Equilibrium constants and heats of reaction

Schumm Selected Values of Chemical Therm ynamlc Properties - Tables for the First Thirty-Four Elements in the Standard Order of Arrangement7 National Bureau of Standards Technical Note 270-3, 1968 

R eM a A E Mart ell. Critical Stability Constants. Vol. 4 Inorganic 

Inorganic Ligands. The Chemical Society, London, Special Publication No. 17 (1964) 

Mestner, The Hydrolysis of Cations, John Wiley fc Sons, New York (1976) 

Mesmer, The Thermodynamics of Cation Hydrolysis , Amer. J. Sol., v281, pp935-962 (1981) 

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It is possible to measure equilibrium constants and heats of reaction in the gas phase by using mass spectrometers of special configuration. With proton-transfer reactions, for example, the equilibrium constant can be determined by measuring the ratio of two reactant species competing for protons. Table 4.13 compares of phenol ionizations. 

In this chapter we have seen that acid dissociation constants are needed to calculate the dependence of apparent equilibrium constants on pH. In Chapter 3 we will discuss the calculation of the effects of ionic strength and temperature on acid dissociation constants. The database described later can be used to calculate pKs of reactants at 298.15 K at desired ionic strengths. Because of the importance of pKs of weak acids, Table 1.3 is provided here. More experimental measurements of acid dissociation constants and dissociation constants of complex ions with metal ions are needed because they are essential for the interpretation of experimental equilibrium constants and heats of reactions. A major database of acid dissociation constants and dissociation constants of metal ion complexes is provided by Martell, Smith, and Motekaitis (2001). 

The procedure for calculating standard formation properties of species at zero ionic strength from measurements of apparent equilibrium constants is discussed in the next chapter. The future of the thermodynamics of species in aqueous solutions depends largely on the use of enzyme-catalyzed reactions. The reason that more complicated ions in aqueous solutions were not included in the NBS Tables (1992) is that it is difficult to determine equilibrium constants in systems where a number of reactions occur simultaneously. Since many enzymes catalyze clean-cut reactions, they make it possible to determine apparent equilibrium constants and heats of reaction between very complicated organic reactants that could not have been studied classically. 

The standard formation properties of species are set by convention at zero for the elements in their reference forms at each temperature. The standard formation properties of in aqueous solution at zero ionic strength are also set at zero at each temperature. For other species the properties are determined by measuring equilibrium constants and heats of reaction. Standard transformed Gibbs energies of formation can be calculated from measurements of K, and so it is really these Maxwell relations that make it possible to calculate five transformed thermodynamic properties of a reactant. 

Use of the third law is not the only way to get large molecules of biochemical reactants into tables of species properties. If apparent equilibrium constants and heats of reaction can be determined for a pathway of reactions from smaller molecules (for which Af G° and Af H° are known with respect to the elements) to form the large molecule, then the properties of the species of the large molecule can be determined relative to the elements in their reference states. This method has its problems in that it is very difficult to determine apparent equilibrium constants greater than about 10 to 10 and the number of reactions in the path may be large and some of the reactants may not be readily available in pure form. Thus it is fortunate that the third law method is available. 

The first step in the numerical solution of this problem is the calculation of the equilibrium constants and heats of reaction for the reactions above. Using the program CHEMEQI obtained ... 

The next step the modeller faces is the determination of all physico-chemical parameters and the suitable correlations for computing their changes with the variations in composition, temperature and pressure at different points in the reactor (in general axially and radially) and also along the depth of the catalyst pellets. These parameters include physical parameters such as specific heats, densities, viscosities etc. transport parameters such as diflfusivities and thermal conductivities kinetic parameters as discussed earlier as well as thermodynamic parameters such as equilibrium constants and heats of reactions. 

FIGURE 8.9 Equilibrium constants and heats of reactions (kcal/mol) for the steps in the hydrogenation of phenanthrene. 

Equation (48) is of the expected form for relations between reaction velocities and activation energies on the one hand, and between equilibrium constants and heats of reaction on the other. However, there are difficulties in the way of using (48) as a quantitative basis-for the BrOnsted relation. In the first place, the quantities E and e in the diagram refer strictly to the behavior of the system at absolute zero since no account is taken of the internal thermal energy of the molecules. In the second place experiment shows that even in a series of similar reactions the observed velocities and equilibrium constants often involve variations in entropies of activation and of reaction, and not only energy changes. These difficulties are not yet fully resolved, but there seems little doubt that diagrams such as Fig. 1 represent the essential molecular basis of the Bronsted relation. 

Analysis of mixtures is possible when the two species have different equilibrium constants and heats of reaction with the titrant. This occurs, for example, in the titration of a mixture of calcium and magnesium with EDTA. Calcium (ATf = 10 ) reacts first and exothermically AH = — 5.7 kcal/mole) magnesium (AT, = 10 - ) reacts second and endothermically AH — +5.5 kcal/mole). This titration is illustrated in Figure 17.16. 

Thermochemical properties, such as equilibrium constants and heats of reaction... 

Hence we can easily calculate the values of the equilibrium constant and heat of reaction of the processes in question, using the relations... 

Table 2. Equilibrium Constants and Heats of Reaction (Used with Pemiission of Sud-Chemie)...

Figure 6.1 Equilibrium Constant and Heat of Reaction as a Function of Temperature for the Toluene Hydrodeallgdation Reaction...

We also account for density, heat capacity, and molecular weight variations due to temperature, pressure, and mole changes, along with temperature-induced variations in equilibrium constants, reaction rate constants, and heats of reaction. Axial variations of the fluid velocity arising from axial temperature changes and the change in the number of moles due to the reaction are accounted for by using the overall mass conservation or continuity equation. 

This field owes a tremendous debt to the experimentalists who have measured apparent equilibrium constants and heats of enzyme-catalyzed reactions and to those who have made previous thermodynamic tables that contain information needed in biochemical thermodynamics. 

If and Aa, A/S, etc.,. re available from thermal measurements, it is possible to derive AHo by utilizing the procedure described in 12k if if is known at any one temperature, it is possible to evaluate the integration constant and the variation of In K (or log K) with temperature can then be expressed in the form of equation (33.30). The accuracy of the resulting expression is limited largely by the thermal data, for these are often not known with great certainty. Care should be taken to ensure that the standard states used in connection with the heat of reaction A// are aL- o those employed for the equilibrium constant. Actually, the standard states chosen in 30b, 31b correspond with those almost invariably employed in both equilibrium studies and heat of reaction measurements. 

The thermodynamics of the more important reactions in catalytic reforming can be discussed conveniently by referring to the equilibria involved in the various interconversions among certain of the C hydrocarbons. Some thermodynamic equilibrium constants at 500°C., a typical temperature in catalytic reforming, and heats of reaction are given in Table I. The equilibrium constants in Table I apply when the partial pressures of the various components are expressed in atmospheres. 

The equilibrium state in a chemical reaction can be considered from two distinct points of view. The first is from the standpoint of classical thermodynamics, and leads to relationships between the equilibrium constant and thermodynamic quantities such as free energy and heat of reaction, from which we can very usefully calculate equilibrium conversion. The second is a kinetic viewpoint, in which the state of chemical equilibrium is regarded as a dynamic balance between forward and reverse reactions at equilibrium the rates of the forward reactions and of the reverse reaction are just equal to each other, making the net rate of transformation zero. 

A. Activation Energies and Heats of Reaction. If we restrict our attention to the general relation between rate constants and the equilibrium constant implied by Eq. (IV.3.15), we can proceed to identify some other rate quantities with thermodynamic quantities. From Eq. (IV.3.16),... 

The equilibrium constant can therefore be calculated for all temperatures when the vapour pressure constant, the heat of reaction at a given temperature, and, finally, the temperature coefficients of the specific heats (and hence 2a) are given. For the formation of water vapour from the elements, the calculation is as follows ... 

Note that there is considerable scatter in the results, which is an indication of the difficulty in obtaining accurate thermodynamic data for some biochemical reactions. It is also interesting to notice that the results for the equilibrium constants, Gibbs energies of reaction, and heats of reaction are all affected by pH. This is typical of reactions involving compounds that can ionize, as discussed earlier and will be considered in greater detail in Chapter 15. ... 

It is often the solvent effect fliat is flie only method of radical change of relative contents of different conformer forms. Thus, with flie help of the isochore equation of chemical reaction, flie data on equilibrium constants and enthalpies of dichloroacetaldehyde conformer transformation allow us to calculate that, to reach the equilibrium constant of axial rotamer formation in cyclohexane as solvent (it is equal to 0.79) to magnitude K=0.075 (as it is reached in DMSO as solvent), it is necessary to cool the cyclohexane solution to 64K (-209"C). At the same time, it is not possible because cyclohexane freezing point is -l-6.5"C. By analogy, to reach flie dimefliylsulfoxide constant to value of cyclohexane , DMSO solution must be heated to 435K (162"C). 

It is frequently stated that kinetics and thermodynamics are two completely different subjects. This is an oversimplification which is misleading if it conveys the impression that thermodynamics is useless in the study of reaction rates. First of all, as was seen in Chapter 2, the theory of reaction rates is essentially an equilibrium theory. It permits us to evaluate pre-exponential factors of rate constants of elementary steps, at least in order of magnitude. As to the estimation of activation barriers, this can be done in certain cases, as will be seen shortly, by means of correlations between activation barriers and heats of reactions. Finally, in the treatment of reactions in concentrated acid solutions, it is frequently possible to relate rate constants to a purely thermodynamic quantity, the acidity function, which will also be introduced in this chapter. 

Because G, H, and S are state functions, the thermodynamic equilibrium constant and the molar reaction quantities evaluated from Egg, g and dE°g g / dT are the same quantities as those for the reaction when it takes place in a reaction vessel instead of in a galvanic cell. However, the heats at constant T and p are not the same (page 318). During a reversible cell reaction, dS must equal dq/T, and dq/d is therefore equal to TArS° during a cell reaction taking place reversibly under standard state conditions at constant T and p. 

A consistent set of the thermodynamic data required for calculations was originally given by Beattie and by Gillespie and Beattie. The equilibrium constant, fugacity coefficients, and heat of reaction can be obtained from the following sources ... 

The first step in designing a reaction system is to establish the thermodynamic equilibrium relationship between the reactants and products and to calculate the heat effects of the reaction. This step is vital because the equilibrium constants and heat effects, which may be readily calculated [88, 89], will immediately tell us whether the reaction is in fact feasible thermodynamically and whether some special precautions are needed to remove the products and... 

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 ). 

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