Average values of the affinity

The average heat of reaction at constant T and V is thus equal to the decrease in internal energy in that reaction. 

The mean affinity during the change is defined by Thus 

The average affinity of a change which corresponds to one equivalent of reaction, is thus equal to the uncompensated heat of that reaction. 

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Equations (5.20) and (5.21) allow us to calculate the average value of the affinity for a change carried out either with T and F, or T and p constant. They must not be confused with equations (4.3) which give the value of the affinity for a given instantaneous state of the system. 

The average value of the orbital energy can be calculated from the assumed wave function. If the wave function were exact, the orbital energy would indeed be constant, as required. For the approximate T°, the average orbital energy is equal to the ionization potential /, according to Koopmans theorem. In Equation 11.13, the electron affinity A has dropped out. 

As we have seen the affinity of a reaction is at any instant a function of state of the system, and does not depend upon the conditions under which changes in the system occur. If we consider not the instantaneous value of the affinity but the average value in the course of a reaction, then this average will depend upon the conditions under which the reaction occurs e.g, whether at constant T and p, or T and V. In this book we shall employ the instantaneous values of the affinity, but to show the relationship between the present methods, and those introduced by Lewis and Randall we now proceed to express the average values of both heat of reaction and affinity in terms of the thermodynamic functions Z7, H, F and G. 

Fluorescence and affinity measurements - Peptide in 25 mM Tris, 100 mM KCl and 1 mM CaCl2 at pH 7.5 and 30 C was titrated with a stock solution of calmodulin in UV transmitting plastic cuvettes since the peptides appear to bind to glass. Fluorescence titration spectra were recorded using a SPEX FluoroMax fluorescence spectrometer with excitation at 280 nm and emission scanned from 310 to 390 nm. The value of fluorescence intensity at 330nm was plotted as a function of calmodulin concentration and fitted using standard non-linear least squares methods (6) to obtain optimal values of the dissociation constant (Kj) and the maximum fluorescence enhancement (F/F ). The detection limit under our experimental conditions was 50 nM peptide and all quoted Kj values are the average of at least 3 independent determinations. 

The objective of any review of experimental values is to evaluate the accuracy and precision of the results. The description of a procedure for the selection of the evaluated values (EvV) of electron affinities is one of the objectives of this book. The most recent precise values are taken as the EvV. However, this is not always valid. It is better to obtain estimates of the bias and random errors in the values and to compare their accuracy and precision. The reported values of a property are collected and examined in terms of the random errors. If the values agree within the error, the weighted average value is the most appropriate value. If the values do not agree within the random errors, then systematic errors must be investigated. In order to evaluate bias errors, at least two different procedures for measuring the same quantity must be available. 

Related procedures for estimating electron affinities make use of the concept of electronegativity (EN). These use the Mulliken [33] definition of absolute electronegativity, the average of the first ionization potential and the first electron affinity, EN = (IP + EA)/2. With an estimate of the Mulliken electronegativity and the experimental value of the ionization potential, the electron affinities can be calculated. When both the electron affinity and ionization potential are measured, the relationship between the EN and experiment can be examined. This has been accomplished for aromatic hydrocarbons and will be discussed in Chapter 10. 

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