Reference state for species

Since the definition of the fugacity (4.3.8) imposes a fixed temperature, the integration leading to (10.3.8) must be done at the system temperature T. Moreover, we invariably choose the reference state for species i to be pure i (x = 1) then the reference state becomes a standard state ( o), and (10.3.8) can be written in terms of the activity... 

The Henry s law limit can be conceptualized as a hypothetical, pure fluid in which the characteristic energy of interaction is that between molecule a and molecule b. If species a is defined by a Lewis/Randall reference state, we call it a solvent, whereas when we describe it by Henry s law, it is termed a solute. If we had a binary mixture of species a with a different molecule c, the Lewis/Randall reference state for species a would be unchanged. However, the Henry s reference state could differ dramatically. The former is independent of any other species in the mixture, while the latter, by definition, depends on the chemical nature of the other species in the mixture. 

In summary, the reference state for species i in the liquid (or solid) phase is no more than a particular state, real or hypothetical, at a given P and Xi (usually that of the system) and at the temperature of the system. We choose the reference state to be that of an ideal solution in which the fugacity is linearly proportional to mole fraction. While the concept of an ideal solution was conjured up in analogy to an ideal gas, there are some interesting differences. A pure gas can be a nonideal gas, while a pure liquid cannot be a nonideal solution because all intermolecular forces in a pure liquid are the same Additionally, an increase in pressure leads to deviations from ideal gas behavior, whereas deviations from ideal solution are caused by changes in composition because nonideal behavior results primarily from the chemical differences of species in a mixture, even at low pressures. 

Consider a binary mixture of a and b atT = 300 K and P = 40 kPa. A graph of the fugacity of species a as a function of mole fraction is shown below. Use Henry s law as the reference state for species a and the Lewis/RandaU rule for species h. Show all your work. 

Applying the Henry s law reference state for species i gives ... 

The protodelithiation enthalpy of n-propyl lithium is very nearly the same as for the n-butyl species, —219 2 kJmoP. From reaction 10 with w-butyl lithium as the benchmark species and the enthalpies of formation of the hydrocarbons in their gaseous reference states, the enthalpy of formation of n-propyl lithium is calculated as ca —91 klmoP, a value consistent with that of —86 kJ moP derived from w-PrMgBr in an earlier section. If the reference state of n-butane is taken as the liquid instead, the enthalpy of formation of n-propyl lithium is ca —70 kJ moP, a value consistent with another previous derivation of ca —73 kJmoP. At least with respect to consistency with the enthalpies of formation in Table 1, the best reference state for ethane and propene is the gas it is not yet clear which is better for butane. 

So far, we have used the pure liquid compound as reference state for describing the thermodynamics of transfer processes between different media (Chapter 3). When treating reactions of several different chemical species in one medium (e.g., water) it is, however, much more convenient to use the infinite dilution state in that medium as the reference state for the solutes. Hence, for acid-base reactions in aqueous solutions, in analogy to Eq. 3-34, we may express the chemical potential of the solute i as ... 

All species are aqueous unless otherwise indicated. The reference state for amalgams is an infinitely dilute solution of the element in Hg. The temperature coefficient, dE°/dT, allows us to calculate the standard potential, E°(T), at temperature T E°(T) — Ec + (dE°/dT)AT. where A T is T — 298.15 K. Note the units mVIK for dE°ldT. Once you know E° for a net cell reaction at temperature T, you can find the equilibrium constant, K, for the reaction from the formula K — lOnFE°,RTln w, where n is the number of electrons in each half-reaction, F is the Faraday constant, and R is the gas constant. 

There are four undetermined quantities Apfx, (Apf ), pf, and (pf) and two equations. We must, therefore, define two of the four quantities, which in turn determines the other two quantities and the relationship between them. We can define the reference states for the component and the species. The difference between the standard chemical potential of the component and that of the species is then expressed in terms of the mole fractions in the reference state. The problem is the determination of this difference. The different species may be known from our knowledge of the chemical system, or they may be assumed. However, a definite decision must be made concerning the species, and all calculations must be carried out based upon this decision. Several examples concerning reference and standard states are discussed here and in the following sections. 

The simplest case is one in which we can use the pure substance as the reference state for both the component and the species. If, then, the pure substance consists entirely of the same molecular entity and this entity is taken as the component and the species, the standard states for the component and the species are identical. Equation (8.168) becomes... 

We choose the pure component to be the reference state for the compound, and therefore also the standard state. We choose the reference state of the M + species to be a fictitious system that contains only M + molecular entities and the reference state of A species to be a fictitious system containing only A molecular entities according to Equation (8.203). The symbols, p t and p% then represent the chemical potentials of the M+ and A species, respectively, in their standard state—the fictitious systems. However, the pure component is also a mixture of the two ions and, according to Equations (8.202) and (8.203), we have... 

The constant-capacitance model (Goldberg, 1992) assigns all adsorbed ions to inner-sphere surface complexes. Since this model also employs the constant ionic medium reference state for activity coefficients, the background electrolyte is not considered and, therefore, no diffuse-ion swarm appears in the model structure. Activity coefficients of surface species are assumed to sub-divide, as in the triplelayer model, but the charge-dependent part is a function of the overall valence of the surface complex (Zk in Table 9.8) and an inner potential at the colloid surface exp(Z F l,s// 7). Physical closure in the model is achieved with the surface charge-potential relation ... 

The reference states may be chosen for computational convenience, since the choice has no effect on the calculated value of A//. You will later learn that Table B.8 lists specific enthalpies of nitrogen relative to N2(g, 25°C. 1 atm), which makes this state a convenient choice for nitrogen. There are no tabulated enthalpy data for acetone in the text, so we will choose one of the process stream conditions, Ac(l, 20°C, 5 atm), as the reference state for this species, which will enable us to set the corresponding H value equal to zero rather than having to calculate it. 

If more than one species is involved or if there are several input or output streams instead of just one of each, the procedure given in Section 8.1 should be followed choose reference states for each species, prepare and fill in a table of amounts and specific internal energies (closed system) or species flow rates and specific enthalpies (open system), and substitute the calculated values into the energy balance equation. The next example illustrates the procedure for a continuous heating process. 

We chose the reference states for CO and CO2 as the gas inlet temperature and 1 atm. We assume ideal gas behavior so that deviations of the pressure from 1 atm have no effect on enthalpies, and accordingly set the inlet enthalpies of the gas species equal to zero. 

In these equations n is the amount (mass or moles) of a species in one of its initial or final states in the process, h is the flow rate (mass or molar) of a species in a continuous stream entering or leaving the process, and 0 and H are respectively the specific internal energy and specific enthalpy of a species in a process state relative to a specified reference state for the same species. 

Choose reference states for specific enthalpy calculations. The best choices are generally reactant and product species at 25 C and 1 atm in the states for which the heat of reaction is known [C3Hg(g), 02(g), C02(g). and H20(l) in the example process], and nonreacting species at any convenient temperature, such as the reactor inlet or outlet temperature or the reference condition used for the species in an available enthalpy table [N2(g) at 25 C and 1 atm, the reference state for Table B.8]. 

Choose reference states for enthalpy calculations. (This is the step that distinguishes the preceding method from this one.) The choices should be the elemental species that con-... 

Since the component amounts of all streams are known, we may proceed directly to the energy balance. We choose as references the elemental species that form the reactants and products at 25°C and 1 atm (the state for which heats of formation are known) and the oonreactive species— Ni(g)—also at 25°C and 1 atm (the reference state for Table B.8). The inlet-outlet enthalpy table is shown below. 

Once again, the reference states for determination of the specific enthalpies in this equation must be those used to determine the value of A//°. If the heats of combustion in Table B.l are used, the reference states would be the fuel, combustion products (including liquid water), and inert species at 25 C and 1 atm. The fuel would be in whichever state (solid, liquid, or gas) Table B.l specifies. 

When performing energy balances on a reactive chemical process, two procedures may be followed in the calculation of AH (or AH or AH) that differ in the choice of reference states for enthalpy or internal energy calculations. In the heat of reaction method, the references are the reactant and product species at 25 C and 1 atm in the phases (solid, liquid, or gas) for which the heat of reaction is known. In the heat of formation method, the references are the elemental species that constitute the reactant and product species [e.g., C(s), 02(g), H2(g), etc.] at 25°C and 1 atm. In both methods, reference slates for nonreactive species may be chosen for convenience, as was done for the nonreactive processes of Chapters 7 and 8. 

Here fi° is the value of fii in a chosen standard state for species i at the same temperature T, and is the thermodynamic activity (Poling, Prausnitz, and O Connell, 2000) of species i relative to that standard state. Several practical expressions for (with correspondingly different standard states) are listed here for future reference ... 

To compare activities of solutes in different solvents, a single reference state for the solute must be chosen. Although from some points of view it is awkward, water is a logical choice for a single reference solvent in which the behavior of solutes in other solvents can be compared. To make comparisons of solute activities among solvents, it is convenient to consider separately the effect of dilution within a given solvent and the difference in the usual reference states of a solute at infinite dilution in different solvents. The activity coefficient yt of a species i in a solvent may be considered the product of two terms... 

Reference State. The infinite dilution reference state for the solute, species 2, on the molal scale is 72 1 as m2 0 (using the label 1 for the solvent... 

AVhile we might use different labels for different activity coefficients (e.g., 7, 7/ ) we prefer to emphasize the matching of the scales with the activity coefficient reference states for different species (solvent, ionic solute, etc.). In Chapters 3 and 6, for example, we use the symbol /, or fi, to discuss activities on a molar scale. The usage will be clear in the context. 

The normal boiling point of sulfur at 1 atm, 717.824 K, is a secondary standard on the International Practical Temperature Scale of 1968. The vapor composition at this temperature is a mixture of several sulfur species, the predominant species being Sg(g), S, (g), and Sg(g). In our reference state for sulfur, we have arbitrarily chosen 0.5 S2(g) to be the gas phase species. 

The square bracket [X] represents the concentration of species X in units of mol If all factors containing c ef are collected on the right side and the reference state for each reactant and product is defined to be an ideal solution with a concentration c f = 1 M, then the same arguments used before for gas-phase reactions show that the dimensionless thermodynamic equilibrium constant K is numerically equal to Kq. 

Calculate K by calculating AG° from tables of AG° for reactants and prodncts, paying careful attention to reference state for each species. 

A chief goal of this book is to help the reader understand controls on the chemical quality of surface-and subsurface-waters, both pristine and polluted. The focus is on inorganic processes and on the chemistry of soil and groundwaters, with less said about the chemistry of precipitation, surface-waters, or the ocean. The book leans heavily on the principles of chemical thermodynamics and the concept of chemical equilibrium. Chemical equilibrium, whether attainable or not, represents the reference state for purposes of explaining the concentrations of aqueous species in the hydrosphere. Concepts of chemical kinetics are introduced when they are known and seem applicable. 

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