Equilibrium constant heterogeneous system

Because the expression for Kn is simpler than that for Kb it is the equilibrium constant of choice for the heterogeneous system. 

The kinetic factor is proportional to the energetic state of the system and (for heterogeneous catalytic systems) the number of active sites per unit volume (mass) of catalyst. The driving-force group includes the influence of concentration and distance from chemical equilibrium on the reaction rate, and the hindering group describes the hindering effect of components of the reaction mixture on the reaction rate. The kinetic factor is expressed as the rate constant, possibly multiplied by an equilibrium constant(s) as will be shown later. 

The system, therefore, is at equilibrium at a given temperature when the partial pressure of carbon dioxide present has the required fixed value. This result is confirmed by experiment which shows that there is a certain fixed dissociation pressure of carbon dioxide for each temperature. The same conclusion can be deduced from the application of phase rule. In this case, there are two components occurring in three phases hence F=2-3 + 2 = l, or the system has one degree of freedom. It may thus legitimately be concluded that the assumption made in applying the law of mass action to a heterogeneous system is justified, and hence that in such systems the active mass of a solid is constant. 

A great many electrolytes have only limited solubility, which can be very low. If a solid electrolyte is added to a pure solvent in an amount greater than corresponds to its solubility, a heterogeneous system is formed in which equilibrium is established between the electrolyte ions in solution and in the solid phase. At constant temperature, this equilibrium can be described by the thermodynamic condition for equality of the chemical potentials of ions in the liquid and solid phases (under these conditions, cations and anions enter and leave the solid phase simultaneously, fulfilling the electroneutrality condition). In the liquid phase, the chemical potential of the ion is a function of its activity, while it is constant in the solid phase. If the formula unit of the electrolyte considered consists of v+ cations and v anions, then... 

It is most important to know in this connection the compressibility of the substances concerned, at various temperatures, and in both the liquid and the crystalline state, with its dependent constants such as change of. melting-point with pressure, and effect of pressure upon solubility. Other important data are the existence of new pol3miorphic forms of substances the effect of pressure upon rigidity and its related elastic moduli the effect of pressure upon diathermancy, thermal conductivity, specific heat capacity, and magnetic susceptibility and the effect of pressure in modif dng equilibrium in homogeneous as well as heterogeneous systems. 

Partition Coefficient A constant ratio that occurs when a heterogeneous system of two phases is in equilibrium the ratio of concentrations (or strictly activities) of the same molecular species in the two phases is constant at constant temperature. 

The mass-action equations have been written in the same form as those given by Marynowski et al. (6) so that the equilibrium constants can be used directly. (Should more accurate data become available, the equilibrium yields calculated here will require revision.) The fourth equation, which applies to the heterogeneous equilibrium between carbon and nitrogen, is included for completeness but is unnecessary for the general solution. It can be shown that when the total pressure of the system is F, the partial pressure of cyanogen radicals is given by the equation ... 

When the system is heterogeneous—i.e., the temperature and pressure are such that solid carbon exists in equilibrium with its vapor, the value of Pci is uniquely determined by the temperature and can be calculated directly from the equilibrium constant Ki. Hence in a heterogeneous system, the partial pressure of cyanogen radicals and of cyanogen depend only on the temperature... 

The production of species i (number of moles per unit volume and time) is the velocity of reaction,. In the same sense, one understands the molar flux, jh of particles / per unit cross section and unit time. In a linear theory, the rate and the deviation from equilibrium are proportional to each other. The factors of proportionality are called reaction rate constants and transport coefficients respectively. They are state properties and thus depend only on the (local) thermodynamic state variables and not on their derivatives. They can be rationalized by crystal dynamics and atomic kinetics with the help of statistical theories. Irreversible thermodynamics is the theory of the rates of chemical processes in both spatially homogeneous systems (homogeneous reactions) and inhomogeneous systems (transport processes). If transport processes occur in multiphase systems, one is dealing with heterogeneous reactions. Heterogeneous systems stop reacting once one or more of the reactants are consumed and the systems became nonvariant. 

A cell may be considered as a heterogenous system at equilibrium with restrictions. In most cells the pressure on each phase is the same and a change of pressure of the system would cause the same change of pressure on all phases. However, it is possible to construct a cell so that the various phases may have different pressures. Then the pressures of some phases may be held constant while the pressures of other phases are changed. In such cases some of the derivatives of the chemical potentials in Equation (12.86) would be zero unless matter would have to be transported across the boundary between phases in order to maintain the equilibrium conditions with a change of pressure. 

According to thermodynamics, when a heterogeneous system is in equilibrium, at constant pressure and temperature, the chemical potential (p) of any given component must be the same in every phase. Therefore, if there is one component in three phases x, y and z and one of these phases, say x is referred to as standard phase, then this fret may be represented in the form of two equations ... 

Electrochemical methods are well established and use relatively inexpensive equipment to produce unique characterization information for molecules and chemical systems qualitative (speciation) and quantitative analytical data, thermodynamic data (equilibrium constants), and kinetic data (heterogeneous and homogeneous reaction rates). 

This equation, combining the first and second laws, is derived for the special case of a reversible process. However, it contains only properties of the system. Properties depend on state alone, and not on the kind of process that produces the state. Therefore, Eq. (6.1) is not restricted in application to reversible processes. However, the restrictions placed on the nature of the system cannot be relaxed. Thus Eq. (6.1) applies to any process in a system of constant mass that results in a differential change from one equilibrium state to another. The system may consist of a single phase (a homogeneous system), or it may be made up of several phases (a heterogeneous system) it may be chemically inert, or it may undergo chemical reaction. The only requirements are that the system be closed and that the change occur between equilibrium states. 

The mechanism given above places no restrictions on the source of the reversible poison. Consequently, the poisoning can be due not to an adsorption competition between the reactant and a diluent but to an adsorption competition between the reactant and one or more of the reaction products. When this occurs the products will determine the kinetics in the flow type and static systems where appreciable conversion is allowed. Under these conditions the kinetics may be expressed by equations similar to equation (6), and the order will be determined by the magnitude of constants similar to H which depend upon the various velocity constants and adsorption equilibrium constants of the heterogeneous reaction. 

It is opportune to recall here the remarks made in 32g in connection with heterogeneous reactions. If the activities of pure solids and liquids taking part in the process are taken as unity, then the true equilibrium constant is obtained only if the total pressure of the system is 1 atm. Unless allowance is made for the effect of pressure on the activities, the constants obtained at other pressures vary with pressure in a manner dependent on the volume change of the solid and liquid phases involved in the reaction [cf. equation (31.7)]. 

Heterogeneous physical equilibria, e.g., between a pure solid and its vapor or a pure liquid and its vapor, can be treated in a manner similar to that just described. If the total pressure of the system is 1 atm., the fugacity of the vapor is here also equivalent to the equilibrium constant. The variation of In/ with temperature is again given by equation (33.16), where MP is now the ideal molar heat of vaporization of the liquid (or of sublimation of the solid) at the temperature T and a pressure of 1 atm. If the total pressure is not 1 atm., but is maintained constant at some other value, the dependence of the fugacity on the temperature can be expressed by equation (29.22), since the solid or liquid is in the pure state thus,... 

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