Equilibrium composition, of a mixture

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 ... 

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 ... 

What is the equilibrium composition of a mixture at 150°C that initially contained 0.0015 mol each of iodine and bromine in a 5.0-L vessel The equilibrium constant Kc for this reaction at 150°C is 1.2 X 10. ... 

For the sake of illustration we have calculated the equilibrium composition of a mixture, formed by decomposition of methane with steam at an initial ratio of 1 2 moles, 900 K and in the 10 to 1000 atm range. Thermochemical data for CH4, H2O, H2, CO will be found in Example 10, for CO2 in Example 11. The calculation was performed according to relations (6.96) — (6.102), constants of the Beattie-Bridgman equation are given in Appendix 11 for the individual pure constituents. The results are plotted in Fig. 24. It will be seen from the plot, that for all constituents 900 K is a high enough temperature for deviations from ideal behaviour to become apparent only at elevated pressure. 

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. 

The equilibrium composition of a reaction mixture is described by the equilibrium constant, which is equal to the activities of the products (raised to powers equal to their stoichiometric coefficients in the balanced chemical equation for the reaction) divided by the activities of the reactants (raised to powers equal to their stoichiometric coefficients). 

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. 

To calculate the equilibrium composition of a reaction mixture, set up an equilibrium table in terms of changes in the concentrations of reactants and products, express the equilibrium constant in terms of those changes, and solve the resulting equation. 

A catalyst is a substance that increases the rate of a chemical reaction without being consumed itself. We shall see a lot more of catalysts later, when we consider reaction rates in Chapter 13. However, it is important to be aware at this stage that a catalyst has no effect on the equilibrium composition of a reaction mixture. A catalyst can speed up the rate at which a reaction reaches equilibrium, but it does not affect the composition at equilibrium. It acts by providing a faster route to the same destination. 

J 9 Use Ee Chatelier s principle to predict how the equilibrium composition of a reaction mixture is affected by adding or removing reagents, compressing or expanding the mixture, or changing the temperature (Examples 9.9, 9.11, and 9.12). 

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. 

Equilibrium in multiphase and/or multireaction systems. If more than one phase is present in the system, a criterion of phase equilibria has to be satisfied together with the chemical equilibrium criterion. For instance, in a gas-liquid system components are in chemical equilibrium in the phase where the reaction occurs, but vapour-liquid equilibria between the gas and the liquid phases must also be taken into account. To determine the equilibrium composition of a reacting mixture in both phases, chemical equilibrium constants as well as data concerning vapour-liquid equilibria for all components of the reaction mixture should be known. In the equilibrium state ... 

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. 

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. 

Any analytical method [312] suitable for determining equilibrium compositions of a reaction mixture at several temperatures can be used to obtain the enthalpy and the entropy of that reaction. The first example we describe involves a common analytical technique (infrared absorption spectroscopy) and addresses the energetics of the hydrogen bond between phenol and acetonitrile. This careful study on the equilibrium 14.6 was made by Sousa Lopes and Thompson more than 30 years ago [313]. 

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 ... 

Determine the vapour phase composition of a mixture in equilibrium with a liquid mixture of 0.5 mole fraction benzene and 0.5 mole fraction of toluene at 338 K. Will the liquid vaporise at a pressure of 101.3 kN/m2 ... 

Thermodynamic data will be used to calculate AH as a function of temperature between 298 and 1000 K. AG and K will then be calculated over the same temperature range. Finally, the equilibrium composition of a stoichiometric mixture of carbon monoxide and hydrogen at a temperature of 600 K and a pressure of 300 atm will be obtained. 

Knowing the value of the equilibrium constant, K, at a given temperature, the composition of a mixture of gases at equilibrium may be calculated as follows. 

L reaction vessel and heated to 1000 K to study its dissociation into Cl atoms. Use the information in Table 9.1 to calculate the equilibrium composition of the mixture. What is the percentage decomposition of the Cl2 (b) If 2.0 mmol F2 was placed into the reaction vessel instead of the chlorine, what would be its equilibrium composition at 1000 K (c) Use your results from (a) and (b) to determine which is more stable relative to its atoms at 1000 K, Cl2 or F2. 

X 10-2 for the reaction, CO(g) + 2H2(g) CH3OH(g). (a) As the reaction approaches equilibrium, will the molar concentration of CH3OH increase, decrease, or remain unchanged (b) What is the equilibrium composition of the mixture ... 

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