Standard state changing

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 states that the standard-state change of F for reaction is simply given by the sum of the properties of formation for each molecule i, with each weighted by its stoichiometric coefficient. Recall that v,y > 0 for products, but V y < 0 for reactants. Properties of formation are zero when the molecule is an element (e.g., H2, O2, N2, etc.). Otherwise, values for properties of formation depend, not only on the standard temperature and pressure, but also on the phase. We first consider corrections for changes in temperature and then for changes in phase. 

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. 

The values of fH° and Ay.G° that are given in the tables represent the change in the appropriate thermodynamic quantity when one mole of the substance in its standard state is formed, isothermally at the indicated temperature, from the elements, each in its appropriate standard reference state. The standard reference state at 25°C for each element has been chosen to be the standard state that is thermodynamically stable at 25°C and 1 atm pressure. The standard reference states are indicated in the tables by the fact that the values of fH° and Ay.G° are exactly zero. 

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 first term, AG°, is the change in Gibb s free energy under standard-state conditions defined as a temperature of 298 K, all gases with partial pressures of 1 atm, all solids and liquids pure, and all solutes present with 1 M concentrations. The second term, which includes the reaction quotient, Q, accounts for nonstandard-state pressures or concentrations. Eor reaction 6.1 the reaction quotient is... 

If Gf is arbitrarily set equal to zero for all elements in their standard states, then for compounds Gf = AG°, the standard Gibbs-energy change of formation for species i. In addition, the fugacity is eliminated in favor of the fugacity coefficient by Eq. (4-79),/ = yi jP. With these substitutions, the equation for becomes... 

But spontaneity depends on the concentrations of reactants and products. If the ratio [Bl YCA] is less than a certain value, the reaction is spontaneous in the forward direction if [Bl YCA] exceeds this value, the reaction is spontaneous in the reverse direction. Therefore, it is useful to define a standard free-energy change (AG°) which applies to a standard state where [A] = [B] = 1 M. 

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 ... 

The free energy change for non-standard-state concentrations is given by... 

In any of these forms, this relationship allows the standard-state free energy change for any process to be determined if the equilibrium constant is known. More importantly, it states that the equilibrium established for a reaction in solution is a function of the standard-state free energy change for the process. That is, AG° is another way of writing an equilibrium constant. 

Equation (3.12) shows that the free energy change for a reaction can be very different from the standard-state value if the concentrations of reactants and products differ significantly from unit activity (1 Mfor solutions). The effects can often be dramatic. Consider the hydrolysis of phosphocreatine ... 

If the AG° for this reaction is —30.5 kJ/mol, what is AG° (that is, the free energy change for the same reaction with all components, including H, at a standard state of 1 AT) ... 

Hexokinase catalyzes the phosphorylation of glucose from ATP, yielding glncose-6-P and ADR Using the values of Table 3.3, calculate the standard-state free energy change and equilibrium constant for the hexokinase reaction. 

Under cellular conditions, this first reaction of glycolysis is even more favorable than at standard state. As pointed out in Chapter 3, the free energy change for any reaction depends on the concentrations of reactants and products. 

We have already noted that the standard free energy change for a reaction, AG°, does not reflect the actual conditions in a ceil, where reactants and products are not at standard-state concentrations (1 M). Equation 3.12 was introduced to permit calculations of actual free energy changes under non-standard-state conditions. Similarly, standard reduction potentials for redox couples must be modified to account for the actual concentrations of the oxidized and reduced species. For any redox couple. 

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