The Advancement and Molar Reaction Quantities

If the properties of the mixture are such that is positive at each mixture composition (except at the extremes xa=0 and Aa=1 where it must be zero), and no portion of the curve of AGm(mix) versus xa is concave downward, there can be no phase separation and the activity a a increases monotonically with xa- This case is illustrated by curve 2 in Figs. 11.5(a) and 11.5(b). 

If a portion of the AGm(mix)-XA curve is concave downward, the condition needed for phase separation, then a maximum appears in the curve of a a versus xa. This case is illustrated by curve 3, and the compositions of the coexisting phases are indicated by open circles. The difference of the compositions at the two circles is a miscibility gap. The portion of curve 3 between these compositions in Fig. 11.5(b) is dashed to indicate it describes unstable, nonequilibrium states. Although the two coexisting phases have different compositions, the activity a a is the same in both phases, as indicated in Fig. 11.5(b) by the horizontal dashed line. This is because component A has the same standard state and the same chemical potential in both phases. 

Coexisting liquid phases will be discussed further in Secs. 12.6 and 13.2.3. 

Many of the processes of interest to chemists can be described by balanced reaction equations, or chemical equations, for the conversion of reactants into products. Thus, for the 

Thermodynamics and Chemistry, second edition, version 3 2011 by Howard De foe. Latest version www.chem.umd.edu/thermobook 

---

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES 11.2 THE Advancement and Molar reaction Quantities... 

The chemical reaction energy variety has a capacitive subvariety in which the basic quantity is the chemical reaction advance or chemical reaction extent with units in mole and the effort is the chemical affinity JA with units in joule per mole. This latter notion has been introduced by Theophile de Bonder in 1923 (Prigogine and Defay 1962) but has disappeared now from the physical chemical landscape, being replaced by the notion of molar free energy of reaction notated A,.G. 

This chapter discusses the thermodynamics of mixing processes and processes described by reaction equations (chemical equations). It introduces the important concepts of molar mixing and reaction quantities, advancement, and the thermodynamic equilibrium constant. The focus is on chemical processes that take place in closed systems at constant pressure, with no work other than expansion work. Under these conditions, the enthalpy change is equal to the heat (Eq. 5.3.7). The processes either take place at constant temperature, or have initial and final states of the same temperature. 

AfX is a molar differential reaction quantity. Equation 11.2.16 shows that A X is the rate at which the extensive property X changes with the advancement in a closed system at constant T and p. The value of A X is in general a function of the independent variables T, p, and... 

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. 

A new advance with regard to the instrumentation and methods available for online monitoring of heterogeneous polymerization reactions was made by using ACOMP for monitoring the evolution of multiple characteristics during polymerization. The information-rich data collected simultaneously by multiple detectors provide absolute, model-independent determination of quantities such as conversion, composition, and molar mass distribution and avoid potentially damaging effects of the reactor environment. 

Figure 14. Time evolution of the composition of the percolating water in the downstream part of the alteration profile of a pyrite-rich sandstone. = 10. The concentration of the dissolved species are given in mol/kg and the quantities of neoformed minerals are given in mol as a function of the parameter of advancement of the reaction t All data are represented as the logarithm of the molality (log m) vs. log. XU(a) corresponds to [U/Fe] = 5 X 10 (molar ratio) leached within the sandstone. U(l)) corresponds to the maximum possible dissolved uranium concentration. All the curves are direct Benson plots from the computer.

The sum of concentrations should remain constant in space and time, if not, something is wrong. Either the reaction does not follow this stoichiometiy or more probably the analysis is not calibrated very exactly. A more advanced way to consider potential calibration errors is to look at the components individually. Let us consider a single reaction. The extent of reaction is defined by - (> , -y0l)/v, where c is the extent of reaction, y,- denotes the molar quantity after some... 

---