Equilibrium constants molality

Table A-39 Equilibrium constants (molal scale) as a function of temperature and enthalpies and entropies of reaction at 25°C all values at/m = 2.204 m.

Equilibrium Basic Consideration, 1 Ideal Systems, 2 K-Factor Hydrocarbon Equilibrium Charts, 4 Non-Ideal Systems, 5 Example 8-1 Raoult s Law, 14 Binary System Material Balance Constant Molal Overflow Tray to Tray,... 

At 900 °F the equilibrium constant for this reaction is 5.62 when the standard states for all species are taken as unit fugacity. If the reaction is carried out at 75 atm, what molal ratio of steam to carbon monoxide is required to produce a product mixture in which 90% of the inlet CO is converted to C02 ... 

Here m>u and m>UCd++ are molal concentrations of the unoccupied and occupied sites, respectively, and aCd++ is the activity of the free ion. Activity coefficients for the surface sites are not carried in the equation they are assumed to cancel. Equilibrium constants reported in the literature are in many cases tabulated in terms of the concentrations of free species, rather than their activities, as assumed here, and hence may require adjustment. 

To evaluate this equation, we use the values of the rate constants k+ and surface areas As (the latter given as the product of specific surface area and mineral mass) for the two minerals and the equilibrium constants K for quartz (1.00 x 10-4) and cristobalite (3.56 x 10-4), and take ysio2 to be one. The resulting steady-state concentration is 1.57 x 10-4 molal, or 9.4 mg kg-1, which agrees with the simulation results in Figure 26.2. 

Mercury-chloride complexes in dilute solutions. This slightly more difficult example will be useful in showing how to handle poorly conditioned systems of equations. It is assumed that mercury chloride HgCl2 is dissolved in pure water with a molality m = 10 5 mol kg-1. Given the equilibrium constants for chloride complex formation... 

The previous summary of activities and their relation to equilibrium constants is not intended to replace lengthier discussions [1,18,25,51], Yet it is important to emphasize some points that unfortunately are often forgotten in the chemical literature. One is that the equilibrium constants, defined by equation 2.63, are dimensionless quantities. The second is that most of the reported equilibrium constants are only approximations of the true quantities because they are calculated by assuming the ideal solution model and are defined in terms of concentrations instead of molalities or mole fractions. Consider, for example, the reaction in solution ... 

It is easily shown that equation 2.65 is a fair approximation only if the ideal solution model is valid and A, B, and C are in very low concentrations. By accepting unity activity coefficients for all the species, equation 2.63 leads one to the equilibrium constant calculated from the molalities (Km) ... 

Equation 2.67 indicates that the standard enthalpy and entropy of reaction 2.64 derived from Kc data may be close to the values obtained with molality equilibrium constants. Because Ar// is calculated from the slope of In AT versus l/T, it will be similar to the value derived with Km data provided that the density of the solution remains approximately constant in the experimental temperature range. On the other hand, the error in ArSj calculated with Kc data can be roughly estimated as R In p (from equations 2.57 and 2.67). In the case of water, this is about zero for most solvents, which have p in the range of 0.7-2 kg dm-3, the corrections are smaller (from —3 to 6 J K-1 mol-1) than the usual experimental uncertainties associated with the statistical analysis of the data. 

C-t, which means, of course, that the ideal solution model is adopted, no matter the nature or the concentrations of the solutes and the nature of the solvent. There is no way of assessing the validity of this assumption besides chemical intuition. Even if the activity coefficients could be determined for the reactants, we would still have to estimate the activity coefficient for the activated complex, which is impossible at present. Another, less serious problem is that the appropriate quantity to be related with the activation parameters should be the equilibrium constant defined in terms of the molalities of A, B, and C. As discussed after equation 2.67, A will be affected by this correction more than A f//" (see also the following discussion). 

Although molalities are simple experimental quantities (recall that the molality of a solute is given by the amount of substance dissolved in 1 kg of solvent) and have the additional advantage of being temperature-independent, most second law thermochemical data reported in the literature rely on equilibrium concentrations. This often stems from the fact that many analytical methods use laws that relate the measured physical parameters with concentrations, rather than molalities, as for example the Lambert-Beer law (see following discussion). As explained in section 2.9, the equilibrium constant defined in terms of concentrations (Kc) is related to Km by equation 14.3, which assumes that the solutes are present in very small amounts, so their concentrations (q) are proportional to their molalities nr, = q/p (p is the density of the solution). 

Because the concentration of CO is not negligible, we can no longer apply the simple relationship between molality and concentration (mi = cjp) to write the equilibrium constant in terms of concentrations. The correct relationship between these two quantities is now given by equation 14.23, where M and n are the molar mass and the amount of substance of the solvent, respectively, and M and , are the corresponding quantities for the three solutes. 

Debye-Huckel parameter H = Henry s constant for molecular solute I = ionic strength = o.5 K = equilibrium constant m = molality, mole kg-1 P = pressure, Pa R = gas constant, J mol K T = temperature, K 3 ]... 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

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. 

The equilibrium constant for the carbamate reaction (eq.VIII) was simplified by assuming a o = an< re placing all other activities by molalities. Numbers for Kg(T) at 20, 40 and 60 oc were determined from experimental results. (Van Krevelen et al. only report discrete numbers or diagrams for some constants. For inter- and extrapolation these numbers were replaced by equations, wherein the dimensions of m and T are moles/ kg H2O and Kelvin, respectively.) ... 

In the equilibrium constant K Q activities were replaced by molalities. Numbers for K- 0 were taken from literature ... 

The procedure of Beutier and Renon as well as the later on described method of Edwards, Maurer, Newman and Prausnitz ( 3) is an extension of an earlier work by Edwards, Newman and Prausnitz ( ). Beutier and Renon restrict their procedure to ternary systems NH3-CO2-H2O, NH3-H2S-H2O and NH3-S02 H20 but it may be expected that it is also useful for the complete multisolute system built up with these substances. The concentration range should be limited to mole fractions of water xw 0.7 a temperature range from 0 to 100 °C is recommended. Equilibrium constants for chemical reactions 1 to 9 are taken from literature (cf. Appendix II). Henry s constants are assumed to be independent of pressure numerical values were determined from solubility data of pure gaseous electrolytes in water (cf. Appendix II). The vapor phase is considered to behave like an ideal gas. The fugacity of pure water is replaced by the vapor pressure. For any molecular or ionic species i, except for water, the activity is expressed on the scale of molality m ... 

This method is applicable to the complete multisolute aqueous solution described before. It is estimated that total solute concentrations up to 10 or 20 molal may be handled. The limitation on temperature results mainly from the limited temperature range for which experimental results for equilibrium constants and Henry s constants are available (cf. Appendix II and tables I and II). Although for some constants this range only extends up to 60 °C, it is expected that by an appropriate extrapolation the method may be used also at temperatures up to 170 oc. 

A. System NH3 H S-H20. The dissociation of water (re-action 9) and the second dissociation of H2S (reaction 6) are neglected at given temperature and total molalities of NHo and H2S there remain four unknown molalities in the liquid phase (e.g. NH3, NH4+, H2S and HS ), the composition of the vapor phase and the total pressure, which are calculated from 8 equations The dissociation constants of ammonia and hydrogen sulfide (eqs.I and III) together with the phase equilibrium for hydrogen sulfide (eq. XII) are combined resulting in a equilibrium constant K 2... 

An equilibrium constant for some reactions can be expressed in terms of mole fractions for some components and molalities for other components. 

Equilibrium constants are also dependent on temperature and pressure. The temperature functionality can be predicted from a reaction s enthalpy and entropy changes. The effect of pressure can be significant when comparing speciation at the sea surface to that in the deep sea. Empirical equations are used to adapt equilibrium constants measured at 1 atm for high-pressure conditions. Equilibrium constants can be formulated from solute concentrations in units of molarity, molality, or even moles per kilogram of seawater. 

Equilibrium constants corrected from molarity to molality units, according to the procedure described in Ref. 2. 

We can calculate the equilibrium constant of reaction 8.230 under any given P-T condition by computing the standard molal Gibbs free energy values of the various components at the P-T of interest—i.e.,... 

In table 9.14, for the sake of completion, we list the thermodynamic parameters of the HKF model concerning neutral molecules in solution (Shock et al., 1989). Calculation of partial molal properties of solutes (see section 8.11), combined with calculation of thermodynamic properties in gaseous phases (Table 9.5), allows rigorous estimates of the various equilibrium constants at all P and T of interest. 

Now consider a primary standard buffer containing 0.025 0 m KH2P04 and 0.025 0 m Na2HP04. Its pH at 25°C is 6.865 0.006.4 The concentration unit, m, is molality, which means moles of solute per kilogram of solvent. For precise chemical measurements, concentrations are often expressed in molality, rather than molarity, because molality is independent of temperature. Tabulated equilibrium constants usually apply to molality, not molarity. Uncertainties in equilibrium constants are usually sufficiently great so that the 0.3% difference between molality and molarity of dilute solutions is unimportant. 

The procedure starts with the specified terminal compositions and applies the material and energy balances such as Eqs. (13.64) and (13.65) and equilibrium relations alternately stage by stage. When the compositions from the top and from the bottom agree closely, the correct numbers of stages have been found. Such procedures will be illustrated first with a graphical method based on constant molal overflow. 

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