Equilibrium constant for gas-phase reaction

Only one equilibrium constant for gas-phase reactions (Chapter 12), the thermodynamic constant K, often referred to as Kp. This simplifies not only the treatment of gaseous equilibrium, but also the discussion of reaction spontaneity (Chapter 17) and electrochemistry (Chapter 18). 

FIGURE 7.5 Thermodynamic equilibrium constant for gas-phase reactions. (From Smith, J. M. and Van Ness, H. C., Introduction to Chemical Engineering Thermodynamics, 4th Ed., McGraw-Hill, New York, 1986.)... 

Although equilibrium constants for gas-phase reactions are evaluated by (15.14) with data for ideal-gas standard states, they are related by Eq. (15.1... 

F ure 7.5 Themodynamic equilibrium constants for gas phase reactions. From J. M. Smith, and... 

In other cases, they have been derived from experimental measurements of the equilibrium constants for gas-phase reactions such as... 

Table 13.21 Comparison of equilibrium constants for gas-phase reaction H O -t- HDS HDO + HjSt...

We have noted before that the determination of equilibrium constants for gas phase reactions is very difficult since (a) reactions do not proceed without a catalyst and (b) catalysts are not specific and lead to simultaneous and consecutive reactions. This is the area where statistical thermodynamics is particularly useful. For a gas phase reaction... 

H humidity, mol water/mol noncondensible gas I inventory, mol / aimual charge against investment k equilibrium constant for gas-phase exchange reaction K total tails flow rate... 

The component reactions in eqn. (2) are very fast, and the system exists in equilibrium. Additional carbon dioxide entering the sea is thus quickly converted into anions, distributing carbon atoms between the dissolved gas phase, carbonate and bicarbonate ions. This storage capacity is clear when the apparent equilibrium constants for the two reactions in eqn. (2) are examined, namely... 

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 ). 

If a chemical equation can be expressed as the sum of two or more chemical equations, the equilibrium constant for the overall reaction is the product of the equilibrium constants for the component reactions. For example, consider the three gas-phase reactions... 

If we introduce the equilibrium constant for the overall reaction in the gas phase. 

For gas-phase reactions, when combining Eqns. (5.4-8) and (5.4-9), the equilibrium constant is expressed as ... 

Basicity in the gas phase is measured by the proton affinity (PA) of the electron donor and in solution by the pAj,. A solution basicity scale for aldehydes and ketones based on hydrogen bond acceptor ability has also been established [186]. Nucleophilicity could be measured in a similar manner, in the gas phase by the affinity for a particular Lewis acid (e.g., BF3) and in solution by the equilibrium constant for the complexation reaction. In Table 8.1 are collected the available data for a number of oxygen systems. It is clear from the data in Table 8.1 that the basicities of ethers and carbonyl compounds, as measured by PA and p , are similar. However, the nucleophilicity, as measured by the BF3 affinity, of ethers is greater than that of carbonyl compounds, the latter values being depressed by steric interactions. 

One word of warning when using the van t Hoff equation for gas-phase reactions, the equilibrium constants must be K, not Kc. If we want a new value for Kc for a gas-phase reaction, we use the van t Hoff equation to calculate the new value of K first, and then convert that K to the new Kc by using Eq. 14. 

The equilibrium constant Kp can be used for gas-phase reactions. It is defined in the same way as Kc except that the equilibrium constant expression contains partial pressures (in atmospheres) instead of molar concentrations. The constants Kp and Kc are related by the equation Kp = Kc(RT)An, where A n = (c + d) — (a + b). 

Table 4.14 Equilibrium constants and compositions for gas-phase reaction (4.16)...

Advances in the development of theoretical methods and computer construction are indispensable for the growing feasibility of ab initio calculations, but this alone does not guarantee a future widespread use of ab initio calculations by chemists in solving their problems. What is demanded by chemists is a high predictive power of theory in various branches of chemistry, A classical example of how the ab initio calculations should meet the needs of chemists was provided as early as in 1967 by dementi and Gayles " in their study on the complex NH. HCl, The calculation of the potential hypersurfaces and a detailed analysis of wave functions of both the complex and the dissociation components showed that NH Cl may exist in the gas phase. For the first time, the results of ab initio calculations were used for the evalua-tion of the equilibrium constant for a chemical reaction. Predicted equilibrium constants for the process NH2(g) + HCl(g) NH Cl(g) at different temperatures suggested the experimental conditions at which... 

The square bracket [X] represents the concentration of species X in units of mol If all factors containing c ef are collected on the right side and the reference state for each reactant and product is defined to be an ideal solution with a concentration c f = 1 M, then the same arguments used before for gas-phase reactions show that the dimensionless thermodynamic equilibrium constant K is numerically equal to Kq. 

Once the chemical reaction equilibrium constant (for a particular reaction) has been determined, one can proceed to estimate the quantities of the participating species at equilibrium. The problem that remains is to relate K to understandable physical quantities. For gas-phase reactions, as in an incinerator operation, the term K may be approximately represented in terms of the partial pressures of the components involved. This functional relationship for the hypothetical reaction... 

There are many other types of solution data that support the half-wave reduction potential and charge transfer complex data. These include the measurement of cell potentials or equilibrium constants for electron transfer reactions. Another important condensed phase measurement involving a negative ion is the determination of electron spin resonance spectra. In these studies the existence of a stable molecular anion is established and the spin densities can be measured [79]. The condensed phase measurements support the electron affinities in the gas phase and extend the measurements to lower valence-state electron affinities. 

So far we have not touched on the fact that the important topic of solvation energy is not yet taken into account. The extent to which solvation influences gas-phase energy values can be considerable. As an example, gas-phase data for fundamental enolisation reactions are included in Table 1. Related aqueous solution phase data can be derived from equilibrium constants The gas-phase heats of enolisation for acetone and propionaldehyde are 19.5 and 13 kcal/mol, respectively. The corresponding free energies of enolisation in solution are 9.9 and 5.4 kcal/mol. (Whether the difference between gas and solution derives from enthalpy or entropy effects is irrelevant at this stage.) Despite this, our experience with gas-phase enthalpies calculated by the methods described in this chapter leads us to believe that even the current approach is most valuable for evaluation of reactivity. 

A gas-solid catalytic reaction of the type A + B Cis believed to occur by a molecule of B in the gas phase reacting with a molecule of A adsorbed on the catalyst surface. Preliminary experimental studies indicate that both external and internal diffusional resistances are negligible. Also, the equilibrium constant for the homogeneous reaction K = (pjpAP g is very large. 

Figure 7. Comparison of rate constants for reactions of ozone in aqueous films (left scales) and hour of reactions required and half-life scales (right) for the given pollutants in presence of 10 l M ozone (aqueous equilibrium cone, for gas-phase cone, of l(>, molecules cm ) )a(a from Hoigne anil Bader (10K3) and Hoigne et a I, (I OKS). ...

Sousa et al [5.76, 5.77] modeled a CMR utilizing a dense catalytic polymeric membrane for an equilibrium limited elementary gas phase reaction of the type ttaA +abB acC +adD. The model considers well-stirred retentate and permeate sides, isothermal operation, Fickian transport across the membrane with constant diffusivities, and a linear sorption equilibrium between the bulk and membrane phases. The conversion enhancement over the thermodynamic equilibrium value corresponding to equimolar feed conditions is studied for three different cases An > 0, An = 0, and An < 0, where An = (ac + ad) -(aa + ab). Souza et al [5.76, 5.77] conclude that the conversion can be significantly enhanced, when the diffusion coefficients of the products are higher than those of the reactants and/or the sorption coefficients are lower, the degree of enhancement affected strongly by An and the Thiele modulus. They report that performance of a dense polymeric membrane CMR depends on both the sorption and diffusion coefficients but in a different way, so the study of such a reactor should not be based on overall component permeabilities. 

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