write thermodynamic equations for these defects ... 

The next step in the development of the extrathermodynamic approach was to find a suitable expression for the equilibrium constant in terms of physicochemical and conformational (steric) properties of the drug. Use was made of a physicochemical interpretation of the dissociation constants of substituted aromatic acids in terms of the electronic properties of the substituents. This approach had already been introduced by Hammett in 1940 [14]. The Hammett equation relates the dissociation constant of a substituted benzoic acid (e.g. meta-chlorobenzoic acid) to the so-called Hammett electronic parameter a ... 

From changes in free energy in standard reference conditions it is possible to calculate equilibrium constants for reactions involving several reactants and products. Consider, for example, the chemical reaction aA + bB = cC + dD at equilibrium in solution. For this reaction we can define a stoichiometric equilibrium constant in terms of the concentrations of the reactants and products as... 

The solubility of a compound refers to the concentration of that compound in solution, either as a molarity or as a mass per unit volume. The solubility product constant is the equilibrium constant in terms of concentrations of ions, for the dissolution equilibrium, raised to their appropriate coefficients. 

Strictly, we should formulate all equilibrium constants in terms of activities rather than concentrations, so Equation (7.32) describes Ksp for dissolving partially soluble AgCI in water ... 

Because the concentration of CO is not negligible, we can no longer apply the simple relationship between molality and concentration (mi = cjp) to write the equilibrium constant in terms of concentrations. The correct relationship between these two quantities is now given by equation 14.23, where M and n are the molar mass and the amount of substance of the solvent, respectively, and M and , are the corresponding quantities for the three solutes. 

The chapter starts with a brief review of thermodynamic principles as they apply to the concept of the chemical equilibrium. That section is followed by a short review of the use of statistical thermodynamics for the numerical calculation of thermodynamic equilibrium constants in terms of the chemical potential (often designated as (i). Lastly, this statistical mechanical development is applied to the calculation of isotope effects on equilibrium constants, and then extended to treat kinetic isotope effects using the transition state model. These applications will concentrate on equilibrium constants in the ideal gas phase with the molecules considered in the rigid rotor, harmonic oscillator approximation. 

This latter equilibrium is called an isotopic exchange equilibrium. Its equilibrium constant in terms of partition functions is from Equation 4.64... 

We can define the left side of Equation 10.20 as AG, where the process described is one mole of reaction at constant chemical potential for reactants and products, that is, for a system large enough so that one mole of reaction can take place in the mixture without any significant change in composition or chemical potential, an infinite-copy model. As AG is a constant at constant temperature, the quantity in brackets is also a constant at constant temperamre, and, in particular, independent of the total pressure and the initial composition of the system. We therefore designate the quantity in brackets as Kp, which is the equilibrium constant in terms of partial pressures for a... 

GIBBS FUNCTION AND TTIE EQUILIBRIUM CONSTANT IN TERMS OE ACTIVITY... 

GIBBS FUNCTION AND THE EQUILIBRIUM CONSTANT IN TERMS OF ACTIVITY... 

Baes and Mesmer [161] have suggested that McDowell and Johnston s data can be satisfactorily explained in terms of only the tetrahydroxy species if one allows for the probable effect of increasing ionic strength. However, this statement is presumably incorrect as McDowell and Johnston reported their equilibrium constant in terms of activities, and kinetic measurements on the complexation reactions of Cu(II) at pH > 13 indicate that two different hydroxy species exist [165]. 

Since kj and k, are constants a new constant can be derived from them. It is named as an equilibrium constant in terms of concentration, and is symbolized as K, . 

The equilibrium constant of the above reaction in terms of partial pressures (Kp) is 6 at 167 °C. What is the equilibrium constant in terms of concentration (K ) ... 

We can now utilize some of the statistical mechanics relationships derived in Chapter 8 to find expressions for the free energy and the equilibrium constant in term of the molecular partition functions. From the definition of the free energy (Eq. 9.1) the expression for the enthalpy of an ideal gas (Eq. 8.121), and recalling that Ho = Eq (for an ideal gas), we obtain... 

Equation 11.81 is thus an expression for the Langmuir adsorption equilibrium constant in terms of the surface and gas molecular partition functions, qs and qg, respectively. 

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