The calculation of D f G i' o for a species is discussed in Section 5.4 and the calculation of D f G i' o for a reactant is discussed in Section 5.5. (49)ĭ f G i' = D f G i' o + RT ln (/ c o). Where N H( i) is the number of hydrogen atoms in species i and N Mg( i ) is the number of magnesium atoms in species i.Īlthough thermodynamic derivations are carried out using the chemical potential, in actual calculations, the chemical potential m i of species i is replaced by the Gibbs energy of formation D f G i and the transformed chemical potential m i ' of species i is replaced by the transformed Gibbs energy of formation D f G i', whereĭ f G i = D f G i o + RT ln (/ c o). The reaction is generally an enzyme-catalyzed reaction, but these concepts apply to any reaction involving a weak acid or metal ion complex when the pH and concentration of free metal ion at equilibrium are specified.Ī consequence of equation 46 is that the chemical potential m i of each species in the system is replaced by the transformed chemical potential m i ' given by Under the appropriate circumstances, the magnesium term can be left out or be replaced by a term in another metal ion. This is the fundamental justification for the use of G ' in biochemistry. It can be shown that (d G ') T,P,pH,pMg 0, so that G ' is at a minimum when T, P, pH, and pMg are held constant. The transformed Gibbs energy G ' is defined in order to obtain a criterion of spontaneous change at T, P, pH, and pMg. Where m(H +) o is the chemical potential of H + at 1 M in an ideal solution at specified T, P, and I. Here n '(H +) is the total amount of H + in the system (bound and unbound) and m(H +) is the specified chemical potential for H +, which is given for an ideal solution by To define a transformed Gibbs energy G ' in terms of the Gibbs energy G. 22) have described the use of transformed Gibbs energies in describing macromolecular components in solution. 20, 21) used a Legendre transform to develop a criterion for equilibrium for the alkylation of benzene by ethylene at a specified partial pressure of ethylene. For example, the internal energy can be transformed directly to G by use of G = U + PV - TS. The Gibbs energy is especially useful because it provides the criterion for equilibrium at specified T and P. To obtain a criterion at specified T and P, the Gibbs energy was defined by the Legendre transform G = H - TS so that (d G ) T,P 0. To obtain a criterion at specifed T and V, the Helmholtz energy was defined by the Legendre transform A = U - TS so that (d A ) T, V 0. To obtain a criterion at specified S and P, the enthalpy was defined by the Legendre transform H = U + PV so that (d H ) S,P 0. That is, if S and V are held constant, U can only decrease and is at a minimum at equilibrium. The criterion for spontaneous change at specified S and V is (d U ) S, V 0. Where U is the internal energy and S is the entropy. The combined first and second law for a closed system involving only pressure-volume work is The definition of a transformed Gibbs energy is a continuation of a process that starts with the first and second laws of thermodynamics, but is not always discussed in terms of Legendre transforms. 5 Thermodynamic Background Recommendations for nomenclature and tables in biochemical thermodynamicsĥ Thermodynamic BackgroundContinued from 4.4 Experimental mattersĥ.4 Adjustment of standard thermodynamic properties of species to the desired pH and pMgĥ.5 Calculation of the standard formation properties of a pseudoisomer group at specified pH and pMgĥ.6 The actual experiment and thought experiments
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