Standard state conditions

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... 

Appendix 3D contains a listing of the standard-state reduction potentials for selected species. The more positive the standard-state reduction potential, the more favorable the reduction reaction will be under standard-state conditions. Thus, under standard-state conditions, the reduction of Cu + to Cu E° = -1-0.3419) is more favorable than the reduction of Zn + to Zn (E° = -0.7618). 

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. 

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. 

Calculate the value of A l,/ for the glyceraldehyde-3-phos-phate dehydrogenase reaction, and calculate the free energy change for the reaction under standard-state conditions. 

The hydrolysis of fructose-1,6-bisphosphate to fructose-6-phosphate (Eigure 23.7), like all phosphate ester hydrolyses, is a thermodynamically favorable (exergonic) reaction under standard-state conditions (AG° = —16.7 kj/mol). Under physiological conditions in the liver, the reaction is also exergonic (AG = —8.6 kJ/mol). Fructose-1,6-bisphosphatase is an allosterically regulated enzyme. Citrate stimulates bisphosphatase activity, hut fructose-2,6-bisphosphate is a potent allosteric inhibitor. / MP also inhibits the bisphosphatase the inhibition by / MP is enhanced by fructose-2,6-bisphosphate. 

Summarizing, ° measures quantitatively the difference between the tendency to minimum energy and tendency to maximum randomness under the standard state conditions. 

Exceptions to the use of SI units are found in Chapter 10 where we work with molecules instead of moles, and units such as cm-1 for energy are common. We will also find the bar unit for pressure to be very useful as we define standard state conditions, but a pressure of one atmosphere (atm) is still the condition that defines the normal boiling point and the normal freezing point of a liquid. 

The determination of ArG° for a chemical reaction is very useful in predicting the course of the reaction. Qualitatively, we will show in Chapter 5 that with ArC°<0, the reaction is spontaneous, at least when products and reactants are in their standard state condition. Quantitatively, we will see in Chapter 9 that ArG° can be used to calculate the equilibrium constant for the reaction, from which the final equilibrium conditions can be determined. 

In defining the activity through equations (6.83) and (6.84), we have made no restrictions on the choice of a standard state except to note that specification of temperature is not a part of the standard state condition. We are free to choose standard states in whatever manner we desire.p However, choices are usually made that are convenient and simplify calculations involving activities. The usual choices differ for a gas, pure solid or liquid, and solvent or solute in solution. We will now summarize these choices of standard states and indicate the reasons. Before doing so, we note that activities for a substance with different choices of standard states are proportional to one another. This can be seen as follows With a particular choice of standard state... 

Later, we will make equilibrium calculations that involve activities, and we will see why it is convenient to choose the ideal gas as a part of the standard state condition, even though it is a hypothetical state/ With this choice of standard state, equations (6.94) and (6.95) allow us to use pressures, corrected for non-ideality, for activities as we make equilibrium calculations for real gases.s... 

Equation (9.5) enables us to calculate ArG for a chemical reaction under a given set of activity conditions when we know the free energy change for the reaction under the standard state condition. Of special interest are the activities when reactants and products are at equilibrium. Under those conditions,... 

Aris obtained from the direct combination of the gaseous elements under the standard state condition. 

For a chemical cell operated under standard state conditions, equation (9.91) becomes... 

List aU chemical species, both elements and compounds, that are believed to exist at equilibrium. By element we mean the predominant species at standard-state conditions, for example, O2 for oxygen at 1 bar and 298.15 K. 

Because AG° = -nFE%c and AG° = -RT InK, the signs and magnitudes of i ceii> AG° and K are related as shown in the following table for different types of reactions under standard state conditions. 

The large positive standard reduction potential for this reaction indicates that the reaction will occur spontaneously, with products being strongly preferred under standard state conditions. 

Here, the concept of linkage implies only that each intermolecular noncovalent bond is sufficiently large compared with kTto withstand ambient thermal collisions. Thus, for near-standard-state conditions (where kT 0.6kcal mol-1), even weak noncovalent interactions of 1-2 kcal mol-1 may be adequate to yield supramolecular complexes with stable equilibrium populations, thereby becoming true constituent units of the phase of lowest free energy. 

Thus far, we have based all of our calculations on the standard cell potential or standard half-cell potentials—that is, standard state conditions. However, many times the cell is not at standard conditions—commonly the concentrations are not 1 M. We may calculate the actual cell potential, Ecell, by using the Nemst equation ... 

The second and third method allow the measurement of surface complexation constants at various transition metal loadings and consequently yield apparent composition dependent constants. In the first method on the contrary a truly thermodynamic constant is obtained under standard state conditions. 

Should we regard 407.1 2.0 kJ mol-1 as the final value for the enthalpy of reaction 2.13 under the experimental conditions Recall that the starting assumption was p = 1 bar and the standard state conditions refer to the ideal gases at that pressure or to the real gases at zero pressure. The ideal gas model (or the ideal gas equation) describes very well the behavior of most gases at 1 bar, so it is... 

The standard state Helmholtz free energy difference, 8AA°, was introduced in Equations 5.9 and 5.11 to show the connection between VPIE and molecular structure and dynamics. Molecular properties are conveniently expressed using standard state canonical partition functions for the condensed and vapor phases, Qc° and Qv° remember A0 = —RT In Q°. The Q s are 3nN dimensional, n is the number of atoms per molecule and N is Avogadro s number. For convenience we have now dropped the superscript o s on the Q s. The o s specify standard state conditions, now to be implicitly understood. For VPIE and a respectively, not too close to the critical region,... 

Equation (1.27) relates the difference in free energy for a gas at any pressure and temperature to the standard state condition at constant temperature. Here dH = 0, and from Eq. (1.15) the relationship of the entropy to the pressure is found to be... 

Very often thermodynamic parameters of adsorption, calculated from different isotherms and reported in the literature, can scarcely be compared because the standard-state conditions used in the calculation are not specified. 

The Gibbs energy of adsorption is a measure of adsorbate-metal interactions. Its values depend, however, on the choice of standard states for the chemical potentials of the components involved in the process. Therefore AG° values determined for different systems can only be compared if they refer to the same standard-state conditions. AG° values of adsorption of thiourea (TU) on several metallic electrodes, calculated for the most often used standard states, are presented in Table 1. 

For the sake of consistency, all AG° values given in the text of this review refer to the standard-state conditions = 1, and <9° = 1, and the reference state 6> = 0. 

---