Enthalpy standard-state changes

More interesting for practical applications is the approach of Pompe et al. [22] where two GC thermodynamic parameters (standard-state changes of enthalpy, AH°, and of entropy, AS°) are estimated. Since these parameters can be used to describe the variation of retention with temperature (see Section 3.2.2), estimations of retention can be extended to other temperature conditions, including programmed temperature. 

This value is one of the many standard molar enthalpies of formation to be foimd in compilations of thermodynamic properties of individual substances, such as the table in Appendix H. We may use the tabulated values to evaluate the standard molar reaction enthalpy AfFf ° of a reaction using a formula based on Hess s law. Imagine the reaction to take place in two steps First each reactant in its standard state changes to the constituent elements in their reference states (the reverse of a formation reaction), and then these elements form the products in their standard states. The resulting formula is... 

Enthalpy is related to internal energy via H =U + PV. For a process at constant pressure (1 bar), AH = AH -i- PAV. The standard state change in volume that occurs in the course of a reaction is determined by the standard state molar volumes of the reactants and products. 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

Since the elements are in their standard states, the enthalpy change for the reaction is equal to the standard enthalpy of COj less the standard enthalpies of C and Oj, which are zero in each instance. Thus,... 

The heal of reaction (see Section 4.4) is defined as tlie enthalpy change of a system undergoing chemical reaction. If the retictants and products are at tlie same temperature and in their standard states, tlie heat of reaction is temied tlie standard lieat of reaction. For engineering purposes, the standard state of a chemical may be taken as tlie pure chemical at I atm pressure. Heat of reaction data for many reactions is available in tlie literature. ... 

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.,... 

Standard Heat of Reaction. This is the standard enthalpy change accompanying a chemical reaction under the assumptions that the reactants and products exist in their standard states of aggregation at the same T and P, and stoichiometric amounts of reactants take part in the reaction to completion at constant P. With P = 1 atm and T = 25°C as the standard state, AH (T,P) can be written as... 

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. 

Enthalpy. Enthalpy is calculated relative to a standard state that is normally chosen as Tq = 298.15 K = 25°C and Pq=1 bar pressure. The change in enthalpy with pressure can usually be ignored. For extreme changes in pressure, use... 

The standard enthalpy of formation AH°f of a compound is defined as the enthalpy change when one mol of the compound is formed from its constituent elements in the standard state. The enthalpy of formation of the elements is taken as zero. The standard heat of any reaction can be calculated from the heats of formation —AH of the products and reactants if these are available or can be estimated. 

In order to have a consistent basis for comparing different reactions and to permit the tabulation of thermochemical data for various reaction systems, it is convenient to define enthalpy and Gibbs free energy changes for standard reaction conditions. These conditions involve the use of stoichiometric amounts of the various reactants (each in its standard state at some temperature T). The reaction proceeds by some unspecified path to end up with complete conversion of reactants to the various products (each in its standard state at the same temperature T). 

The effect of pressure on AG° and AH0 depends on the choice of standard states employed. When the standard state of each component of the reaction system is taken at 1 atm pressure, whether the species in question is a gas, liquid, or solid, the values of AG° and AH0 refer to a process that starts and ends at 1 atm. For this choice of standard states, the values of AG° and AH0 are independent of the system pressure at which the reaction is actually carried out. It is important to note in this connection that we are calculating the enthalpy change for a hypothetical process, not for the actual process as it occurs in nature. This choice of standard states at 1 atm pressure is the convention that is customarily adopted in the analysis of chemical reaction equilibria. 

A/Tf, the standard molar enthalpy of formation of a substance, is the enthalpy change for a reaction in which 1 mole of the substance in a specific state is formed from its elements in their standard states. 

The standard enthalpy change of atomisation of an element, AHtt, is the enthalpy change when one mole of gaseous atoms is produced from the element in its standard state, under standard conditions. 

The standard enthalpy of formation, A fH, of a compound at 0 K reflects the strength of the chemical bonds in the compound relative to those in the constituent elements in their standard state. The standard enthalpy of formation of a binary oxide such as CaO is thus the enthalpy change of the reaction... 

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... 

In much the same fashion as the AH° was tabulated, the standard molar entropies (S°) of elements and compounds are tabulated. This is the entropy associated with 1 mol of a substance in its standard state. Unlike the enthalpies, the entropies of elements are not zero. For a reaction, it is possible to calculate the standard entropy change in the same fashion as the enthalpies of reaction ... 

Enthalpies of reaction can also be calculated from individual enthalpies of formation (or heats of formation), AHf, for the reactants and products. Because the temperature, pressure, and state of the substance will cause these enthalpies to vary, it is common to use a standard state convention. For gases, the standard state is 1 atm pressure. For a substance in an aqueous solution, the standard state is 1 molar concentration. And for a pure substance (compound or element), the standard state is the most stable form at 1 atm pressure and 25°C. A degree symbol to the right of the H indicates a standard state, AH°. The standard enthalpy of formation of a substance (AHf) is the change in enthalpy when 1 mol of the substance is formed from its elements when all substances are in their standard states. These values are then tabulated and can be used in determining A//°rxn. 

In the bomb process, reactants at the initial pressure pi and temperature 7 are converted to products at the final pressure pf and temperature Tf. The primary goal of a combustion calorimetric experiment, however, is to obtain the change of internal energy, Ac//°(7r), associated with the reaction under study, with all reactants and products in their standard states pi = pf = O.IMPa) and under isothermal conditions at a reference temperature 7r (usually 298.15 K). Once AC//°(298.15K) is known, it is possible to derive the standard enthalpy of combustion, AC77°(298.15K), and subsequently calculate the standard enthalpy of formation of the compound of interest from the known standard enthalpies of formation of the products and other reactants. 

The experiments are usually carried out at atmospheric pressure and the initial goal is the determination of the enthalpy change associated with the calorimetric process under isothermal conditions, AT/icp, usually at the reference temperature of 298.15 K. This involves (1) the determination of the corresponding adiabatic temperature change, ATad, from the temperature-time curve just mentioned, by using one of the methods discussed in section 7.1 (2) the determination of the energy equivalent of the calorimeter in a separate experiment. The obtained AT/icp value in conjunction with tabulated data or auxiliary calorimetric results is then used to calculate the enthalpy of an hypothetical reaction with all reactants and products in their standard states, Ar77°, at the chosen reference temperature. This is the equivalent of the Washburn corrections in combustion calorimetry... 

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