Standard state cycles

The application of waste-management practices in the United States has recently moved toward securing a new pollution prevention ethic. The performance of pollution prevention assessments and their subsequent implementation will encourage increased activity into methods that 1 further aid in the reduction of hazardous wastes. One of the most important and propitious consequences of the pollution-prevention movement will be the development of life-cycle design and standardized hfe-cycle cost-accounting procedures. These two consequences are briefly discussed in the two paragraphs that follow. Additional information is provided in a later subsection. 

Figure 2.1 Thermochemical cycle, showing how to relate the enthalpy of the experimental reaction 2.1 with reaction 2.2, where reactants and products are in their standard states.

We have assumed throughout the previous discussion that the temperature of reaction 2.1 is 298.15 K. What if the reaction enthalpy at a different temperature is required Let us assume, for instance, that we need to evaluate Ar//(2.1) at 310 K. As shown by the cycle in figure 2.2 or by equation 2.9, the first step in this exercise is to evaluate the temperature effect on the standard state reaction 2.2. 

We have illustrated how standard enthalpy of formation values can be handled to yield data for practical conditions. The procedure always involves thermochemical cycles, relating the standard state processes with those observed in... 

A primary use of titration calorimetry is the determination of enthalpies of reaction in solution. The obtained results may of course lead to enthalpies of formation of compounds in the standard state by using appropriate thermodynamic cycles and auxiliary data, as described in chapter 8 for reaction-solution calorimetry. Moreover, when reactions are not quantitative, both the equilibrium constant and the enthalpy of reaction can often be determined from a single titration run [197-206], This also yields the corresponding ArG° and ATS° through equations 2.54 and 2.55. 

L OX , + eligand coordinated with redox particles and ejsTD, is the electron in the gaseous standard state at the outer potential of the aqueous solution (Refer to Chap. 4.). The following reaction cycle may be used to obtain the energy relationship between the two redox reactions ... 

The stability of electrocatalysts for PEMFCs is increasingly a key topic as commercial applications become nearer. The DoE has set challenging near-term durability targets for fuel cell technology (automotive 5,000 h by 2010 stationary 40,000 h by 2011) and has detailed the contribution of the (cathode) catalyst to these. In particular, for automotive systems as well as steady-state stability, activity after simulated drive cycles and start-stop transients has been considered. In practice, both these treatments have been found to lead to severe degradation of the standard state-of-the-art Pt/C catalyst, as detailed next. 

The relationships between the two different states and between the enthalpy of formation from the elements at standard state (H°) and the lattice energy (U) are easily understood by referring to the Born-Haber-Fayans thermochemical cycle. In this cycle, the formation of a crystalline compound from isolated atoms in the gaseous state is visualized as a stepwise process connecting the various transformations. Let us follow the condensation process of a crystal MX formed from a metal M and a gaseous molecule X2 ... 

We then close the cycle by transforming crystal MX into its component elements in the standard state. To do this, we must furnish energy corresponding to the enthalpy of formation from the elements ... 

Table 5.12 reports a compilation of thermochemical data for the various olivine components (compound Zn2Si04 is fictitious, because it is never observed in nature in the condition of pure component in the olivine form). Besides standard state enthalpy of formation from the elements (2) = 298.15 K = 1 bar pure component), the table also lists the values of bulk lattice energy and its constituents (coulombic, repulsive, dispersive). Note that enthalpy of formation from elements at standard state may be derived directly from bulk lattice energy, through the Bom-Haber-Fayans thermochemical cycle (see section 1.13). 

A Born-Haber cycle is the application of Hess s Law to the enthalpy of formation of an ionic solid at 298 K. Hess s law states that the enthalpy of a reaction is the same whether the reaction takes place in one step or in several. A Born-Haber cycle for a metal chloride (MCI) is depicted in Figure 1.56 the metal chloride is formed from the constituent elements in their standard state in the equation at the bottom, and by the clockwise series of steps above. From Hess s law, the sum of the enthalpy changes for each step around the cycle can be equated with the standard enthalpy of formation, and we get that ... 

An appropriate cycle is presented in Figure 1.65. Note that sulfur is a solid in its standard state not a gas. 

Using the same symbolism as the previous sub-section, Figure 2.7 shows a thermodynamic cycle for the formation of the cation of element M by treating the element in its standard state with an acid solution containing hydrated protons and producing the hydrated cation and an equivalent amount of dihydrogen ... 

Another key feature of redox thermodynamic cycles is that the free energy change in solution is still defined to involve a gas-phase electron, that is, the solvation free energy of the electron is happily not an issue. And, once again, redox potentials in soludon typically assume 1 M standard states for ad species (but not always in this chapter s case study, for instance, all redox potentials were measured and computed for chloride ion concentrations buffered to 0.001 M). So, free energy changes associated with concentration adjustments must also be properly taken into account. 

F (jE°(/=o.2) — J5°(/=o)) (1) This cycle holds for every medium. Equation 1 connects the four basic quantities T Ks0, Ks0, E°(j=o>, and E° 1) without any nonthermo-dynamic assumptions. This enables us to evaluate solubility constants for every appropriate ionic medium using data which have been determined with reference to the usual aqueous standard state. The conversion of Ks into TKs and vice-versa may also be performed using the Debye-Hiickel equation and its extensions as shown in Equation 2. 

Radical heats of formation are defined in the usual way, that is, as enthalpy of formation of the radical in question from the elements in their standard states. The heats of formation and the bond dissociation energies are derivable from each other and are based on the same data. Thus, in Reaction 9.7, the heat of formation of R- is readily found from the bond dissociation energy by means of the enthalpy cycle shown in Scheme 3 if heats of formation of R—X and X are known conversely, D( R—X) may be found once heats of formation of RX, R-,... 

The standard enthalpy of formation of a compound, AHf, is defined as the increment in enthalpy associated with the reaction of forming a given compound from its elements, with each substance in its thermodynamic standard state at the given temperature.2 The thermodynamic cycle for the enthalpy of formation of methane (CH4) from the standard states of carbon and hydrogen (graphite and hydrogen molecules) is shown in Figure 1. 

The effect of increasing tlie compression ratio, defined as tlie ratio of the volumes at the begimiing and end of tlie compression stroke, is to increase the efficiency of tlie engine, i.e., to increase the work produced per imit quantity of fuel. We demonstrate this for an idealized cycle, called the air-standard Otto cycle, shown in Fig. 8.9. It consists of two adiabatic and two constant-volume steps, which comprise a heat-engine cycle for which air is tlie working fluid. In step DA, sufficient heat is absorbed by tlie air at constant volmiie to raise its temperature and pressure to the values resulting from combustion in an actual Otto engine. Then the air is expanded adiabatically and reversibly (step AB), cooled at constant volume (step BC), and finally compressed adiabatically and reversibly to the initial state at D. 

The addition of another water to the aqueous reaction, such as in reaction 11 or 12, also results in more calculations. This increases computational error in determining pKar as the total number of manipulated numbers increases from reaction 1 to reaction 12. For a thorough understanding of the standard state issues that arise when adding water to thermodynamic cycles, study the recent Goddard group paper [9]. 

Recent work on using explicit waters in cluster continuum or implicit-explicit thermodynamic cycles show much promise, as long as the standard state issues... 

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