New Recommendations 4.1

Contents of Section

4 Additional New Recommendations
4.1 Recommendations concerning chemical reactions
References for this Section

4.1 Recommendations Concerning Chemical Reactions

The thermodynamics of reactions of species in aqueous solution is discussed in every textbook on physical chemistry, but this section is included to contrast the nomenclature with that of the next section and to respond to the special needs of biochemistry. As mentioned in Section 3, equilibrium constants of chemical reactions that are used in biochemistry are taken to be functions of T, P, and I. Therefore, the standard thermodynamic properties are also functions of T, P, and I. The standard Gibbs energy of reaction D_r G ^o for reaction 9 is calculated using

D_r G ^o = - RT ln K . . . . . . . . (11)

and there are corresponding values of D_r H ^o and D_r S ^o that are related by

D_r G ^o = D_r H ^o - TD_r S ^o . . . . . . . . (12)

The standard enthalpy of reaction is given by

. . . . . . . . (13)

If D_r H ^o is independent of temperature in the range considered, it can be calculated using

D_r H ^o = [RT₁T₂/(T₂ - T₁)] ln (K₂/K₁) . . . . . . . . (14)

If the standard molar heat capacity change D_r CP ^o is not equal to zero and is independent of temperature, the standard molar enthalpy of reaction varies with temperature according to

D_r H^o(T) = D_r H^o(T *) + D_r C_P^o(T - T *) . . . . . . . . (15)

The reference temperature T * is usually taken as 298.15 K. In this case, D_r G ^o and K vary with temperature according to (ref. 6)

D_r G ^o(T) = - RT ln K(T )

= D_r H^o(T *) + D_r C_P^o(T - T *) + T {D_r G ^o(T *) - D_r H ^o(T *)}/T * - T D_r C_P^o ln (T/T *) . . . . . . . . (16)

Additional terms containing (D_r C_P^o/T )_P and higher order derivatives may be needed for extremely accurate data or for a very wide temperature range.

Equations 13 and 14 are exact only when the equilibrium constants are based on a molality standard state. If the equilibrium constants were determined with a standard state based on molarity, these equilibrium constants should be converted to a molality basis prior to using equation 13. For dilute aqueous solutions, m_i = c_i/r where m_i and c_i are, respectively, the molality and the molarity of substance i and r is the mass density of water in kg L^-1. If this conversion is not made, there is an error of RT ²(lnr /T)_P,I for each unsymmetrical term in the equilibrium constant. This quantity is equal to 0.187 kJ mol^-1 for dilute aqueous solutions at 298.15 K. Similar statements pertain to equations 27 and 28, which are given later in this document.

Since the standard thermodynamic properties D_r G ^o and D_r H ^o apply to the change from the initial state with the separated reactants at c ^o to the final state with separated products at c ^o, it is of interest to calculate the changes in the thermodynamic properties under conditions where the reactants and products have specified concentrations other than c ^o. The change in Gibbs energy D_r G in an isothermal reaction in which the reactants and products are not all in their standard states, that is, not all at 1 M, is given by

D_r G = D_r G^o + RTlnQ . . . . . . . . (17)

where Q is the reaction quotient of specified concentrations of species. The reaction quotient has the same form as the equilibrium constant expression, but the concentrations are arbitrary, rather than being equilibrium concentrations. Ideal solutions are assumed. The change in Gibbs energy D_r G in an isothermal reaction is related to the change in enthalpy D_r H and change in entropy D_r S by

D_r G = D_r H - TD_r S . . . . . . . . (18)

The corresponding changes in entropy and enthalpy are given by

D_r S = D_r S^o - RlnQ . . . . . . . . (19)

D_r H = D_r H^o . . . . . . . . (20)

The standard reaction entropy can be calculated from the standard molar entropies of the reacting species: D_r S ^o = S n_i^o(i ), where n_i is the stoichiometric number (positive for products and negative for reactants) of species i.

The electromotive force E of an electrochemical cell is proportional to the D_r G for the cell reaction.

D_r G = - |n_e|FE . . . . . . . . (21)

where |n_e| is the number of electrons transferred in the cell reaction and F is the Faraday constant (96 485.31 C mol^-1). Substituting equation 17 yields

. . . . . . . . (22)

where E ^o = - D_r G ^o/|ne|F is the standard electromotive force, that is the electromotive force when all of the species are in their standard states, but at the ionic strength specified for D_r G ^o. The electromotive force for a cell is equal to the difference in the electromotive forces of the half cells.

The standard Gibbs energy and enthalpy of reaction can be calculated from the formation properties of the species.

D_r G ^o = S n_iD_f G ^o(i) . . . . . . . . (23)

D_r H ^o = S n_iD_f H ^o(i) . . . . . . . . (24)

where the n_i is the stoichiometric numbers of species i. The standard entropy of formation of species i can be calculated using

D_f S ^o(i) = D_f H ^o(i) - D_f G ^o(i)]/T . . . . . . . . (25)

Two special needs of biochemistry are illustrated by considering the seven species in Table I. The first part of Table I gives the standard thermodynamic properties as they are found in the standard thermodynamic tables (see Appendix). The standard thermodynamic tables give the standard formation properties for the standard state, which is the state in a hypothetical ideal solution with a concentration of 1 M but the properties of an infinitely dilute solution and the activity of the solvent equal to unity. This means that the tabulated thermodynamic properties apply at I = 0. Since many biochemical reactions are studied at about I = 0.25 M, the tabulated values of D_f G ^o(i) and D_f H ^o(i) in The NBS Tables of Chemical Thermodynamic Properties and the CODATA Key Values for Thermodynamics have to be corrected to ionic strength 0.25 M, as described in Section 5.3. The values at I = 0.25 M are given in the second part of Table I. No adjustments are made for H₂O, MgHPO₄, and glucose because the ionic strength adjustment is negligible for neutral species. We will see in Section 5.1 that the transformed Gibbs energy G ' is the criterion of equilibrium at specified pH and pMg. In Section 5.4, we will see that the calculation of transformed thermodynamic properties involves the adjustment of the standard formation properties of species to the desired pH and pMg by use of formation reactions involving H⁺ and Mg²⁺. The standard transformed formation properties of species can be calculated at any given pH and pMg in the range for which the acid dissociation constants and magnesium complex dissociation constants are known. However, for the purpose of making tables, it is necessary to choose a pH and pMg that is of general interest. For the tables given here, pH = 7 and pMg = 3 are used because they are close to the values in many living cells. Table II shows the result of these calculations for the species in Table I. The ions H⁺ and Mg²⁺ do not appear in this table because it applies at pH = 7 and pMg = 3. These methods have been applied to calculate the transformed formation properties of P_i (ref. 4); glucose 6-phosphate (ref. 5); adenosine, AMP, ADP, and ATP (ref. 7).

Table I. Standard Formation Properties of Aqueous Species at 298.15 K.

In making these calculations, the pH has been defined by pH = - log₁₀([H⁺]/c ^o), rather than in terms of the activity, as it is in more precise measurements. The reason for doing this is that approximations are involved in the interpretation of equilibrium experiments on biochemical reactions at the electrolyte concentrations of living cells. Even Na⁺ and K⁺ ions are bound weakly by highly charged species of biochemical reactants, like ATP. As an approximation the acid dissociation constants and magnesium complex dissociation constants are taken to be functions of the ionic strength and the different effects of Na⁺ and K⁺ are ignored. These approximations can be avoided in more precise work, but only at the cost of a large increase in the number of parameters and the amount of experimental work required.

4. Alberty, R. A. (1992) Biophys. Chem. 42, 117-131.

5. Alberty, R. A. (1992) Biophys. Chem. 43, 239-254.

6. Clarke, E. C. W., and D. N. Glew, D. N. (1966) Trans. Faraday Soc. 62, 539-547.

7. Alberty, R. A., and Goldberg, R. N. (1992) Biochemistry 31, 10610-10615.

8. Wilhoit, R. C. (1969) Thermodynamic Properties of Biochemical Substances, in Biochemical Microcalorimetry, H. D. Brown, ed., Academic Press, New York.

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