Enthalpy standard-state

Enthalpy changes for biochemical processes can be determined experimentally by measuring the heat absorbed (or given off) by the process in a calorimeter (Figure 3.2). Alternatively, for any process B at equilibrium, the standard-state enthalpy change for the process can be determined from the temperature dependence of the equilibrium constant ... 

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. 

Standard state, for molecules, 24 687—688 Standard state enthalpy change for methanol synthesis, 25 305 Standard-state heat, 24 688 Standard-state heat of reaction, 24 688 Standards-writing organizations, 15 760 Standard Test Conditions (STC), 23 38 Standard test methods, 15 747—748 Standpipe pressure profiles, 11 818 Standpipes, in circulating fluidized beds, 11 817-819 Stand-retting, 11 606 Stannane, 13 613, 24 813... 

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 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). 

Table 5.12 Thermochemical data for various olivine end-members (7) = 298.15 K P, = 1 bar). Listed values in kJ/mole (from Ottonello, 1987). = standard state enthalpy of formation...

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

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. 

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

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).

Because Ef= lE, b = AH, where AH is the standard state enthalpy change of the reaction, we have. 

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. 

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

The first quantity to consider is A HJ, which is the standard enthalpy of formation of a compound. It is the standard-state enthalpy H° of the compound minus the standard-state enthalpy of the elements from which the compound is formed. The superscript o indicates standard-state conditions, which for a gas is now taken to be a pressure of 1 bar. However, H° can be specified at any temperature, H = H°(T). 

A single reference temperature Tr must be defined, at which the standard-state enthalpy H°(Tr) of the elements (in their most stable form) are all defined to be zero, H°(Tr) = 0. This reference temperture is taken to be Tr = 298.15 K. The enthalpy of an element at a temperature other than Tr is nonzero, in general, that is, H°(T Tr) 0 (for an element). 

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),... 

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

The variation of AW , the change in standard state enthalpy by the process, with temperature can be calculated from the heat capacity of the species involved in the process. ... 

This equation can be extended to calculate the standard-state enthalpy change for any chemical reaction by adding up the standard-state enthalpy of formation for all the products (each multiplied by its stoichiometric coefficient in the balanced chemical equation) and subtracting off the total for all the reactants (each multiplied by its stoichiometric coefficient in the balanced chemical equation). In mathematical form, this procedure is represented by the equation... 

The change in standard state enthalpy for any reaction can be calculated from the standard state enthalpy of formation of its products and reactants as... 

In the meantime, Benson had developed an additive approach to the thermochemistry of molecules, based on the idea that thermodynamic properties like A H29i can, at least to a certain extent, be regarded as the sum of A fH29i values ascribed to constituent parts of the molecule, such as the C-C bond or the -CH2 - group. These constituent values he called bond additivity values or group additivity values. We shall see the distinction below. Although the objective of these calculations is the standard state enthalpy of formation, superscript ° will not be used in the notation because calculated AfH29S values are approximate by definition. 

The initial work at Bartlesville has concentrated on measurements of enthalpy changes from dilution and adsorption for surfactant systems. From the observed dilution enthalpy changes, critical micelle concentrations have been determined, and standard state enthalpies of micel lization have been calculated. In the studies on adsorption, several properties are of interest the enthalpy of adsorption, the amount of surfactant adsorbed, the surface area of the solid and determining whether the adsorption is reversible. The kinetics of adsorption and desorption are also of interest. 

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