Equilibrium constant pressure dependency

Whereas the equilibrium constant itself depends on the temperature only, the conversion at equilibrium depends on the composition of the original reaction mixture and, in general, on the pressure. If the equilibrium constant is very high, the reaction may be treated as being irreversible. If the equilibrium constant is low, however, it may be possible to obtain acceptable conversions only by using high or low pressures. Two important examples are the reactions ... 

At 25 °C observed values of the rate constant k and the equilibrium constant K depend on pressure as follows ... 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

The equilibrium constant K depends only on the temperature and not on the pressure. 

Because NO formation involves an alteration of n, the equilibrium constant K2 depends not only on the temperature, but also on the total pressure p. 

The numerical value of kt in (2-3) depends on how activity is defined and on the units in which concentration is expressed (molarity, mole fraction, partial pressure). Measurement of the absolute activity, or chemical potential, of an Individual ion is one of the classical unsolved problems. Since we cannot measure absolute ion activity, we are then necessarily interested in the next best—comparative changes in activities with changing conditions. To obtain comparative values numerically, we measure activity with respect to an arbitrarily chosen standard state under a given set of conditions of temperature and pressure, where the substance is assigned unit activity. The value of ki in (2-3) thus depends on the arbitrary standard state chosen accordingly, the value of the equilibrium constant also depends on the choice of standard states. 

This form of equation (2.5.79) does not allow us to make any conclusions about the form of the pOw-pO dependence and its slope, since the transformation of this equation into logarithmic values does not result in explicit solutions. Therefore, the calculations of magnitudes were performed for specific values of oxide-ion concentrations, partial pressures of water vapour and equilibrium constants. The dependences obtained in such a manner are presented in Fig. 2.5.11. It should be noted that not all of these plots are strictly linear, and have an appreciable bending toward the abscissa axis. 

The equilibrium constant Keq depends on the nature of the reactants and products, the temperature, and the pressure (particularly In reactions Involving gases). Under standard physical conditions (25 "C and 1 atm pressure, for biological systems), the Keq Is always the same for a given reaction, whether or not a catalyst Is present. 

At low concentrations the equilibrium constant k depends on the temperature (and perhaps pH, ionic simegth, or pressure) but not on the concentrations of the other solutes. Then the solute velocity for linanr systems is... 

It is known from thermodynamics that the boiling point at constant pressure depends on the purity of the more volatile component. The majority of chemical reactions under reflux conditions are performed in a solvent for the reactants. Due to the change in composition of the reaction mixture, changes in the boiling temperature may be observed. In the case of irreversible reactions, this change in composition will occur until the limiting component has been consumed or until the equilibrium conversion has been reached. This fact usually results in differing calibration factors determined be-... 

The equation can be normalized, because F(l) will refer to the sum of the partial pressures. The equilibrium constant is dependent on the temperature. 

Before a reaction-equilibrium calculation can be performed, we must select an appropriate standard state for each species. Moreover, we must clearly distinguish quantities, such as fugacities and activities, that depend on the final equilibrium state (T, P, x ), from those quantities, such as equilibrium constants, that depend only on the equilibrium temperature T, the standard-state pressures P , and the phase. Typically, the standard-state pressure and phase are chosen according to whether the real substance is gas, liquid, or solid at the equilibrium conditions. Those three possibilities are discussed, in turn, here, and each discussion culminates with a particular expression for the activity. Those expressions can be used either in the stoichiometric development, via (10.3.14), or in the nonstoichiometric development, via (10.3.38). We emphasize that when we use the stoichiometric approach, the standard states used for the fugacities must be consistent with those associated with the equilibrium constant. 

In Figure 10.7 the center of the graph is at the oxygen partial pressure that is in equilibrium with the stoichiometric oxide MjOi. The value of the equilibrium constants and depends on the reaction heat for oxidation or reduction of the oxide. Ki depends exponentially on the bandgap. This figure shows how oxygen pressures affect the electic behavior of the oxide ... 

The equilibrium constant only depends on the partial pressure of the steam and hydrogen sulfide ... 

The equilibrium constant Kp depends only on ArG, defined at standard pressure Po, and thus JCp depends on temperature only but not on pressure. Formally, this is expressed as ... 

The equilibrium constant Kp depends only on ArG°, defined at standard pressure Po, and thus Kp depends on temperature only and not on pressure. This does not mean that the amounts of the species at equilibrium, that is, the composition, do not depend on the total pressure p, if the reaction leads to a difference between the number of moles of the reactants and products. For example, an increase of the number of gas particles (Sv, >0) leads to a decrease of Ky with increasing pressure (Le Chatalier sprinciple). 

The equilibrium constant does depend on what pressure we choose for our values of Ag°. If we always choose these as states at which the pressure = 1.00 bar—which most current tables of properties do—then there is little opportunity for confusion here. Unfortunately, some tables of properties also have other choices, so that the values of K calculated from them are different from those calculated for P= 1.00 bar. If we are careful to learn what values of Ag° are used, we will always get the correct calculated concentrations. (Older tables mostly used P= 1.00 atm newer ones mostly use P = 1.00 bar. The differences are small, but not zero, see Problem 12.15.)... 

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

Figure B2.5.7 shows the absorption traces of the methyl radical absorption as a fiinction of tune. At the time resolution considered, the appearance of CFt is practically instantaneous. Subsequently, CFl disappears by recombination (equation B2.5.28). At temperatures below 1500 K, the equilibrium concentration of CFt is negligible compared witli (left-hand trace) the recombination is complete. At temperatures above 1500 K (right-hand trace) the equilibrium concentration of CFt is appreciable, and thus the teclmique allows the detennination of botli the equilibrium constant and the recombination rate [54, M]. This experiment resolved a famous controversy on the temperature dependence of the recombination rate of methyl radicals. Wliile standard RRKM theories [, ] predicted an increase of the high-pressure recombination rate coefficient /r (7) by a factor of 10-30 between 300 K and 1400 K, the statistical-adiabatic-chaunel model predicts a...

Equilibrium constants for protein-small molecule association usually are easily measured with good accuracy it is normal for standard free energies to be known to within 0.5 kcal/mol. Standard conditions define temperature, pressure and unit concentration of each of the three reacting species. It is to be expected that the standard free energy difference depends on temperature, pressure and solvent composition AA°a also depends on an arbitrary choice of standard unit concentrations. 

These data can be used to obtain the value of the equilibrium constant at any temperature and this in turn can be used to calculate the degree of dissociation through the equation for the conceiiuation dependence of the constant on the two species for a single element, die monomer and the dimer, which coexist. Considering one mole of the diatomic species which dissociates to produce 2x moles of the monatomic gas, leaving (1 — jc) moles of the diatomic gas and producing a resultant total number of moles of (1 +jc) at a total pressure of P atmos, the equation for the equilibrium constant in terms of these conceiiU ations is... 

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. 

Clausius-Clapeyron equation An equation expressing the temperature dependence of vapor pressure ln(P2/Pi) = AHvapCl/Tj - 1/T2)/R, 230,303-305 Claussen, Walter, 66 Cobalt, 410-411 Cobalt (II) chloride, 66 Coefficient A number preceding a formula in a chemical equation, 61 Coefficient rule Rule which states that when the coefficients of a chemical equation are multiplied by a number n, the equilibrium constant is raised to the nth power, 327... 

The ambiguity results from the failure to recognize that the Rossini statement applies to the thermodynamic equilibrium constant, As we have already noted, the other forms that we have derived do depend upon the pressure. For example, for a gas phase reaction, Kp is related to K by equation (9.11)... 

Given any two of the four quantities EC, Aik, pH, Pco,/ the other two can always be calculated provided appropriate equilibrium constants are available (the equilibrium constants depend on temperature, salinity and pressure). Hydrogen ion concentration, for example, be calculated from Aik and EC with the equation... 

As previously noted, the equilibrium constant is independent of pressure as is AG. Equation (7.33) applies to ideal solutions of incompressible materials and has no pressure dependence. Equation (7.31) applies to ideal gas mixtures and has the explicit pressure dependence of the F/Fq term when there is a change in the number of moles upon reaction, v / 0. The temperature dependence of the thermodynamic equilibrium constant is given by... 

Hence, the reaction order is seen to depend both on the equilibrium constant K2, which depends on temperature, and the actual partial pressure p2- We shall later see that the latter term for a catalyst is related to the extent that the surface is covered by a reactant. 

The material balance was calculated for EtPy, ethyl lactates (EtLa) and CD by solving the set of differential equation derived form the reaction scheme Adam s method was used for the solution of the set of differential equations. The rate constants for the hydrogenation reactions are of pseudo first order. Their value depends on the intrinsic rate constant of the catalytic reaction, the hydrogen pressure, and the adsorption equilibrium constants of all components involved in the hydrogenation. It was assumed that the hydrogen pressure is constant during... 

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