Equilibrium constant molar

A more realistic approach attempts to describe each equilibrium in terms of its thermodynamic equilibrium constant, molar volumes of specific aggregates, and a heat of reaction to estimate the chemical contribution to excess enthalpy Hchem- The first two parameters contribute to the excess Gibbs energy model. 

Ku = equilibrium constant, molar/bar iCj = equilibrium constant, molar K2 = equilibrium constant, molar K = equilibrium constant, molar ... 

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. 

Other conventions for treating equiUbrium exist and, in fact, a rigorous thermodynamic treatment differs in important ways. Eor reactions in the gas phase, partial pressures of components are related to molar concentrations, and an equilibrium constant i, expressed directiy in terms of pressures, is convenient. If the ideal gas law appHes, the partial pressure is related to the molar concentration by a factor of RT, the gas constant times temperature, raised to the power of the reaction coefficients. 

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. 

Kinetic data provide information only about the rate-determining step and steps preceding it. In the hypothetical reaction under consideration, the final step follows the rate-determining step, and because its rate will not affect the rate of the overall reaction, will not appear in the overall rate expression. The rate of the overall reaction is governed by the second step, which is the bottleneck in the process. The rate of this step is equal to A2 multiplied by the molar concentration of intermediate C, which may not be directly measurable. It is therefore necessary to express the rate in terms of the concentrations of reactants. In the case under consideration, this can be done by recognizing that [C] is related to [A] and [B] by an equilibrium constant ... 

Taking known values for the molar refractivities of water and methanol, and again assuming a range of values for the equilibrium constant (k) and the refractive index (ni) of the methanol/water associate, the actual values that fit the equation for these... 

Data Source Equilibrium Constant (k) Mol.Vol. of Associate Density of Associate Molar Refractivity of Associate Refractive Index of Associate... 

Using the average value for the equilibrium constant, the distribution concentration of the different components of a methanol water mixture were calculated for initial methanol concentrations ranging from zero to 100%v/v. The curves they obtained are shown in Figure 28. The molar refractivities of 11.88 is also in accordance with that expected since the molar refractivity s of water and methanol are 3.72 and 8.28 respectively. The refractive index of the associate of 1.3502 is, as would be expected, higher than that of either water or methanol. 

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. 

The numerical values of AG and A5 depend upon the choice of standard states in solution kinetics the molar concentration scale is usually used. Notice (Eq. 5-43) that in transition state theory the temperature dependence of the rate constant is accounted for principally by the temperature dependence of an equilibrium constant. 

The equilibrium constant at room temperature corresponds to pKi, = 4.74 and implies that a 1 molar aqueous solution of NH3 contains only 4.25 mmol 1 of NH4+ (or OH ). Such solutions do not contain the undissociated molecule NH4OH, though weakly bonded hydrates have been isolated at low temperature ... 

When the added water has a molarity n, let a fraction g of positive ions be alcoholic ions, while the fraction (1 — g) is in the form of (HjO)+ ions, On extrapolating to infinite dilution, the equilibrium constant of the reaction (43) may be written... 

In the dilute aqueous solution normally used for measuring acidity, the concentration of water, H20], remains nearly constant at approximately 55.4 M at 25 °C. We can therefore rewrite the equilibrium expression using a new quantity called the acidity constant, Ka. The acidity constant for any acid HA is simply the equilibrium constant for the acid dissociation multiplied by the molar concentration of pure water. 

Notice that the piO, value shown in Table 2.3 for water is 15.74, which results from the following calculation the Ka for any acid in water is the equilibrium constant /vet) for the acid dissociation multiplied by 55.4, the molar concentration of pure water. For the acid dissociation of water, we have... 

The equation just written is generally applicable to any system. The equilibrium constant may be the K referred to in our discussion of gaseous equilibrium (Chapter 12), or any of the solution equilibrium constants (Rw Ra, Rj, K, . . . ) discussed in subsequent chapters. Notice that AG° is the standard free energy change (gases at 1 atm, species in solution at 1M). That is why, in the expression for K, gases enter as their partial pressures in atmospheres and ions or molecules in solution as their molarities. 

The Equilibrium Constant in Terms of Molar Concentrations of Gases... 

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

K is the equilibrium constant in terms of molar concentrations of gases (Section 9.6). 

Now we come to the most important point in this chapter. At equilibrium, the activities (the partial pressures or molarities) of all the substances taking part in the reaction have their equilibrium values. At this point the expression for Q (in which the activities have their equilibrium values) has become the equilibrium constant, K, of the reaction. That is,... 

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 equilibrium constant in Eq. 2 is defined in terms of activities, and the activities are interpreted in terms of the partial pressures or concentrations. Gases always appear in K as the numerical values of their partial pressures and solutes always appear as the numerical values of their molarities. Often, however, we want to discuss gas-phase equilibria in terms of molar concentrations (the amount of gas molecules in moles divided by the volume of the container, [I] = j/V), not partial pressures. To do so, we introduce the equilibrium constant Kt., which for reaction E is defined as... 

Step 1 Write the balanced chemical equation for the equilibrium and the corresponding expression for the equilibrium constant. Then set up an equilibrium table as shown here, with columns labeled by the species taking part in the reaction. In the first row, show the initial composition (molar concentration or partial pressure) of each species... 

Step 4 Use the equilibrium constant to determine the value of x, the unknown change in molar concentration or partial pressure. 

Experimentally, fCsp = 1.6 X 10 10 at 25°C, and the molar solubility of AgCl in water is 1.3 X 10 5 mol-IT. If we add sodium chloride to the solution, the concentration of Cl ions increases. For the equilibrium constant to remain constant, the concentration of Agf ions must decrease. Because there is now less Ag+ in solution, the solubility of AgCl is lower in a solution of NaCl than it is in pure water. A similar effect occurs whenever two salts having a common ion are mixed (Fig. 11.16). 

The units of AG are joules (or kilojoules), with a value that depends not only on E, but also on the amount n (in moles) of electrons transferred in the reaction. Thus, in reaction A, n = 2 mol. As in the discussion of the relation between Gibbs free energy and equilibrium constants (Section 9.3), we shall sometimes need to use this relation in its molar form, with n interpreted as a pure number (its value with the unit mol struck out). Then we write... 

The kinetic equilibrium constant is estimated from the thermodynamic equilibrium constant using Equation (7.36). The reaction rate is calculated and compositions are marched ahead by one time step. The energy balance is then used to march enthalpy ahead by one step. The energy balance in Chapter 5 used a mass basis for heat capacities and enthalpies. A molar basis is more suitable for the current problem. The molar counterpart of Equation (5.18) is... 

An equilibrium constant expression contains concentrations, each of which has been divided by the reference concentration. For convenience, we omit these reference concentrations when we write the expressions for Q or for. S eq You should remember, however, that the implicit presence of reference concentrations means that K values are dimensionless but that concentrations must be in bar for gases and molarity for solutes. 

Remember that although equilibrium calculations require concentrations in molarities for solutes, the equilibrium constant expression is dimensionless. The solubility product has a... 

The equilibrium constant K for (por)Fe(OH2) (por)Fe, which determines the molar fraction of the 5-coordinate redox-active Fe catalyst. This constant was estimated from analysis of the catalytic turnover frequencies in the presence of varying concentrations of an inhibitor, CN, which competes with both O2 and H2O for the 5-coordinate Fe porphyrin. 

The system is ideal, with equilibrium described by a constant relative volatility, the liquid components have equal molar latent heats of evaporation and there are no heat losses or heat of mixing effects on the plates. Hence the concept of constant molar overflow (excluding dynamic effects) and the use of mole fraction compositions are allowable. 

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... 

A batch still corresponding to a total separation capacity equivalent to eight theoretical plates (seven plates plus the still) is used to separate a hydrocarbon charge containing four (A, B, C, D) simple-hydrocarbon components. Both the liquid and vapour dynamics of the column plates are neglected. Equilibrium data for the system is represented by constant relative volatility values. Constant molar overflow conditions again apply, as in BSTILL. The problem was originally formulated by Robinson (1975). 

As anticipated, SA conversion increases with increasing residence time (1/LHSV) and with increasing temperature to a maximum of about 98%. This limit is most likely caused by equihbrium. This limit and thus the equilibrium constant were not affected by the temperature range studied, consistent with a low heat of reaction. The sum of the molar heats of combustion of stearic acid (11320 kJ/mol) and methanol (720 kJ/mol) is almost the same as the heat of combustion of methyl stearate (12010 kJ/mol), meaning that the change in enthalpy of this reaction is nearly zero and that the equihbrium constant is essentially temperature independent. 

The method proposed by Lewis and Matheson (1932) is essentially the application of the Lewis-Sorel method (Section 11.5.1) to the solution of multicomponent problems. Constant molar overflow is assumed and the material balance and equilibrium relationship equations are solved stage by stage starting at the top or bottom of the column, in the manner illustrated in Example 11.9. To define a problem for the Lewis-Matheson method the following variables must be specified, or determined from other specified variables ... 

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