Average affinity of reaction

We shall now show that the formulae linking the affinity to the heat of reaction developed in chap. IV, 2, can be applied also to the average heat and average affinity of reaction. 

These last two relations have also been used extensively for finding the average affinity of reaction. ... 

The physical quantity that we usually call the affinity of a reaction corresponds to the average affinity of the reaction. Generally, the affinity of a reaction at constant T and V differs numerically from that at constant 2"and p, as compared to the heat of reaction whose... 

This is the direct relation connecting the average affinity and the average heat of reaction. 

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

The latter equation is of great importance as it allows a calculation of the average affinity - (AG)2r from a knowledge of the average heat (AH)t,2) average entropy of reaction ASYrr r ... 

Equations (4.8) and (4.9) can also be written in terms of the average affinity and average heat of reaction. We start from the Gibbs-Helmholtz relation (4.33) and apply this to one state in which = 1, and another in which T and V have the same values but = 0 ... 

However, if the total affinity A is spread over, let us say, n = 10 reaction steps, then each individual reaction step corresponds, on average, to a reduced chemical affinity of 0.1A/RT0 = 0.5, with a reduced chemical velocity of 0.4, according to Figure 4.3. So, the same chemical "distance" is now covered with a much smaller velocity and the corresponding lost work rate has been reduced accordingly. Point C in Figure 4.5. shows the reduced lost work per step, and Point C the total lost work for the multistep reaction. Point C in... 

Equation 4.20 indicates that the average affinity at constant T and p is equivalent to the decrease (AG)t in the free enthalpy (Gibbs energy) that occurs during the advancement of one equivalent extent of the reaction. 

We see that the average affinity A of a reaction at a temperature T can be calculated, if we know (a) the average affinity A 11 at one specified temperature T0 at the pressure p (b) the heat of reaction (AH)T(j p at T0 and (c) the partial molar heat capacities of the constituent substances as a function of temperature throughout the whole range from roto T. 

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. 

Relations between the Heat of Reaction and Average Affinity. 

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