Elements in their reference states

These are the properties of the monatomic gas at a pressure of 1 bar. It should be pointed out that this standard molar Gibbs energy is not the AfG° of thermodynamic tables because there the convention in thermodynamics is that the standard formation properties of elements in their reference states are set equal to zero at each temperature. However, the standard molar entropies of monatomic gases without electronic excitation calculated using equation 2.8-11 are given in thermodynamic tables. 

In choosing a reference state, we are allowed to make a choice for each element, because elements cannot be transformed into each other by chemical means. The choice usually made for the reference state of an element is the form in which it is stable at temperature T and the standard pressure =1.0 bar. For example, at most temperatures, for 02 this would be gaseous diatomic molecules for iron, it would be the solid metal, and for bromine, it would be the diatomic in the liquid state below 59°C and in the gaseous state above 59°C. We call the standard enthalpy change of the reaction in which 1 mol of compound i is formed from its component elements in their reference states the heat of formation of compound i, A H°(T). The heat of reaction is related to heats of formation as... 

The term formation and symbol f denote the formation of the substance from elements in their reference state (usually the most stable state of each element at the chosen temperature and standard pressure). The corresponding reaction equation is written so that the stoichiometric number v of the substance is +1. 

A eiei is the number of atoms of element i in the crystalline substance and (j m (298.I5 is the standard molar entropy of element i in its thermodynamic reference state. This equation makes it possible to calculate Af5 ° for a species when Sm ° has been determined by the third law method. Then Af G° for the species in dilute aqueous solution can be calculated using equation 15.3-2. Measurements of pATs, pA gS, and enthalpies of dissociation make it possible to calculate Af G° and Af//° for the other species of a reactant that are significant in the pH range of interest (usually pH 5 to 9). When this can be done, the species properties of solutes in aqueous solution are obtained with respect to the elements in their reference states, just like other species in the NBS Tables (3). 

Use of the third law is not the only way to get large molecules of biochemical reactants into tables of species properties. If apparent equilibrium constants and heats of reaction can be determined for a pathway of reactions from smaller molecules (for which Af G° and Af H° are known with respect to the elements) to form the large molecule, then the properties of the species of the large molecule can be determined relative to the elements in their reference states. This method has its problems in that it is very difficult to determine apparent equilibrium constants greater than about 10 to 10 and the number of reactions in the path may be large and some of the reactants may not be readily available in pure form. Thus it is fortunate that the third law method is available. 

A fH"" represents the standard enthalpy of formation, which is the increment in enthalpy associated with the reaction of forming the given compound from its elements in their reference states, with each substance in its thermodynamic standard state at the given temperature. 

The most frequently used symbols for processes are AfG and A,//, the Gibbs energy and the enthalpy of formation of a compound or complex from the elements in their reference states cf. Table 11-6). 

The heats of formation of some gaseous atoms from the elements in their reference state are given in Table XVIII. 

The thermodynamic data for each compound are either the standard Gibbs energy AG° or equilibrium constant Keq for forming the compound from its constituent elements in their reference states. The reference states are generally the stable form of an element at the ambient temperature. For example, the reaction... 

This is done by rewriting equation (5) in terms of the thermodynamic activity of Fe (a,Fe), the equilibrium constants (K ) for forming the Fe-bearing gases from the constituent elements in their reference states, and the thermodynamic activities and fugacities of all other elements combined with iron in the gases. 

Tabulated values of A/G° and AfH° for the elements in their reference states at various temperatures therefore appear as a column of zeros—see Table 7.1 for example. This of course does not mean that the absolute values G and H are zero. ... 

You might be wondering why the calculation of AH from AHf" values by this method works. The answer lies in the definition of standard enthalpy of formation, which requires AHf" values for elements in their reference states to be zero. Although the standard enthalpies (i.e. energies) of compounds and elements cannot be measured or calculated, the difference between the standard enthalpies of two substances is equal to the difference in the corresponding standard enthalpies of formation. This is the reason why equation (13.15) strongly resembles equation (13.2). 

The AHf of elements in their reference states is zero. AHf (NH4CI04(s)) is obtained from Table 13.2. 

The formation reaction of a substance is the reaction in which the substance, at a given temperature and in a given physical state, is formed from the constituent elements in their reference states at the same temperature. The reference state of an element is usually chosen to be the standard state of the element in the allotropic form and physical state that is stable at the given temperature and the standard pressure. For instance, at 298.15 K and 1 bar the stable allotrope of carbon is crystalline graphite rather than diamond. 

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... 

Molar integral enthalpies of solution and dilution are conveniently expressed in terms of molar enthalpies of formation. The molar enthalpy of formation of a solute in solution is the enthalpy change per amount of solute for a process at constant T and p in which the solute, in a solution of a given molality, is formed from its constituent elements in their reference states. The molar enthalpy of formation of solute B in solution of molality will be denoted by Afi/(B, hib). 

An amount b of the pure solute decomposes to the constituent elements in their reference states. This is the reverse of the formation reaction of the pure solute. 

The Gibbs free energies of formation of a number of gaseous and condensed species from their elements in their reference states were obtained from the JANAF tables. Chase (1982). These were then converted to the energies of formation from the elements in their neutral ideal monatomic gaseous state, and polynomials of the type... 

The problem with eqn 1.22 is that we have no way of knowing the absolute enthalpies of the substances. To avoid this problem, we can imagine the reaction as taking place by an indirect route, in which the reactants are first broken down into the elements and then the products are formed from the elements (Fig. 1.24). Specifically, the standard enthalpy of formation, AfH, of a substance is the standard enthalpy (per mole of the substance) for its formation from its elements in their reference states. The reference state of an element is its most stable form under the prevailing conditions (Table 1.7). Don t confuse reference state with standard state the reference state of carbon at 25 C is graphite (not diamond) the standard state of carbon is any specified phase of the element at 1 bar. For example, the standard enthalpy of formation of liquid water (at 25 C, as always in this text) is obtained from the thermochemical equation... 

The values of some standard enthalpies of formation at 25°C are given in Table 1.8, and a longer list is given in the Resource section. Tlie standard enthalpies of formation of elements in their reference states are zero by definition (because their formation is the null reaction element element). Note, however, that the standard enthalpy of formation of an element in a state other than its reference state is not zero ... 

Note that in the preceding equations, the absolute values of entropy and iso-baric heat capacity are used. As it is known from thermodynamics, the absolute values of Gibbs energy and enthalpy are not known, but the absolute values of their temperature and pressure derivatives are known. Also, we should keep in mind that the Gibbs energies and enthalpies of formation of all chemical elements in their reference state conventionally equal zero at any temperature. In addition, the absolute values of entropy, heat capacity, etc. (all other derivatives) of... 

For historical reasons, G°, is also defined to be zero for the pure elements in their reference states. For other substances, G° is the reaction Gibbs energy for making the substances in their standard state from the constituting elements in their reference states. This is a point that one should be aware of, because its implication is that when using tabulated values, generally... 

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