Chemical equilibrium constant defined

The previous summary of activities and their relation to equilibrium constants is not intended to replace lengthier discussions [1,18,25,51], Yet it is important to emphasize some points that unfortunately are often forgotten in the chemical literature. One is that the equilibrium constants, defined by equation 2.63, are dimensionless quantities. The second is that most of the reported equilibrium constants are only approximations of the true quantities because they are calculated by assuming the ideal solution model and are defined in terms of concentrations instead of molalities or mole fractions. Consider, for example, the reaction in solution ... 

C-t, which means, of course, that the ideal solution model is adopted, no matter the nature or the concentrations of the solutes and the nature of the solvent. There is no way of assessing the validity of this assumption besides chemical intuition. Even if the activity coefficients could be determined for the reactants, we would still have to estimate the activity coefficient for the activated complex, which is impossible at present. Another, less serious problem is that the appropriate quantity to be related with the activation parameters should be the equilibrium constant defined in terms of the molalities of A, B, and C. As discussed after equation 2.67, A will be affected by this correction more than A f//" (see also the following discussion). 

Since solid carbon vaporizes as a result of its vapor pressure, p p,c, the chemical equilibrium constant s defined as... 

Dissociation constants, which are chemical equilibrium constants for dissolution of acids, are defined in a manner similar to the definition of pH in the case of water. As discussed before, a weak acid such as H3PO4 goes through step-by-step ionization in water given by Eqs. 4.7-4.9. In each step, the dissociation constant is experimentally found to be... 

The equilibrium constants are related to the thermodynamic Gibb s free energy in the regular manner ksTlnKn = AG ° = Af/ - TASj, where kg is Boltzmann s constant and T is the temperature, and ideal mixing (no volume change) is assumed. The chemical equilibrium constants can also be written in terms of the activities of the different species, defined in terms of the chemical potential, of specie k, as a/ expi/hJkgT). Thus, at equilibrium... 

In spite of the outlined above formulation of chemical equilibrium problem in terms of rigorous thermodynamics (equilibrium constants defined as quotients of activities) which is well known and does not pose any special difficulty when it is compared with formulation in terms of conditional equilibrium constants (defined as quotients of concentrations), the former approach is not very popular, and many equilibrium constants of surface reactions reported in published papers were defined in terms of concentrations. Even praise of use of concentrations rather than activities in modeling of adsorption can be found in recent literature. Many publications do not address this question explicit, and then it is difficult to figure out how the equilibrium constants of surface species were defined K, or Accordingly, the equilibrium constants of surface species reported in tables of Chapter 4 constitute a mixture of constants defined in different ways (K, or The details regarding the definition of equilibrium constants can be found (but not always) in the original publications. 

In this method the chemical equilibrium state is defined by the chemical equilibrium constant [10]. The chemical equilibrium constants can be derived from (6.48) provided that appropriate expressions are introduced for the chemical potential. A change in chemical potential for an isothermal process is related to a change in the fugacity of the species [13] ... 

In some databases—for example, in the very extensive NIST Chemistry Web-Book " —the data reported for each substance are the the standard state heat of formation AfW" and the absolute entropy both at 25°C. Here by absolute entropy is meant entropy based on the third law of thermodynamics as defined in Sec. 6.8. The reason for reporting these two quantities is that they are determined directly by thermal or calorimetric measurements, unlike the Gibbs energy of formation, which is obtained by measuring chemical equilibrium constants. 

Note the absence of the subscript a on in the equation above, indicating that this is not a true equilibrium constant. Instead, K a is referred to as an apparent equilibrium constant and is a measured quantity that depends on the solution conditions (ionic strength, pH, etc.), unlike the thermodynamic equilibrium constant, which depends only on the standafSli tate and temperature. This apparent equilibrium constant is one of the concentration chemical equilibrium ratios defined in Table 13.1-3. As... 

The principle of equilibrium can also be applied when an excess of a solid is added to water to form a saturated solution. The solubility product (K p) is an equilibrium constant defined by the law of chemical equilibrium. Solubility is an equilibrium position, and the K p value of a solid can be determined by measuring its solubility. Conversely, the solubility of a solid can be determined if its K p value is known. 

The chemical equilibrium constant for the reaction considered is defined as follows jMTBE//MTBE... 

The equilibrium constant for a chemical equilibrium is defined as the molar concentrations of the products of the reaction, raised to the power of their respective balancing coefficients and multiplied together, divided by the molar concentrations of the reactants of the reaction, raised to the power of their balancing coefficients and multiplied together. Thus, for the general reaction... 

To proceed fiirther, to evaluate the standard free energy AG , we need infonnation (experimental or theoretical) about the particular reaction. One source of infonnation is the equilibrium constant for a chemical reaction involving gases. Previous sections have shown how the chemical potential for a species in a gaseous mixture or in a dilute solution (and the corresponding activities) can be defined and measured. Thus, if one can detennine (by some kind of analysis)... 

Most chemical reactions do not progress completely from reactants to products. Instead, the net reaction stops in the forward direction when equilibrium is established. Analysis of the contents of the reaction vessel would show a constant concentration of monomers and polymer once equilibrium is reached. This situation is actually a dynamic equilibrium, where the monomers are forming polymers at the same rate as the polymers depolymerize to monomer. Therefore, at equilibrium, the net concentrations of any one species remains constant. The amount of monomer converted into polymer will be defined by the equilibrium constant, K. This constant is the ratio of the concentration of the products to the reactants, with each concentration raised to the stoichiometric coefficients in the balanced equation. For Eq. 3.5 ... 

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... 

In fact, an equilibrium constant is only ever useful when we have carefully defined the chemical process to which it refers. 

One of the most basic requirements in analytical chemistry is the ability to make up solutions to the required strength, and to be able to interpret the various ways of defining concentration in solution and solids. For solution-based methods, it is vital to be able to accurately prepare known-strength solutions in order to calibrate analytical instruments. By way of background to this, we introduce some elementary chemical thermodynamics - the equilibrium constant of a reversible reaction, and the solubility and solubility product of compounds. More information, and considerably more detail, on this topic can be found in Garrels and Christ (1965), as well as many more recent geochemistry texts. We then give some worked examples to show how... 

Stoichiometric saturation defines equilibrium between an aqueous solution and homogeneous multi-component solid of fixed composition (10). At stoichiometric saturation the composition of the solid remains fixed even though the mineral is part of a continuous compositional series. Since, in this case, the composition of the solid is invariant, the solid may be treated as a one-component phase and Equation 6 is the only equilibrium criteria applicable. Equations 1 and 2 no longer apply at stoichiometric saturation because, owing to kinetic restrictions, the solid and saturated solution compositions are not free to change in establishing an equivalence of individual component chemical potentials between solid and aqueous solution. The equilibrium constant, K(x), is defined identically for both equilibrium and stoichiometric saturation. 

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