Composition of equilibrium mixtures

Boltzmann Equation. The equation which relates the composition of equilibrium mixtures to relative thermochemical stabilities and temperature. 

A mixture of reactants and products in the equilibrium state is called an equilibrium mixture. In this chapter, we ll address a number of important questions about the composition of equilibrium mixtures What is the relationship between the concentrations of reactants and products in an equilibrium mixture How can we determine equilibrium concentrations from initial concentrations What factors can be exploited to alter the composition of an equilibrium mixture This last question is particularly important when choosing conditions for the synthesis of industrial chemicals such as hydrogen, ammonia, and lime (CaO). 

We can make the following generalizations concerning the composition of equilibrium mixtures ... 

The electronic nature of the amine incorporated into these imine complexes should play an important role in determining the stability of Cu1 complexes, and therefore the composition of equilibrium mixtures when several amines compete as subcomponents. To investigate the influence of electronic effects, we ran a series of competition experiments between unsubstituted and substituted anilines [46] (Scheme 1.19). 

High speed computers as a supplement to graphical methods-V. HALTAFALL, a general program for calculating the composition of equilibrium mixtures. Talanta 14, 1261-1286 (1967). 

Newton and Dodge and von Wettberg and Dodge measured the composition of equilibrium mixtures of CO, Hj, and CH3OH in the methanol synthesis. Compute the value of K and AF° at 309°C from the following data taken from their work ... 

General Electric Company Properties of Combustion Gases, vol. 1, Thermodynamic Properties vol. 2, Chemical Composition of Equilibrium Mixtures McGraw-Hill Book Company, Inc., New York, 1956. 

According to the limitation stated above, our standard functions /u. = pI, T) depend only on temperature and therefore also equilibrium constants depend on temperature only and by (4.474) give restrictions on the values of activities a° in chemical equilibrium (denoted by superscript cf. Sect.4.7). Equations (4.473) and (4.474) permit calculations of chemical equilibria KLp may be calculated from the right-hand side of (4.473) (e.g. from thermodynamic data for pure constituents if they are taken as the standard state) and composition of equilibrium mixture is restricted by (4.474) if we know the relation of activities to composition simple results follow for important case (4.469), which will be used below (4.475). 

Dunsmore HS, Midgley D (1972) Computer calculatiodoi 10.1016/0039-9140(88)80166-8n of the composition of equilibrium mixtures in solution. Anal Chim Acta 72 121-126. doi 10.1016/S0003-2670(01)82955-X... 

The rate-determining step for this equilibration is the separation of olefin (dehydroboration) 18). Addition of B—H bonds to olefins (hydro-boration) is very rapid at room temperature 15, 19, 20, 21, 45), while dehydroboration generally does not beeome significant until 100° C. Compositions of equilibrium mixtures (see Table I) of simple triorgano-boranes may be determined by gas chromatography (5, 6,22). The course of... 

The following sources may be cited as examples of the study of equilibria by thermodynamics to ascertain the composition of equilibrium mixtures and to obtain thermodynamic data on chemical reactions. 

Uquidus curve The freezing point of a molten mixture of substances varies with the composition of the mixture. If the freezing points are plotted as a function of the composition, the line joining the points is called a liquidus curve. Such mixtures usually freeze over a range of temperature. If the temperature at which the last traces of liquid just solidify (assuming that sufficient time has been allowed for equilibrium to be established) are plotted against composition the resulting line is called a solidus curve. 

Continuum models go one step frirtlier and drop the notion of particles altogether. Two classes of models shall be discussed field theoretical models that describe the equilibrium properties in temis of spatially varying fields of mesoscopic quantities (e.g., density or composition of a mixture) and effective interface models that describe the state of the system only in temis of the position of mterfaces. Sometimes these models can be derived from a mesoscopic model (e.g., the Edwards Hamiltonian for polymeric systems) but often the Hamiltonians are based on general symmetry considerations (e.g., Landau-Ginzburg models). These models are well suited to examine the generic universal features of mesoscopic behaviour. 

Table 1.1 Equilibrium composition of gas mixtures at 2300 K and 0.1 atmos pressure (mole fraetions of the major gases only)...

The position of equilibrium depends upon the identity of the alcohol and the composition of the mixture. Figure 8-4, given by Bums and England, shows the... 

The term ff denotes the number of independent phase variables that should be specified in order to establish all of the intensive properties of each phase present. The phase variables refer to the intensive properties of the system such as temperature (T), pressure (P), composition of the mixture (e.g., mole fractions, x ), etc. As an example, consider the triple point of water at which all three phases—ice, liquid water, and water vapor—coexist in equilibrium. According to the phase rule,... 

FIGURE 8.36 The composition of the vapor in equilibrium with a mixture of two volatile liquids (here, benzene and toluene) and its variation with the composition of the liquid. Note that the vapor is richer in benzene than the liquid mixture for each composition of the mixture. For instance, when the mole fraction of benzene is 0.133 in the liquid, in the vapor it is 0.619. 

The initial pressure of BrCl(g) in a reaction vessel is 1.4 mbar. If the vessel is heated to 500. K, what is the equilibrium composition of the mixture See Table 9.2 for data on the reaction. 

To calculate the equilibrium composition of a mixture at a given temperature, we first need to calculate the equilibrium constant from thermodynamic data valid under the standard conditions of 298 K and 1 bar, as in Tab. 2.2. Differentiating Eq. (22) and using AG° = A - TAS° we obtain the Van t Hoff equation ... 

As equation 2.4.8 indicates, the equilibrium constant for a reaction is determined by the temperature and the standard Gibbs free energy change (AG°) for the process. The latter quantity in turn depends on temperature, the definitions of the standard states of the various components, and the stoichiometric coefficients of these species. Consequently, in assigning a numerical value to an equilibrium constant, one must be careful to specify the three parameters mentioned above in order to give meaning to this value. Once one has thus specified the point of reference, this value may be used to calculate the equilibrium composition of the mixture in the manner described in Sections 2.6 to 2.9. 

Calculate the equilibrium composition of a mixture of the following species. 

The extension of thermodynamic calculations to low temperatures requires knowledge of how the equilibrium composition of a mixture, which varies at different temperatures, can be derived from the standard relation between AG and the equilibrium constant (Equation 8.12) to give the van t Hoff equation for the variation of the equilibrium constant with temperature ... 

An aromatic hydrocarbon feedstock consisting mainly of m-xylene is to be isomerised catalytically in a process for the production of / -xylene. The product from the reactor consists of a mixture of p-xylene, m-xylene, o-xylene and ethylbenzene. As part of a preliminary assessment of the process, calculate the composition of this mixture if equilibrium were established over the catalyst at 730 K. 

The simultaneous gas phase reactions take place at 1 atm, beginning with stoichiometric proportions of A and B. Find the equilibrium composition of the mixture. 

Considering the multistage industrial unit, in any equilibrium stage, the quantity of solution in the underflow may be a function of the concentration of the solution in the thickener, and the concentration of the overflow solution will be the same as that in the underflow. If the curved line EF (Figure 10.18) represents the experimentally determined composition of the underflow for various concentrations, any point f on this line represents the composition of a mixture of pure B with a solution of composition g, and Of/fg is the ratio of solution to solids in the underflow. If the amount of solution removed in the underflow is not affected by its concentration, the fractional composition of the underflow with respect to the insoluble material B (xB) is a constant, and is represented by a straight line, through E, parallel to the hypotenuse, such as EF. Point E represents the composition of the underflow when the solution is infinitely weak, that is when it contains pure solvent. If K is the mass of solution removed in the underflow per unit mass of solids, the ordinate of E is given by ... 

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