Equilibria constant

The free energy change in the form of equation (1.1.4) can be related to the equilibrium constant (K), assuming unit activity for electrons  

This relationship is an example of the power of electrochemistry. A single experimental measurement, such as EP, can be used to directly calculate K. For example, a cell consisting of a silver electrode and a silver electrode coated with solid silver iodide can be used to determine the solubility product (K p) of silver iodide. For the net chemical reaction of the cell  

The value obtained for the change in free energy can be then substituted into equation (1.3.6) and calculated for 25 °C as follows  

An important thermodynamic result is that the free-energy change can be related to the reaction equilibrium constant. Begin by considering again the reaction of Eq. 9.3, which describes chemical conversion of A and B to X and Y in the molar ratios shown. If the reaction proceeds by some infinitesimal amount dS, then the number of moles of each chemical species changes by an amount 

Equation 9.37 shows the change in free energy when the reaction proceeds by an infinitesimal amount. 

Substituting Eq. 9.21 for each of the four chemical species, Eq. 9.39 becomes 

The subscript e has been added above to indicate that the pressures in Eq. 9.41 are the pressures of the gases at equilibrium. (Recall from Eq. 9.21 that the pressures in Eq. 9.41 are actually unitless, i.e., the pressures are in units of p°, the standard-state pressure.) 

Since the right-hand side of Eq. 9.41 is a constant for a given T, the term involving the logarithm of the pressures must also equal a constant. The equilibrium constant Kp for reaction 9.3 is thus defined as 

Many biogeochemical reactions that occur in nature are reversible, and under most conditions reactions never reach 100% completion, thus reaching equilibrium. The stage at which reaction approaches steady state is usually expressed as equilibrium constant For a system at equilibrium, the rates of forward and backward reactions are equal. 

In Section 11.1, we introduced the concept of equilibrium by suggesting a classroom experiment in which students in a class split into two groups and line up on two sides of the classroom, with one group on each side. We stated that as students pass from one side of the room to the other at the same time and at the same rate, there is no net change in the count of students on either side. Because there is no change in these counts, we can divide the number of students on one side by the number of students on the other side and always obtain the same number. This same concept applied to a chemical equilibrium system results in a number called the equilibrium constant. 

In a chemical equilibrium system, the count is the molar concentration of the chemical species involved. For the purpose of symbolizing this molar concentration (and the equilibrium constant), we now introduce the symbolism of the brackets, [ ]. The molar concentration (molarity) of a chemical species is symbolized by enclosing the formula of this species within brackets. For example, [H+] refers to the molar concentration of the hydrogen ion, [NH3] refers to the molar concentration of ammonia, and [CF] refers to the molar concentration of the chloride ion. 

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 

Knowing the molar concentrations of all the chemicals involved in the equilibrium, we can calculate the number that is given by the equilibrium constant. For Equation 11.7, K q is as shown in Equation 11.13 

Equations 11.8 and 11.9 represent ionization equilibria in which an uncharged chemical species (molecule or formula unit) splits apart into 

But if Qn is the partition function for an ideal gas of N identical molecules, we have the relation 

If we separate out the zero-point energies of the species and write the residual partition functions as Q°, where Q = then this can be 

When independent data are available (as from spectroscopy) for the vibration frequencies and values of Eq. (IX. 11.7) yields excellent results for Xe,.  

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To describe this chemical equilibrium quantitatively, we use a chemical equilibrium constant... 

Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

IF BINARY SYSTEM CONTAINS NO ORGANIC ACIDS. THE SECOND VIRTAL coefficients ARE USED IN A VOLUME EXPLICIT EQUATION OF STATE TO CALCULATE THE FUGACITY COEFFICIENTS. FOR ORGANIC ACIDS FUGACITY COEFFICIENTS ARE PREDICTED FROM THE CHEMICAL THEORY FOR NQN-IOEALITY WITH EQUILIBRIUM CONSTANTS OBTAINED from METASTABLE. BOUND. ANO CHEMICAL CONTRIBUTIONS TO THE SECOND VIRIAL COEFFICIENTS. 

If the mixture includes organic acids, the equations of Hayden and O Connell yield equilibrium constants for all possible dimerization reactions. 

In thermodynamic terms the equilibrium constant is related to the standard chemical potential by the equation... 

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. 

Na -f-OH -kCHjCOOH and the equilibrium constant, K, for this reaction is given by... 

Soave, G. (1972), Equilibrium constants from a modified Redlich-Kwong equation of state . Chem. Eng. Sci., Vol. 27, p. 1197. 

When oil and gas are produced simultaneously into a separator a certain amount (mass fraction) of each component (e.g. butane) will be in the vapour phase and the rest in the liquid phase. This can be described using phase diagrams (such as those described in section 4.2) which describe the behaviour of multi-component mixtures at various temperatures and pressures. However to determine how much of each component goes into the gas or liquid phase the equilibrium constants (or equilibrium vapour liquid ratios) K must be known. 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

While a number of proteins have been crystallized in this manner, the majority of studies have focused on a robust system comprising the tetrameric protein streptavidin and the vitamin biotin. The choice of this system is primcirily motivated by the strong bond between biotin and streptavidin (having an association equilibrium constant, Ka Tbe binding properties were recently... 

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)... 

The value of the standard free energy AG depends on the choice of reference state, as does the equilibrium constant. Thus it would be safer to write the equilibrium constant K for a gaseous reaction as... 

This important relation between the temperature derivative of the equilibrium constant K and the standard... 

The validity of equation (A2.1.70) has sometimes been questioned when enthalpies of reaction detennined from calorimetric experiments fail to agree with those detennined from the temperature dependence of the equilibrium constant. The thennodynamic equation is rigorously correct, so doubters should instead examine the experunental uncertainties and whether the two methods actually relate to exactly the same reaction. 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

It is possible to detemiine the equilibrium constant, K, for the bimolecular reaction involving gas-phase ions and neutral molecules in the ion source of a mass spectrometer [18]. These measurements have generally focused on tln-ee properties, proton affinity (or gas-phase basicity) [19, 20], gas-phase acidity [H] and solvation enthalpies (and free energies) [22, 23] ... 

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