Ideal equilibrium constants

The effect of temp on chemical equilibria is conventially determined via the free energy function AG°/RT and the ideal equilibrium constant K. Table 1 gives the free, energy function G°/RT for the important detonation products of CHNO expls. From these data A G°/(RT) can be obtained for different temps for the reactions of interest, and ideal equilibrium constants computed according to ... 

Since K is a concentration equilibrium constant, it is a non-ideal equilibrium constant, and so k is also a non-ideal rate constant, which incorporates all the factors causing non-ideality. Since these factors will be different for different reactions, these rate constants and their derived kinetic parameters should not be used for comparisons of reactions, but must first be converted to ones where the effects of non-ideality have been taken care of, i.e. ideal values. 

The ideal equilibrium constant for the formation of the activated complex is given in terms of activities ... 

This ideal equilibrium constant can also be written as... 

Note the quotient of activity coefficients in the equation for the rate constant, i.e. Equation (7.17), is the reciprocal of the quotient of activity coefficients appearing in equations for the ideal equilibrium constants, Equations (7.11) and (7.12). This is because Equation (7.17) is in terms of the non-ideal rate constant. 

Giauque and Kemp (1.) calculated Idealized equilibrium constants for the reaction NgO (g) = 2 NO (g) from the work of Bodenstein and Boes (2), Verhoek and Daniels 3) and Wourtzel (4). The 2nd and 3rd law analysis of these equilibrium constants has been repeated using more recent functions. The results are shown below. 

Experimental determinations made in terms of concentrations give concentration quotients which are non-ideal constants. Corrections for non-ideality are made in terms of the calculated ionic strength and the various Debye-Huckel expressions. However, emf experiments, including pH measurements, can sometimes furnish equilibrium constants directly in terms of activities, and as such these will be ideal equilibrium constants. 

This is a quotient of activities and thus is an ideal equilibrium constant. 

Since this involves a quotient of concentrations it is a non-ideal equilibrium constant. 

Other conventions for treating equiUbrium exist and, in fact, a rigorous thermodynamic treatment differs in important ways. Eor reactions in the gas phase, partial pressures of components are related to molar concentrations, and an equilibrium constant i, expressed directiy in terms of pressures, is convenient. If the ideal gas law appHes, the partial pressure is related to the molar concentration by a factor of RT, the gas constant times temperature, raised to the power of the reaction coefficients. 

It is reasonable to expeet that models in ehemistry should be capable of giving thermodynamic quantities to chemical accuracy. In this text, the phrase thermodynamic quantities means enthalpy changes A//, internal energy changes AU, heat capacities C, and so on, for gas-phase reactions. Where necessary, the gases are assumed ideal. The calculation of equilibrium constants and transport properties is also of great interest, but I don t have the space to deal with them in this text. Also, the term chemical accuracy means that we should be able to calculate the usual thermodynamic quantities to the same accuracy that an experimentalist would measure them ( 10kJmol ). 

The values of the equilibrium constant K listed in Table A are those obtained from data at low pressures, where the gases behave ideally. At higher pressures the mole percent of ammonia observed is generally larger than the calculated value. For example, at 400°C and 300 atm, the observed mole percent of NH3 is 47 the calculated value is only 41. 

Alternative forms of the equilibrium constant can be obtained as we express the relationship between activities, and pressures or concentrations. For example, for a gas phase reaction, the standard state we almost always choose is the ideal gas at a pressure of 1 bar (or 105 Pa). Thus... 

Assume that the gases are ideal and find the equilibrium constant for the reaction at 600 K. 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Within experimental error, Guldberg and Waage obtained the same value of K whatever the initial composition of the reaction mixture. This remarkable result shows that K is characteristic of the composition of the reaction mixture at equilibrium at a given temperature. It is known as the equilibrium constant for the reaction. The law of mass action summarizes this result it states that, at equilibrium, the composition of the reaction mixture can be expressed in terms of an equilibrium constant where, for any reaction between gases that can be treated as ideal,... 

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

As previously noted, the equilibrium constant is independent of pressure as is AG. Equation (7.33) applies to ideal solutions of incompressible materials and has no pressure dependence. Equation (7.31) applies to ideal gas mixtures and has the explicit pressure dependence of the F/Fq term when there is a change in the number of moles upon reaction, v / 0. The temperature dependence of the thermodynamic equilibrium constant is given by... 

Reconciliation of Equilibrium Constants. The two approaches to determining equilibrium constants are consistent for ideal gases and ideal solutions of incompressible materials. For a reaction involving ideal gases, Equation (7.29) becomes... 

Reverse Reaction Rates. Suppose that the kinetic equilibrium constant is known both in terms of its numerical value and the exponents in Equation (7.28). If the solution is ideal and the reaction is elementary, then the exponents in the reaction rate—i.e., the exponents in Equation (1.14)—should be the stoichiometric coefficients for the reaction, and Ei mettc should be the ratio of... 

Please note that the correction corresponds to introducing a corrected equilibrium constant K(T)/X . The correction has hardly any influence on the mole fraction of ammonia in the mixture at low pressures, but for ptot = 100 bar and higher the correction becomes significant. The results are presented in the last column of Tab. 2.4 and in Fig. 2.1. It should be noted that correction procedures exist for cases where the mixture does not behave ideally, but this goes beyond the scope of the present treatment. 

All in aqueous solution at 25°C standard states are 1 M ideal solution with an infinitely dilute reference state, and the pure liquid for water equilibrium constants from reference 100, except as noted. 

The temperature is high enough for the gases to be considered ideal, so the equilibrium constant is written in terms of partial pressure rather than fugacity, and the constant will not be affected by pressure. Mol fraction can be substituted for partial pressure. As the total mols in and out is constant, the equilibrium relationship can be written directly in mols of the components. 

Solution The ideal gas equilibrium constants can be corrected for real gas behavior by multiplying the ideal gas equilibrium constant by K,f as defined by Equation 6.23, which for this problem is ... 

The feed stream consists of 60 mole percent hydrogen, 20% nitrogen, and 20% argon. Calculate the composition of the exit gases, assuming equilibrium is achieved in the reactor. Make sure that you take deviations from the ideal gas law into account. The equilibrium constant expressed in terms of activities relative to standard states at 1 atm may be assumed to be equal to 8.75 x 10 3. The fugacity of pure H2 at 450 °C and 101.3 MPa may be assumed to be equal to 136.8 MPa. 

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