Equilibrium expressions involving pressures

This equilibrium constant is often given the symbol Kp to emphasize that it involves partial pressures. Other equilibrium expressions for gases are sometimes used, including Kc ... 

The expression for K involving the concentrations of the species involved is found to be independent of volume. This implies that any change of pressure is not going to change the final state of equilibrium. The same result can be obtained by taking into consideration the alternative expression involving the partial pressures. If the pressure on the system is increased to n times its original value then all the partial pressures will be increased in the same proportion. This obviously implies that the equilibrium is independent of the pressure. The effect of some other factors on this reaction may now be considered. One such factor can be the addition of substances. For example, on addition of more A2, the partial pressure of A2 in the reactor would increase momentarily from pAl to some value, p A/. It has already been seen that... 

The fact that the curvature of the surface affects a heterogeneous phase equilibrium can be seen by analyzing the number of degrees of freedom of a system. If two phases a and are separated by a planar interface, the conditions for equilibrium do not involve the interface and the Gibbs phase rule as described in Chapter 4 applies. On the other hand, if the two coexisting phases a and / are separated by a curved interface, the pressures of the two phases are no longer equal and the Laplace equation (6.27) (eq. 6.35 for solids), expressed in terms of the two principal curvatures of the interface, defines the equilibrium conditions for pressure ... 

Although one can probably find exceptions, most equilibrium calculations involving flue gas slurries are performed with temperature as a known variable. With temperature known, the numerical values of the appropriate equilibrium constants can be immediately calculated. The remaining unknown variables to be determined are the activities, activity coefficients, molalities, and the gas phase partial pressures. The equations used to determine these variables are formulated from among the equilibrium expressions presented in Table 1, the expressions for the activity coefficients, ionic strength, material balance expressions, and the electroneutrality balance. Although there are occasionally exceptions, the solution sequence generally is an iterative or cyclic sequence. 

Commonly, gas-liquid partitioning is expressed by the saturated liquid vapor pressure, pi, of the compound i. This important chemical property will be discussed in detail in Chapter 4. Briefly, pi is the pressure exerted by the compound s molecules in the gas phase above the pure liquid at equilibrium. Since this pressure generally involves only part of the total pressure, we often refer to it as a partial pressure due to the chemical of interest. In this case, when there is no more build up of vapor molecules in a closed system, we say that the gas phase is saturated with the compound. Note that because pa. is strongly temperature dependent, when comparing vapor pressures of different compounds to see the influence of chemical structure, we have to use pi values measured at the same temperature (which also holds for all other equilibrium constants discussed later see Section 3.4). 

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... 

The conditions of equilibrium expressed by Equations (5.25)—(5.29) and (5.46) involve the temperature, pressure, and chemical potentials of the components or species. The chemical potentials are functions of the temperature, pressure or volume, and composition, according to Equations (5.54) and (5.56). In order to study the equilibrium properties of systems in terms of these experimentally observable variables, expressions for the chemical potentials in terms of these variables must be obtained. This problem is considered in this chapter and in Chapter 8. 

The convention we follow in this book is to describe chemical equilibrium in terms of the thermodynamic equilibrium constant K, even when analyzing reactions empirically. Consequently, for gaseous reactions we will state values of K without dimensions, and we will express all pressures in atmospheres. The Pref factors will not be explicitly included because their value is unity with these choices of pressure unit and reference pressure. Following this convention, we write the mass action law for a general reaction involving ideal gases as... 

The equilibrium pressures can now be calculated from the expressions involving x ... 

In general, activities are difficult to measure experimentally. Various ideal approximations to the equilibrium constant involving the use of concentrations and partial pressures in place of activities are in more prevalent use than the exact expression. In ideal gaseous systems. 

We will often omit the P° from equilibrium constant expressions involving gases and write a, = with the understanding that P, is a dimensionless quantity numerically equal to the partial pressure in bar. 

From the quadratic formula, the correct value for x is jc = 3.55 X 10 atm. The equilibrium pressures can now be calculated from the expressions involving x ... 

For each of the expressions given above, equilibrium values of activities, partial pressures, and molarities are implied. Also, these are thermodynamic equilibrium expressions since they are written in terms of their activities. The values of the thermodynamic equilibrium constant will be dimensionless. All the expressions given above for K include factors involving powers of c" or P". As described in the text (page 611), we can avoid the complication of having to evaluate these factors by judiciously choosing to express concentrations in mol/L and pressures in bar. 

---