Fractionation of species

Additional property relations follow directly from Eq. (4-8). Since nj = Xin, where x, is the mole fraction of species i, this equation may be rewritten ... 

Da en the ionic fraction of species A in the resin is very small and Dg when the ionic fraction of A in the resin approaches unity, indicating that the ion present in smaller concentration has the stronger effect on the local interdiffusion rate. 

We have found expressions for the fractions, /, of species in a solution of carbonic acid. They are easily generalized to any diprotic acid H2A ... 

We can also calculate /, the fraction of species that are committed to reaction, from (45). Using (39), (43) and (45), we obtain (46). Substitution... 

Figure 5.12 (a) The p-T phase diagram of Si. The melting lines for the low-pressure polymorph of Si and the liquid-liquid phase transition are calculated by using the two-state model and the parameters given in Table 5.2. (b) Iso-concentration lines for species B in the p-T plane, (c)) The fraction of species B as a function of temperature at constant pressure p = 2 GPa. 

In this section we will consider only equilibria in which the number of moles of solute does not change. In such cases the population of a given contributor to the equilibrium may be calculated by using a standard Boltzmann formalism, i.e., the fraction of species A is... 

The heart of a traditional atomic absorption spectrometer is the burner, of which the most usual type is called a laminar flow burner. The stability of the flame is the most important factor in AAS. Typical working temperatures are 2200 2400°C for an air-acetylene flame, up to 2600-2800°C for acetylene-nitrous oxide. The fraction of species of a particular element that exist in the excited state can be calculated at these temperatures using the Boltzmann equation ... 

In these equations gv is the change in Gibbs free energy on taking one atom from a normal lattice site to the surface of the crystal and (gt + gv) the change when an atom is taken from a normal lattice site to an interstitial site, both at constant temperature and pressure. cr denotes a site fraction of species r on its sublattice, and is the chemical potential of a normal lattice ion in the defect-free crystal. 

Figure 12 Mole fraction of species found at 34-115 GPa and 2000 K. The filled circles correspond to H30+, whereas the open circles correspond to OH-.

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