Pressure-based equilibrium constants

Because pressures arc easier to measure than particle numbers for gases, it is often more convenient to use equilibrium constants Kp based on pressures rather than equilibrium constants K based on the numbers of molecules. Combining Equation (13.18) with the ideal gas law N = pV/kT gives... 

In contrast to sulfur oxidation to SO2, the oxidation to SO3 is limited by thermodynamic constraints (Example 4.2.3), and is the crucial reaction step in H2SO4 production. According to Eqs. (4.2.19) and (4.2.20), the equilibrium constant Ky based on the molar fractions of SO2, O2, and SO3 (with p as total pressure) is given by ... 

The rate constant k has the dimension of mol/g of the catalyst, while the partial pressures are given in bar. The equilibrium constant is based on partial pressures, Kp (bar ). The rate of the reaction is negligible below 670 K,... 

The thermite reaction is an oxidation-reduction reaction that uses powdered aluminum metal as a reducing agent to reduce a metal oxide, such as Fe203, to the free metal. The thermodynamic equilibrium constant, K, is an equilibrium constant expression based on activities. In dilute solutions activities can be replaced by the numerical values of molarities and in ideal gases, by the numerical values of partial pressures in bar. The activities of pure solids and liquids are 1. 

Since in most practical circumstances at temperatures where vapour transport is used and at around one atmosphere pressure, die atomic species play a minor role in the distribution of atoms, it is simpler to cast the distribution equations in terms of the elemental molecular species, H2, O2 and S2, tire base molecules, and the derived molecules H2O, H2S, SO2 and SO3, and eliminate any consideration of the atomic species. In this case, let X, be tire initial mole fraction of each atomic species in the original total of atoms, aird the variables Xi represent the equilibrium number of each molecular species in the final number of molecules, N/. Introducing tire equilibrium constants for the formation of each molecule from tire elemental atomic species, with a total pressure of one aurros, we can write... 

In the case of tire direct oxidation, the oxygen partial pressure must be greater than that at the Pb/PbO equilibrium, while in the process involving sodium-based salts, the oxygen pressure is less than this. The two equilibrium constants for the refining reactions... 

The pressure-jump (P-jump) method is based on the pressure dependence of the equilibrium constant, Eq. (4-28), where AV is the molar volume change of the reaction. 

We have seen that the value of an equilibrium constant tells us whether we can expect a high or low concentration of product at equilibrium. The constant also allows us to predict the spontaneous direction of reaction in a reaction mixture of any composition. In the following three sections, we see how to express the equilibrium constant in terms of molar concentrations of gases as well as partial pressures and how to predict the equilibrium composition of a reaction mixture, given the value of the equilibrium constant for the reaction. Such information is critical to the success of many industrial processes and is fundamental to the discussion of acids and bases in the following chapters. 

The calculation is based on the rule of thermodynamics, which states that a system will be in equilibrium when the Gibbs free energy is at a minimum. Cl The objective then is the minimization of the total free energy of the system and the calculation of equilibria at constant temperature and volume or at constant pressure. It is a complicated and lengthy calculation but, fortunately, several computer programs are now available that considerably simplify the task. PI... 

Specific heat Molar flow of inert air Equilibrium constant Overall mass transfer capacity coefficient base on the gas phase Molar flow of solute-free water Pressure Density... 

KP Equilibrium constant of reaction based on partial pressure in the vapor phase (-)... 

Expressions for 9 SM and H2 can be derived and related to rate (k) and equilibrium constants (K). The SI and S2 site balances are 9SM +9a + S, = 1 and //2 + S2 = 1 respectively 9sx, S2 are empty sites). Based on Henry s law, the gas-phase hydrogen pressure and the liquid-phase hydrogen concentration may be used interchangeably. The rate expression can be written as follows ... 

All partitioning properties change with temperature. The partition coefficients, vapor pressure, KAW and KqA, are more sensitive to temperature variation because of the large enthalpy change associated with transfer to the vapor phase. The simplest general expression theoretically based temperature dependence correlation is derived from the integrated Clausius-Clapeyron equation, or van t Hoff form expressing the effect of temperature on an equilibrium constant Kp,... 

The equilibrium state is generated by minimizing the Gibbs free energy of the system at a given temperature and pressure. In [57], the method is described as the modified equilibrium constant approach. The reaction products are obtained from a data base that contains information on the enthalpy of formation, the heat capacity, the specific enthalpy, the specific entropy, and the specific volume of substances. The desired gaseous equation of state can be chosen. The conditions of the decomposition reaction are chosen by defining the value of a pair of variables (e.g., p and T, V and T). The requirements for input are ... 

GASEQ A Chemical Equilibrium Program for Windows. GASEQ is a PC-based equilibrium program written by C. Morley that can solve several different types of problems including composition at a defined temperature and pressure, adiabatic temperature and composition at constant pressure, composition at a defined temperature and at constant volume, adiabatic temperature and composition at constant volume, adiabatic compression and expansion, equilibrium constant calculations, and shock calculations. More information can found at the website http //www.arcl02.dsl.pipex.com/gseqmain.htm. 

Many different types of reversible reactions exist in chemistry, and for each of these an equilibrium constant can be defined. The basic principles of this chapter apply to all equilibrium constants. The different types of equilibrium are generally denoted using an appropriate subscript. The equilibrium constant for general solution reactions is signified as or K, where the c indicates equilibrium concentrations are used in the law of mass action. When reactions involve gases, partial pressures are often used instead of concentrations, and the equilibrium constant is reported as (p indicates that the constant is based on partial pressures). and are used for equilibria associated with acids and bases, respectively. The equilibrium of water with the hydrogen and hydroxide ions is expressed as K. The equilibrium constant used with the solubility of ionic compounds is K p. Several of these different K expres-... 

Step 16. Fit C6 adsorption equilibrium constants h Kh) at the base conditions by using C6 data at 756 K and 1220 kPa H2 partial pressure. 

In applying equation 33, Cpsl (the constant-pressure molar heat capacity of the stoichiometric liquid) is usually extrapolated from high-temperature measurements or assumed to be equal to Cpij of the compound, whereas the activity product, afXTjafXT), is estimated by interjection of a solution model with the parameters estimated from phase-equilibrium data involving the liquid phase (e.g., solid-liquid or vapor-liquid equilibrium systems). To relate equation 33 to an available data base, the activity product is expressed... 

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