Dilute Solution of A in

In the preceding section we derived the characteristic expression for the chemical potential in a symmetrical ideal solution. Here, we derive another ideal behavior, which is obtained whenever one component (the solute) is very dilute in the second component (the solvent). 

We start from the general expression (6.5.9) and take the limit - O. Of course, if we take this limit we obtain pure 5, and the chemical potential of A is not defined. 

However, if we start from pure B and add one A, we obtain the following expression for the chemical potential 

Note that the coupling work of A is against pure B. We shall later in this chapter see that this expression is valid not only in the extreme condition of = I, but also in a solution for which Na Nb in such a way that correlations between A particles can be neglected. 

This limit is known as the dilute-ideal limit. It is equivalent to the region in which Henry s law is obeyed. 

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For a binary mixture of solute A in solvent B, the diffusion coefficient D°ab of A diffusing in an infinitely dilute solution of A in B implies that each molecule A is in an environment of essentially pure B. In engineering work, however, DAB is assumed to be a representative diffusion coefficient even for concentrations of A up to 5 and, perhaps, 10 mol%. 

When only the molecules of one component, say A, are associated e,g. in the system ethanol + carbon tetrachloride), it is more convenient to employ as system of reference a very dilute solution of A in B. As 1 A is present as monomers only. It follows that in this reference system and hence from (26.11) that... 

As noted above, for systems of this kind it is more convenient to use the asymmetrical system of reference of a very dilute solution of A in B. Then, using (26.20), equations (26.13) and (26.13 ) lead to... 

Choosing now a very dilute solution of A in B as standard reference state, and employing (26.26), we obtain... 

The discrepancy between the two expressions only enters with the term of second order in 9, In a dilute solution of A in B, the difference in size of the complexes compared with the monomer play only a negligible role since xa close to unity. However, if the association is... 

In general, we shall assume in this section that we are dealing with dilute solutions and the diffusion coefficient D,4 g corresponds to an infinitely dilute solution of A in B. In other words, each molecule A is in an environment of pure B solvent, there are A-B and B-B interactions in the system but no A-A interactions. In practice, we assume also that D>i g is representative of the diffusion coefficient up to concentrations of the order of 5 to 10% [5], which happens to be the range within which preparative chromatography is usually carried out. 

The second extreme case occurs when pA —> 0. Note, however, that we still have two A s at fixed positions (R1, R"), but otherwise the solvent (here in the conventional sense) is pure B. We have the case of an extremely dilute solution of A in pure B. Note also that at the limit pA —> 0, both the pair and the singlet distribution functions of A tend to zero, i.e.,... 

The dilute-ideal (DI) solutions. This is the case which has attracted the most attention in solution chemistry. Unfortunately, this is also the case where most of the misconceptions have been involved. Here, we only focus on one aspect of the problem, namely the identification of the so-called mixing terms. Consider the case of a very dilute solution of A in B, such that NA [Pg.343]

Compound A absorbs light in the near-UV region of the spectrum. The onset of absorption is 375 nm. A dilute solution of A in an organic solvent exhibits fluorescence (onset=26,900 cm ) and phosphorescence (onset 6800 A). What are the energies of the Si and Ti states of A ... 

Similar considerations apply to the extreme right-hand side of the diagram where we are concerned with an ideal dilute solution of A in B, In equation (8 14) fi will now stand for the real chemical potential of pure B and fi will stand for the chemical potential of A in a non-realizable state—and, of course, is not the same as the value of fi for the ideal solution on the left of the diagram. 

Diffusion of traces of A through B Diffusion in laminar flow (dilute solutions of A in B) Steady diffusion in solids... 

The simplest condensed phase VER system is a dilute solution of a diatomic in an atomic (e.g. Ar or Xe) liquid or crystal. Other simple systems include neat diatomic liquids or crystals, or a diatomic molecule bound to a surface. A major step up in complexity occurs with poly atomics, with several vibrations on the same molecule. This feature guarantees enonnous qualitative differences between diatomic and polyatomic VER, and casts doubt on the likelihood of understanding poly atomics by studying diatomics alone. 

When the ascending solvent-front has reached a convenient height, the strip is removed, the position of the solvent-front marked, and the paper strip dried. The positions of the various solutes, if they are coloured compounds, now appear as clear separate spots. Frequently however, the solutes are colourless, and the position of their spots must be determined by indirect methods, such as their fluorescence in ultraviolet light, or their absorption in such light (when the spots appear almost black), or by spraying the paper with a dilute solution of a reagent which will give a coloured insoluble derivative with the solutes. 

Fluorescein test paper Is prepared by dipping filter paper into a dilute solution of fluorescein in ethyl alcohol it dries rapidly and is then ready for use. The test paper lias a lemon yellow colour. 

H2C=CH-C=CH-C3h7. All glassware of the distillation apparatus was rinsed AcHi with a dilute solution of diethylamine in diethyl ether. 

Hate 3. All glassware used for the work-up and distillation must be rinsed with a dilute solution of triethylamine in diethyl ether or acetone in order to be sure that traces of acids on the glass walls have been neutralized. Allenic sulfides with the structure C=C=C(SR)-CH- isomerize under the influence of acids to give conjugated dienes, C=C-C(SR)=C. 

The ratio of reactants had to be controlled very closely to suppress these impurities. Recovery of the acrylamide product from the acid process was the most expensive and difficult part of the process. Large scale production depended on two different methods. If soHd crystalline monomer was desired, the acrylamide sulfate was neutralized with ammonia to yield ammonium sulfate. The acrylamide crystallized on cooling, leaving ammonium sulfate, which had to be disposed of in some way. The second method of purification involved ion exclusion (68), which utilized a sulfonic acid ion-exchange resin and produced a dilute solution of acrylamide in water. A dilute sulfuric acid waste stream was again produced, and, in either case, the waste stream represented a... 

In tire transition-metal monocarbides, such as TiCi j , the metal-rich compound has a large fraction of vacairt octahedral interstitial sites and the diffusion jump for carbon atoms is tlrerefore similar to tlrat for the dilute solution of carbon in the metal. The diffusion coefficient of carbon in the monocarbide shows a relatively constairt activation energy but a decreasing value of the pre-exponential... 

The austenite phase which can contain up to 1.7 wt% of carbon decomposes on cooling to yield a much more dilute solution of carbon in a-iroii (b.c.c), Fenite , together with cementite, again rather diaii the stable carbon phase, at temperatures below a solid state eutectoid at 1013 K (Figure 6.3). 

When a dilute solution of a polymer (c << c ) is equilibrated with a porous medium, some polymer chains are partitioned to the pore channels. The partition coefficient K, defined as the ratio of the polymer concentration in the pore to the one in the exterior solution, decreases with increasing MW of the polymer (7). This size exclusion principle has been used successfully in SEC to characterize the MW distribution of polymer samples (8). 

A more proper comparison regarding Vl-group nucleophilic reagents would be between the pairs PhO and PhS , and MeO" and MeS. However, both phenoxide and alkylsulfide ions are more basic than phenylsulfide ion, and their reactions are less amenable to study in alcoholic solution. For dilute solutions of phenoxide in methanol the equilibrium (9) shifts nearly half-way toward the right if a stoichiometric excess of phenol is not present. If phenoxide ion is less reactive... 

The steel will be considered to be an ideal ternary solution, and therefore at all temperatures a, = 0-18, Ani = 0-08 and flpc = 0-74. Owing to the Y-phase stabilisation of iron by the nickel addition it will be assumed that the steel, at equilibrium, is austenitic at all temperatures, and the thermodynamics of dilute solutions of carbon in y iron only are considered. 

A similar drop in electrical conductivity, though not so marked, is observed on adding a trace of water to a dilute solution of HC1 in methanol, which is attributed to the proton transfer... 

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