Reaction quantity molar integral

AX/ A is a molar integral reaction quantity, the ratio of two finite differences between the final and initial states of a process. These states are assumed to have the same temperature and the same pressure. This book will use a notation such as A//ni(rxn) for a molar integral reaction enthalpy ... 

For certain kinds of processes, it may happen that a partial molar quantity X, remains constant for each species i as the process advances at constant T and p. If X, remains constant for each i, then according to Eq. 11.2.15 the value of AfX must also remain constant as the process advances. Since ArX is the rate at which X changes with in such a situation X is a linear function of This means that the molar integral reaction quantity AXm(rxn) defined by AX/ A is equal, for any finite change of f, to AfX. 

In dealing with the change of an extensive property X as changes, we must distinguish between molar integral and molar differential reaction quantities. 

Since the value of a standard molar reaction quantity is independent of the standard molar integral and differential quantities are identical (page 317) ... 

The mol -1 in the units identifies the quantities in this example as the change per extent of reaction. They may be called the molar enthalpy and entropy of reaction, and a subscript m may be added to the symbol, to emphasize the difference from the integral quantities if required. 

Since the charge of an electron is 1.6 x 1(T coulombs, one mole of electrons contains a total charge of 96,487 coulombs. This quantity, known as Faraday s constant, relates the current to the molar rate of product formation or reactant consumption in an electrochemical reaction. Molar rate expressions for the forward and backward reactions of Equation (26.13) are integrated to give Faraday s Law ... 

The important feature of Eqs. 14.3-3 and 14.3-4 is that they contain only the total mass, heat, and work flows into the system, and the total molar extents of reaction, rather than the flow rates and rates of change of these quantities. Therefore, although Q, W, and Xj can be evaluated from integrals here, Eqs. 14.3-3 and 14.3-4 can also be used to interrelate Q, W, and Xj even when the detailed information needed to do these integrations is not available. This is demonstrated in Illustration 14.3-1. 

This relation can be used to define various other isochoric heat quantities such as integral and differential, molar and specific heats of reaction and the corresponding heat capacities. The most well known of these quantities is the (global or integral) heat capacity at constant volume or isochoric heat capacity, which we got to know briefly in Sect. 9.1 ... 

As we have seen in the case above of internal energy [Eq. (24.12)], this relation can be useful for defining various isobaric heat quantities such as integral and differential, molar and specific heats of reaction, transition, solution, mixing, etc. These are all produced similarly at constant p and T and, depending upon the process in question, each one can have various symbols and names. We will be content with only two examples, one integral quantity and one differential quantity ... 

---