Equilibrium expression with pressures

Reaction quotient (Q) An expression with the same form as Kbut involving arbitrary rather than equilibrium partial pressures, 333-334 Reaction rate The ratio of the change in concentration of a species divided by the time interval over which the change occurs, 285 catalysis for, 305-307 collision model, 298-300 concentration and, 287-292,314q constant, 288 enzymes, 306-307 egression, 288... 

This is a useful expression for calculating equilibrium concentrations. One can easily see that for an exothermic process (AH negative) the equilibrium concentration of products decreases with temperature, while it will also increase with pressure if the process consumes gas (vc + t A - < ) ... 

To construct such a diagram, a set of defect reaction equations is formulated and expressions for the equilibrium constants of each are obtained. The assumption that the defects are noninteracting allows the law of mass action in its simplest form, with concentrations instead of activities, to be used for this purpose. To simplify matters, only one defect reaction is considered to be dominant in any particular composition region, this being chosen from knowledge of the chemical attributes of the system under consideration. The simplified equilibrium expressions are then used to construct plots of the logarithm of defect concentration against an experimental variable such as the log (partial pressure) of the components. The procedure is best illustrated by an example. 

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. 

For first-order reactions then, there is no compressibility term in the expression for In k, no matter what concentration scale is used. For higher order reactions involving molar concentrations, Eq. (22) could be applied when accurate rate data are available. Whether Eq. (27) should be applied depends on the method used for obtaining the data. If a spectrophotometric determination of the relative decrease in [A] is used, a relative measure of (d In k/dp)T is obtained from Eq. (27). If an absolute determination of [A] can be made at various times, Eq. (24) can be used directly, and k and (d In k/dp)T can be immediately obtained. The situation is easily generalized to higher order kinetics. In some cases, where AVf < 0 and the method of measurement detects [A] but not [X ], there may be a slight displacement of the quasi-equilibrium with pressure which leads to different initial concentrations of A. When AVf can be determined from Eq. (22), it may appear pressure-dependent, i.e.,... 

This assumes H2O = 1, which is nearly true, even in seawater. For example, H2O = 0.98 at 35%o, 25°C, and 1 atm. As with other equilibrium expressions, and can be rewritten as stoichiometric constants that are specific for a particular temperature, pressure, and ionic strength. 

If the combustion products of a propellant attain a state of thermal equilibrium, the combustion temperature may be determined theoretically, as described in Chapter 2. However, the combustion in a rocket motor is incomplete and so the flame temperature remains below the adiabatic flame temperature.bl If one assumes that the flame temperature, T, varies with pressure, p, in a rocket motor, T is expressed byl5]... 

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). 

Equation (11.116) requires that the thermodynamic equilibrium constant cannot vary with pressure. There are, however, alternate expressions for the equilibrium constant that do change with pressure. For a gas-phase reaction such as the one that we are considering, the concentrations of species are often given in terms of their partial pressures, pt. Then,... 

Relationships (40.6) and (40.7) recognise the proportionality between concentration, c and partial pressure, pi (atm) at constant temperature, T (having the proportionality constant = 1 /RT). The former measure (concentration, c/) can be used when dealing with solutions which are present in reactions (see notes about solids in equilibrium expressions later - Frame 43). 

Component a making up a liquid phase (L) in contact with a gas phase (G) forms a two phase system. In the equilibrium state, the chemical potential of component a in the gas and contacting phase are equal. The equilibrium saturated vapor pressure of pure component a in the gas phase over the pure liquid phase a can be designated with p. Using the expression for a perfect gas, Eq. (4-1), for the chemical potential of a, one gets an expression of the chemical potential of component a in liquid a, p (L), in the equilibrium state ... 

Respired CO2 exit the soil largely via molecular diffusion, resulting in the more rapid escape of the lighter CO2 molecule with an expected kinetic fractionation, Sq, of 8.8 %c between soil CO2 at the soil-air interface and the flux of CO2 into the atmosphere. This theoretical value of 8.8%o is based on simple kinetic theory and the reduced mass of CO2 and air (Craig, 1953) but has not been measured, and it does not consider any effect of pressure gradients between the soil and the atmosphere. Sq can only be fully expressed if CO2 and water are in complete isotopic equilibrium until the soil surface. Since CO2 diffuses out of the soil faster than it can equilibrate with soil water, CO2 remaining in the soil will be enriched in 0, relative to its equilibrium value with water, as also predicted for in soils (Cerhng,... 

Thus for an exothermic reaction the equilibrium constant decreases with increasing temperature, the reverse being true of an endothermic reaction. This is one instance of Le Chatelie/s principle (1885) viz. the equilibrium always changes in such a way as to oppose any change in conditions. Similarly an increase in pressure facilitates a reaction which leads to a decrease in volume, as may be seen by expressing partial pressure in in terms of amounts of A, B etc. and an increase in amounts of reactants makes the reaction proceed further by its effect on Q. ... 

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... 

A is correct. Kp is equal to the partial pressure of COz" is the equilibrium expression for this reaction. If were less than the partial pressure of C02, the reaction would want to go to the left, but there would be no CaO to react to form CaC03. Regarding choice D, although solid CaO is required to achieve equilibrium, solid CaO could be formed with the decomposition of CaC03. 

In these expressions, the terms in the square brackets show how the Arrhenius constants are modified with further factors of temperature and pressure. It is evident from Eq. (4.8.11) that for > 0 and d < 0 the reaction rate will increase with pressure, for both the factor P in front increases and the equilibrium is shifted favorably by the decrease of P. ... 

Although the heat of adsorption or enthalpy change accompanying adsorption is directly obtained by calorimetry, it can conveniently be evaluated from the adsorption isostere. According to thermodynamics, the relationship between temperature T and pressure P under a state of -(J> phase equilibrium can generally be expressed with the Clausius-Clapeyron equation ... 

For this hydrate, Kp = P(n2o)5, so the partial pressure of water vapor that will be in equilibrium with the hydrate and the dehydrated solid (remember that both solids must be present to have equilibrium ), expressed in atmospheres, will be (12.5/760)5 = 1.20 x 1(T9. 

Gases in equilibrium constant expressions are often described with pressures instead of concentrations (mol/L). When an equilibrium constant is derived from gas pressures, we represent it with the symbol Kp. 

Given a balanced equation for a reversible chemical reaction that involves at least one gaseous substance, write its equilibrium constant, K/>, expression with the reactants and products described in terms of gas pressures. 

Figure 7 shows that the rate of adsorption, expressed as the time dependence of the fractional approach to equilibrium, decreased with increased partial pressure of SO2, which is rather unexpected. 

In its most general form, the fullerene synthesis could be treated as a complex kinetic scheme described by a huge number of kinetic differential equations. The equilibrium composition comes as the limiting case for infinite time. If we treat the problem from a thermodynamic point of view, we should realize that the conventional standard pressure of 1 atm is considerably different from the actual fullerene synthesis conditions. We should expect lower cluster pressures in the carbon-arc synthesis. The actual entropy and Gibbs free energy change with pressure as can be demonstrated [208-212] on the Cgo and C70 cases based on computed or observed [213] data. For example, the equilibrium constant Xgo/yo for an interconversion between the two clusters, expressed in partial pressures p, offers a deeper insight into the problem [208-212] ... 

Weiss and co-workers reported solubilities for He, " He, Ne, Ar, Kr as well as for O2 and N2 as a function of temperature and salinity for fresh and ocean waters (Table 1 Weiss 1970, 1971 Weiss and Kyser 1978). As this fundamental piece of work was strongly motivated by practical oceanographic research, the noble gas solubilities were expressed in the form of equilibrium concentrations with moist atmospheric air. For the atmosphere, it is justified to assume that its major elemental composition remains constant over the relevant time scales controlling gas exchange. Hence the gas partial pressure pi can be expressed by the total atmospheric pressure ptot corrected for water vapor content, Cw(T), and the volume or mole fraction Zi of the gas i in dry air (Ozima and Podosek 1983). 

Figure 12.3(b) shows that the equilibrium temperatures depend on the pressure, since the intersection points depend on pressure. The Clapeyron equation expresses the quantitative dependence of the equilibrium temperature on pressure, Eq. (12.12a), or the variation in the equilibrium pressure with temperature, Eq. (12.12b). Using this equation, we can plot the equilibrium pressure versus temperature schematically for any phase transformation. 

Several different subscripts are used with the equilibrium constant When all reactants or products that appear in the equilibrium expression are gases, and pressures are used instead of molarity, the symbol for the equilibrium constant is Kp. If weak acids and bases are under investigation, the equilibrium constant symbol is written as K or K,. When the equilibrium constant refers to the autoionization of water, the symbol K, is used. Solubility product equilibria express the ion concentrations of partially soluble salts. The equilibrium constant symbol K p is used for solubility product equilibria. ... 

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