Standard-state free energies

ESTIMATE OF RELATIVE FREE ENERGIES STANDARD STATES... 

Estimate of Relative Free Energies Standard States 47... 

Table 16-1 compiles some data for S°, the molar entropy, and AGp the free energy of formation from the elements. All values in Table 16-1 are presented at 25°C and at standard states. Notice that the units of entropy and free energy are stated per mole, mol-1. This means that the moles used to balance a chemical reaction are included by the multiplication of the coefficient (mol in balanced equation) and the value from the table so that unit mol cancels. This is also the way in which we handled calculations involving AH values. 

Standard free energy Standard free energy of a reaction gives die increase of free energy when the reactants, all in their standard states of unit pressure or unit concentration are converted at constant temperature (7) into the products, which are also in their standard states. The standard free energy is given by the expressions,... 

For the electrostatic component, the free energy varies in a harmonic fashion with respect to deviations from equilibrium with a constant force constant (Figure 11.19). This is a standard result from dielectric theory and means that the mean square fluctuations of the energy on the two surfaces (the second terms in Equation (11.41)) will cancel, leaving just the first term. This leads to a value of for the electrostatic component (i.e. d = 0 5). A simple test of this theory is to calculate the electrostatic contribution to solvation free energies. Here, state X corresponds to the situation where all of the solvent-solvent and intramolecular solute interactions are present but the interaction between the solute and solvent is only described... 

The value of the standard free energy AG depends on the choice of reference state, as does the equilibrium constant. Thus it would be safer to write the equilibrium constant K for a gaseous reaction as... 

A2.1.6.7 STANDARD STATES AND STANDARD FREE ENERGIES OF FORMATION... 

Conventions about standard states (the reference states introduced earlier) are necessary because otherwise the meaning of the standard free energy of a reaction would be ambigrious. We sunnnarize the principal ones ... 

For a free energy of fonnation, the preferred standard state of the element should be the thennodynamically stable (lowest chemical potential) fonn of it e.g. at room temperature, graphite for carbon, the orthorhombic crystal for sulfiir. 

The confinement term is unique because it alone causes a dependence of the binding free energy on the choice of unit concentration in the standard state the volume available per ligand molecule in the free state, and hence the compression factor, depend on the unit concentration. 

Clearly, a free energy of binding computed with (9), (10) and (13) refers to a highly restricted state of the dissociated ligand. In order to convert such a free energy to a free energy relative to a normal standard state with volume per molecule Vg and no restriction on the molecular orientation, the following term must be added... 

The free energy differences obtained from our constrained simulations refer to strictly specified states, defined by single points in the 14-dimensional dihedral space. Standard concepts of a molecular conformation include some region, or volume in that space, explored by thermal fluctuations around a transient equilibrium structure. To obtain the free energy differences between conformers of the unconstrained peptide, a correction for the thermodynamic state is needed. The volume of explored conformational space may be estimated from the covariance matrix of the coordinates of interest, = ((Ci [13, lOj. For each of the four selected conform-... 

To reiterate a point that we made earlier, these problems of accurately calculating the free energy and entropy do not arise for isolated molecules that have a small number of well-characterised minima which can all be enumerated. The partition function for such systems can be obtained by standard statistical mechanical methods involving a summation over the mini mum energy states, taking care to include contributions from internal vibrational motion. 

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... 

The values given in the following table for the heats and free energies of formation of inorganic compounds are derived from a) Bichowsky and Rossini, Thermochemistry of the Chemical Substances, Reinhold, New York, 1936 (h) Latimer, Oxidation States of the Elements and Their Potentials in Aqueous Solution, Prentice-Hall, New York, 1938 (c) the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards and (d) the tables of Selected Values of Chemical Thermodynamic Properties of the National Bureau of Standards. The reader is referred to the preceding books and tables for additional details as to methods of calculation, standard states, and so on. 

II The increment in the free energy, AF, in the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are for a gas, fugacity (approximately equal to the pressure) of 1 atm for a pure liquid or solid, the substance at a pressure of 1 atm for a substance in aqueous solution, the hyj)othetical solution of unit molahty, which has all the properties of the infinitely dilute solution except the property of concentration. 

ITlie free energy of solution of a given substance from its normal standard state as a sohd, liquid, or gas to the hyj)othetical one molal state in aqueous solution may he calculated in a manner similar to that described in footnote for calculating the heat of solution. 

Thus, the standard state concentration cancels from these double free energy differences. The calculation can be done by mutating L to L (or R to R ) both in the complex and in solution (horizontal legs of Fig. la). 

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. 

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