Transformed enthalpy

Determination of transformation enthalpies in binary systems. Just as consistent values of for elements can be obtained by back-extrapolation from binary systems, so it is possible to obtain values of by extrapolating the enthalpy of mixing vs composition in an alloy system where the phase has a reasonable range of existence. The archetypal use of this technique was the derivation of the lattice stability of f.c.c. Cr from the measured thermodynamic properties of the Ni-based f c.c. solid solution (7) in the Ni-Cr system (Kaufman 1972). If it is assumed that the f.c.c. phase is a regular solution, the following expression can be obtained ... 

This equation reproduces the second column of Table 3.1 to 0.1% accuracy. The coefficient RT2(da/dT)P in the equation for the standard transformed enthalpy of formation of a species is given by... 

Application of the Gibbs-Helmholtz equation to equation 4.4-1 yields the standard transformed enthalpy of reaction... 

There is a corresponding equation for the transformed enthalpy of formation of... 

Thus the availability of AtH (I = 0) for a species makes it possible to calculate ArH j and vice versa. Note that the standard transformed enthalpy of a species is independent of pH, even when it contains hydrogen atoms. At temperatures other than 298.15 K the numerical coefficient of the ionic strength term has different values, as discussed in Section 3.7. 

The standard transformed enthalpy of formation of the pseudoisomer group is a... 

The values of AtH ° calculated using this table can be used to calculate apparent equilibrium constants at other temperatures not too far from 298.15 K. Note that standard transformed enthalpies of reactants that consist of a single species are not a function of pH (see equation 4.4-12). The standard transformed enthalpies of reactants are functions of pH when there are more than two species because rt depends on pH. As indicated by the pH dependencies in Table 4.3, these differences are often small. 

Figure 4.3 shows the dependence of the standard transformed enthalpy of this reaction on pH. Figure 4.4 shows the dependence of ArS ° on pH. The enthalpy does not vary much with pH, but the entropy increases significantly above pH 6. This causes the equilibrium to shift further in the direction of hydrolysis at higher pHs. 

The transformed enthalpy of a biochemical reaction is a function of temperature, pH, and ionic strength. Knowledge of AfG°, AfH°, and CPm for all the species in a biochemical reaction makes it possible to calculate ArG °, ArH °, ArC P°, and K for the biochemical reaction at the desired T, pH, and ionic strength. Note that when ions are involved there is an electrostatic contribution that varies with temperature (see Section 3.7). 

CALORIMETRIC DETERMINATION OF THE STANDARD TRANSFORMED ENTHALPY OF REACTION... 

When a biochemical reaction that is affected by pH and pMg is carried out in a calorimeter in a buffer, the hydrogen ions and magnesium ions that are produced or consumed react with the buffer to produce a heat effect that is characteristic of the buffer, rather than the reaction being studied. Therefore this contribution should be calculated and should be used to correct the calorimetric heat effect to obtain the standard transformed enthalpy of the biochemical reaction ArH °. The analysis by Alberty and Goldberg (1993) shows that the enthalpy change in the calorimetric experiment ArH(cal) is given by... 

CALCULATION OF STANDARD TRANSFORMED ENTHALPIES OF REACTIONS FROM THE STANDARD ENTHALPIES OF FORMATION OF SPECIES... 

If the enthalpies of formation of all the species involved are known, the standard transformed enthalpy of a biochemical reaction Ar// ° at a specific T, P, pH, etc.,... 

Equation 10.2-7 shows that there are three contributions to the transformed enthalpy of reaction in this case the effects of the standard enthalpies of formation of the species, the effect due to the change in binding of hydrogen ions, and the... 

The determination of standard transformed enthalpies of biochemical reactions at specified pH, either from temperature coefficients of apparent equilibrium constants or by calorimetric measurements, makes it possible to calculate the corresponding standard transformed entropy of reaction using... 

McQuarrie (2000) gives a nice table like this for several types of partition functions. The further transformed enthalpy H of the system at specified pFI can be calculated by use of the Gibbs-Helmholtz equation ... 

The subscripts on the partial derivatives have been omitted because they are complicated, as indicated by the fundamental equation. The change in binding of coenzymes in a reaction can be studied at constant concentrations of coenzymes, just as the change in binding of hydrogen ions in a reaction can be studied at constant pH. The further transformed enthalpy H" of the system can be calculated by use of the Gibbs-Helmholtz equation or from G" = II" — TS". 

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