Equilibrium standard change

Steps 1 and 2 require thermodynamic data. Eigure 2-1 shows the equilibrium constants of some reactions as a function of temperature. The Appendix at the end of this chapter gives a tabulation of the standard change of free energy AG° at 298 K. 

It is important to note that, for any given temperature, the [thermodynamic] equilibrium constant is directly related to the standard change in free energy. Since, at any given temperature, the free energy in the standard state for each reactant and product, G°, is independent of the pressure, it follows that the standard change in free energy for the reaction, AfG°, is independent of the pressure.g Therefore, at constant temperature, the equilibrium constant K. .. is also independent of the pressure. That is,... 

Readings should only be taken when the signal has reached equilibrium. When a new sample is presented, several seconds will elapse before the system reaches equilibrium. Particular care must be taken when the concentration of the samples or standards changes markedly, especially if the new solution is more dilute. 

The equilibrium product is related to the standard change of free energy, AG, when the transition state is formed from the reactants. 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

Over the years, many experiments have been carried out which confirm the third law. The experiments have generally been of two types. In one type the change of entropy for a change of phase of a pure substance or for a standard change of state for a chemical reaction has been determined from equilibrium measurements and compared with the value determined from the absolute entropies of the substances based on the third law. In the other type the absolute entropy of a substance in the state of an ideal gas at a given temperature and pressure has been calculated on the basis of statistical mechanics and compared with those based on the third law. Except for well-known, specific cases the agreement has been within the experimental error. The specific cases have been explained on the basis of statistical mechanics or further experiments. Such studies have led to a further understanding of the third law as it is applied to chemical systems. 

Equations (15.25) and (15.26) afford a means of determining the validity of experimental data when values of [Ge(T) — H°(0)] or [Ge(7 ) — He(298)] are known for each of the reacting substances. Assume that values of AGe (T) have been determined at various temperatures for some standard change of state from the experimental measurement of the equilibrium conditions of the system. Then the value of viHe(0)i or viHe(298)i is calculated from the value of AG°(T) for each experimental point. All of the values of... 

Equilibrium constant K) of the process at temperature T is related to standard change in the Gibbs energy, AG°, by the following equation ... 

AH 9 is the difference in enthalpy between the products and reactants in their standard states for one mole of reaction. For systems not at equilibrium the change in free energy for a mole of reaction, all concentrations being maintained constant is, as before,... 

In this chapter the focus will be on K, the equilibrium constant, and the following thermodynamic quantities, U, the energy, H, the enthalpy, G, the free energy, S, the entropy, V, the volume, C the heat capacity, and /x, the chemical potential. The significance of standard changes in the values of these quantities. At/, A//, AG, AS, ACp, and AV for the study of electrolyte solutions will be discussed. 

During clinical interviews focusing on the system CaCOs o CaO + CO2, nearly all physical chemistry students from an American university (94%), failed to mention the standard change in entropy and enthalpy as factors that determine the value of equilibrium constants (Thomas Schwenz, 1998). 

At the boiling-point, the vapour pressure of the solvent attains a standard value equal to the fixed external pressure. The addition of a solute lowers the vapour pressure so that the system is no longer in equilibrium. The change is given by Raoult s law,... 

We have noted that the equilibrium constant Kj for reaction depends only on the system temperature T and the standard state. Often, we need to determine how the equilibrium constant changes with temperature. For example, during a reactor design we routinely want to know whether product yield can be improved by an increase or decrease in operating temperature. Furthermore, many tables (discussed at the end of 10.4.2) give values for equilibrium constants only at selected temperatures then we must correct those values to the temperature of our situation. 

Value of equilibrium constant at 300 K. We substitute the value for the standard change in Gibbs energy into (10.3.14) and find... 

In both the stoichiometric and nonstoichiometric approaches to reaction-equilibrium calculations, we need values for the standard change in the Gibbs energy Ag. In the stoichiometric development, is used in (10.3.14) to obtain values for the equilibrium constant K in the nonstoichiometric development, is used to obtain values for the standard-state chemical potentials that appear in (10.3.38). Since is a state function, values for can be measured or computed along any convenient process path that starts with the desired reactants in their standard states and ends with products in their standard states. Of those many possibilities, the most convenient is to determine Ag° by combining the Gibbs energies of formation for each species. That procedure is developed here. However, values for molecular properties of formation are often available only at a particular temperature T°, so we must be able to correct those values to the reaction temperature T. Such corrections for A require values for the standard heat of reaction Aft and, perhaps, values for the standard isobaric heat capacities Ac. ... 

If a multiphase multicomponent system is to be at equilibrium (no change with time of the intensive variables) obviously temperature and pressure must be the same for all phases and also the chemical compositions (mole fractions of each constituent). In any given phase there are (C—1) independent mole fractions (their sum is unity by definition), so there are P.(C—1) composition variables involved and thus [P.(C—1) -1-2] intensive variables in total. But if chemical equUibrium in all phases simultaneously is to hold, the chemical potential of each constituent (a function of the composition) must be the same in each phase thus there are C.(P—1) independent constraints on the composition variables arising from the equilibrium condition (the chemical potential in one of the phases is used as the reference standard for the other phases). Thus F = [P.(C—1) -1-2] — [C.(P—1)] =C—P-F2. This is the famous Gibbs Phase Rule. 

The equilibrium constant for a certain reaction increases by a factor of 6.67 when the temperature is increased from 300.0 K to 350.0 K. Calculate the standard change in enthalpy (A//°) for this reaction (assuming AH° is temperature-independent). 

The first, up to now more conventional approach sets out from a description of the overall chemical conversion of the given system by means of a set of chemical reactions, and the corresponding standard changes of free enthalpy or equilibrium constants. Assuming R linearly independent reactions and ideal behaviour of the gas mixture, this procedure converts to the solution of a non-linear set of R equations for R unknown variables < i, 2 ... 

Here AG = Ai/ — TA5 represents a standard change in the Gibbs free energy in the course of a realized chemical reaction. We have seen above that in the case of so-called ideal systems the equilibrium constant, coincides with the kinetically introduced equilibrium constant, and can easily be expressed as the ratio of the corresponding equilibrium concentrations of reagents to the power of their stoichiometric coefficients, i.e., as the left side of (2.4). In principle, this allows us to determine experimentally the equilibrium constant, by measuring the equilibrium concentrations of the reagents. 

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