Standard states enthalpy and

We have seen in chapter 2 that the heat capacity at constant P is of fundamental importance in the calculation of the Gibbs free energy, performed by starting from the standard state enthalpy and entropy values... 

Table 2-2 lists some important chemical reactions along with their standard state enthalpies and free energies of reaction, all in kj/mole. 

Standard State Enthalpy and Free Energy Changes in This Book. All values are in kj/mole of the first... 

Here Xa and Xb are the mole fractions of component A and B, respectively, and are related by Xa + Xg) = 1. We have used a superscript circle on the enthalpies and entropies of pure components A and B to indicate that these are standard state enthalpies and entropies of the pnre components. The standard state of a component in a condensed system is its stable state at the particular temperature and pressure of interest. So, depending on the temperatnre and pressure of the system, the standard state conld be either a liqnid or a solid for either of components A and B. 

Where and are, respectively, the standard state enthalpy and entropy. On the other hand, the chemical potential of a dissolved H atom is [15] ... 

Our computed standard state enthalpies and free energies at 298 K and 2000 K are listed in Tables 2-4. The energy minima at 0 K upon which these are based can be found in our earlier papers, as can also the optimized geometries of the boron- [32, 35] and aluminum-... 

If G (r) is given as a function of temperature, the standard-state enthalpy and entropy can be obtained as follows ... 

The standard state for a pure liquid or solid is taken to be the substance in that state of aggregation at a pressure of 1 bar. This same standard state is also used for liquid mixtures of those components that exist as a liquid at the conditions of the mixture. Such substances are sometimes referred to as liquids that may act as a solvent. For substances that exist only as a solid or a gas in the pure component state at the temperature of the mixture, sometimes referred to as substances that can act only as a solute, the situation is more complicated, and standard states based on Henry s law may be used. In this case the pressure is again fixed at 1 bar, and thermal properties such as the standard-state enthalpy and heat capacity are based on the properties of the substance in the solvent at infinite dilution, but the standard-state Gibbs energy and entropy are based on a hypothetical state.of unit concentration (either unit molality or unit mole fraction, depending on the form of Henry s law used), with the standard-state fugacity at these conditions extrapolated from infinite-dilution behavior in the solvent, as shown in Fig. 9.1-3a and b. Therefore just as for a gas where the ideal gas state at 1 bar is a hypothetical state, the standard state of a substance that can only behave as a solute is a hypothetical state. However, one important characteristic of the solute standard state is that the properties depend strongly upon the solvent. used. Therefore, the standard-state properties are a function of the temperature, the solute, and the solvent. This can lead to difficulties when a mixed solvent is used. 

Dalton s law is used to express partial pressures in terms of mole fractions and total pressure. Total pressure must be expressed in atmospheres if equilibrium, p IS Calculated via the dimensionless thermodynamic equation for / equilibrium, /, which is based on standard-state enthalpies and entropies of reaction at 298 K. Furthermore, the dimensions of / equilibrium, p are the same as those of / s°tondard state P (atm) for this problem]. The latter equilibrium constant, which is based on standard-state fugacities of pure components at 1 atm and 298 K, has a magnitude of 1 when total pressure in the kinetic rate law is expressed in atmospheres. Hence,... 

Equation 7.3.8 is applicable to both reactive and non-reactive systems. For the latter the standard state enthalpies and enthalpies of formation cancel because input and output flowrates are equal. A more convenient form of equation 7.3.8 for reactive systems is obtained by introducing the enthalpy change for the reaction. For a reaction described by the general stoichiometric equation (equation 7.2.7), the standard enthalpy change is defined as... 

Finally, this analysis allows calculation of the adiabatic temperature increase (AT ) with standard state enthalpy, and heat capacity and Cp of the reaction. In order to... 

Data for species in the gas phase at 1 bar have been summarized in Tables 1 to 5. Standard state enthalpies and free energies of formation, and entropies have been given at 298 K. In deriving reliable A,7/298 values from A, //(/ results corrections have been made on the basis of data in the literature. Values of A,G298 ... 

In order to compare the thermodynamic parameters of different reactions, it is convenient to define a standard state. For solutes in a solution, the standard state is normally unit activity (often simplified to 1 M concentration). Enthalpy, internal energy, and other thermodynamic quantities are often given or determined for standard-state conditions and are then denoted by a superscript degree sign ( ° ), as in API", AE°, and so on. 

Standard-State Enthalpy Changes (AH°). To expedite calculations, thermochemical data are ordinarily presented in the form of standard-state enthalpy changes of the system AH°(T,P), with the requirement that materials start and end at the same temperature (T) and pressure (P) and in their standard states of aggregation, i.e.,... 

For a Raoulf s law standard state, H° = Hf and L, = //, — Hf. These are the differences described in Chapter 5. For a Henry s law standard state, H° is the enthalpy in a hypothetical m = 1 (or X2 — 1 or c = 1) solution that obeys Henry s law. To help in understanding the nature of these standard state enthalpies, we will show that... 

The first ACH° is AfH for C02 at 298.15 K, since elements in their naturally occurring state are combining to give C02(g). This combustion reaction is the standard state enthalpy of formation if we carry it out at p = 1 bar and make small corrections to change the C02(g) to the ideal gas condition. 

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 ... 

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). 

These values of A Hr are standard state enthalpies of reaction (aU gases in ideal-gas states) evaluated at 1 atm and 298 K. 7VU values of A are in kilojoules per mole of the first species in the equation. When A Hr is negative, the reaction hberates heat, and we say it is exothermic, while, when A Hr is positive, the reaction absorbs heat, and we say it is endothermic. Tks Table 2-2 indicates, some reactions such as isomerizations do not absorb or liberate much heat, while dehydrogenation reactions are fairly endothermic and oxidation reactions are fairly exothermic. Note, for example, that combustion or total oxidation of ethane is highly exothermic, while partial oxidation of methane to synthesis gas (CO + H2) or ethylene (C2H4) are only slightly exothermic. 

Figure 2-8 The equilibrium constant of Reaction 2-79 as a function of temperature in InK versus lOOO/T plot. The rough straight line means that the standard state enthalpy change of Reaction 2-79 is constant. Solid circles are 1-atm data from Zhang et al. (1997a) and open circles are 500-MPa data from Zhang (unpublished data).

But the enthalpy of a compound at the reference temperature and pressure is its standard-state enthalpy of formation (or heat of formation ) ... 

The two thermodynamic quantities AS° and A H° are the net difference in standard-state entropy and enthalpy of the energized molecule C and the stabilized reactant molecule C. 

If we want to determine the heat of reaction, where do we even begin The easiest place is to look at a measurement known as the standard enthalpy of formation, A H°f This is based on two different units, the enthalpy of formation, AHfi which represents the enthalpy change that occurs when a compound is formed from its constituent elements, and the standard enthalpy of reaction, AH0, which is the enthalpy for a reaction when all reactants and products are in their standard state (the state they exist in at 25°C and 1 atm). The standard enthalpy of formation is 1 mole of a compound from its constituent elements in their standard states. Enthalpies of formation can be found in many different reference books. Let s take a look at how we can use enthalpies of formation to determine the enthalpy of reaction for the combustion of ethanol. 

For a standard reaction, products and reactants are always at the same standard-state pressure of 1 bar or l(atm). Standard-state enthalpies are therefore functions of temperature only, and their change with T is given by Eq. (2.25),... 

Table B9 Approximate standard reaction enthalpy and standard reaction Gibbs energy for some selected reactions at standard state T = 25°C, P = 1 atma...

If the whole process is carried out at constant pressure, then all the heat generated goes into increasing the enthalpy of the products. This internally generated heat is designated as Q, where Q = n AH (heat generated by the reaction at standard state conditions), and Q = n Ai/[products] (heat absorbed by the products of the reaction, at adiabatic conditions). 

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