FURTHER EXAMPLES

Further examples. Three independent components. Consider a system composed of water and two soluble salts which have a common ion, and which form a double salt, e.g. magnesium chloride and potassium chloride. These two salts can combine according to the equation MgCl2+2KCl = MgCl2.2KC1 (carnallite). We have thus four different types of molecules and one chemical equation connecting them, hence three independent components. The maximum number of coexistent phases is therefore five, e.g. the three solid salts, saturated solution, and water vapour. The coexistence of these phases is, however, only possible at one temperature, namely, the transition temperature of the double salt. 

At all other temperatures the solution can only be saturated vdth respect to two salts, viz. the two simple salts, or one of the simple salts and the double salt. The concentration of the solution and the vapour pressure are then determined by the 

When only one sohd phase is present, the total concentration of the solution is indeterminate, and may be altered by addition of the other simple salt or of the double salt. The solubility of a salt is therefore not affected by the addition of a salt with a common ion. For the graphical representation of the equihbria in a three-component system, it is convenient to use a three-dimensional system of coordinates, of which the axes are the temperature and the concentrations of the two simple salts. Each point in the space corresponds to a definite vapour pressure. Monovariant equilibria are represented by lines, and bivariant equihbria by surfaces in the space model. (See van t Hoff, Bildung und Spaltung von Doppelsalzen, Leipzig 1897 also van t Hoff u. Meyerhoffer, Zeitschr. /. physikcd. Chemie, 30, 64 (1899), and others. Experimental methods of determining the transition point are also described there.) 

Four independent cmnpomnts. Water and two salts which have no ion in common are an example of a four-component system, because the two salts can form a second pair of salts by double decomposition, according to the equation 

Use is made of this double decomposition in the technical preparation of potassium nitrate from Chih saltpetre. Four salts connected by an equation of the above kind are caUed reciprocal pairs of salts. A further example of this kind is the manufacture of sodium bicarbonate by the Solvay process, viz. 

In this section, we look at a few examples that develop the basic ideas that have been introduced in the previous sections. When confronted with a molecule of unknown structure it is often useful to build towards it from segments that are well known, and using hypothetical intermediates to help. 

The first example is quite simple, but serves to introduce the idea. The structure of water has already been discussed. You will recall that it is a bent triatomic molecule based on a tetrahedron, with the two lone pairs of the oxygen pointed towards the unoccupied comers of the tetrahedron. Given this structure, what is the shape of the closely related compound, hydrogen peroxide, H202  

In this case, we will start with diatomic oxygen, which must be linear, because there are only two atoms in it. Write down its electronic configuration. 

Each oxygen has a full octet, so if an electron is to be added then at least one of the oxygen/oxygen bonds must be broken. Write down a mechanism whereby one of the oxygen/oxygen bonds is broken homolytically, and an electron is added to form the superoxide anion, 02.  

Adding another electron forms the peroxide anion, 022. Write down the electron configuration of this anion. 

The advantage of partial differentiating emerges more distinctly in systems with infinitely many components. In the following, we discuss another simple example with finitely many components. The expression (1 — x )/(l — x) expands, as well known, into the geometric series 

Using this relationship, we now gain the number of the linear alkane homologues  

Equation (13.22) is the generating function for the number of the linear alkanes in h and c. 

Question 13.2. What is now the ratio of the number of hydrogen atoms and the number of carbon atoms, H/C, in this series of alkanes We obtain it either on the right side of Eq. (13.22) by counting or on the left side by differentiating. We may build simply the expression 

Going to the limit is necessary here because of 0/0. Further, we obtain the limit value H/C = 2 for large n. 

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Two further examples of type I ternary systems are shown in Figure 19 which presents calculated and observed selectivities. For successful extraction, selectivity is often a more important index than the distribution coefficient. Calculations are shown for the case where binary data alone are used and where binary data are used together with a single ternary tie line. It is evident that calculated selectivities are substantially improved by including limited ternary tie-line data in data reduction. 

Figure III-9u shows some data for fairly ideal solutions [81] where the solid lines 2, 3, and 6 show the attempt to fit the data with Eq. III-53 line 4 by taking ff as a purely empirical constant and line 5, by the use of the Hildebrand-Scott equation [81]. As a further example of solution behavior, Fig. III-9b shows some data on fused-salt mixtures [83] the dotted lines show the fit to Eq. III-SS.

A few of the most frequently used techniques are discussed briefly in this chapter references to those not covered are given in the table. Useful reviews are Refs. 2-5 and 6 and, for organic surfaces. Refs. 7-9 and 10. Also, many of the various measurements have found use in the study of the adsorbed state, and further examples of their use are to be found in Chapters VII, XVI, and XVII. 

Figure A3.14.13. Further examples of the various Turing patterns observable in a 2D gel reaetor. (a) and (b) spots, (e) and (d) stripes, (e) and (1) wider field of view showing long-range defeets in basie stnietine. The seale bar alongside eaeh figure represents 1 nnu. (Reprinted with pemrission from [39], The Ameriean Institute of Physios.)...

The vibronic coupling model has been applied to a number of molecular systems, and used to evaluate the behavior of wavepackets over coupled surfaces [191]. Recent examples are the radical cation of allene [192,193], and benzene [194] (for further examples see references cited therein). It has also been used to explain the lack of structure in the S2 band of the pyrazine absoiption spectrum [109,173,174,195], and recently to study the photoisomerization of retina] [196],... 

For a further example of the Fischer-Speier method, see Ethyl cinnamate,... 

These coloration changes are given by most compounds which possess the -CHj-CO— group for further examples, see Tests 4 (a) and (b) for Ketones, p. 344. 

The reaction is applicable to the preparation of amines from amides of aliphatic aromatic, aryl-aliphatic and heterocyclic acids. A further example is given in Section IV,170 in connexion with the preparation of anthranilic acid from phthal-imide. It may be mentioned that for aliphatic monoamides containing more than eight carbon atoms aqueous alkaline hypohalite gives poor yields of the amines. Good results are obtained by treatment of the amide (C > 8) in methanol with sodium methoxide and bromine, followed by hydrolysis of the resulting N-alkyl methyl carbamate ... 

A further example is given below illustrating the use of a dibasic anhydride (succinic anhydride) the succinoylation reaction is a valuable one since it leads to aroyl carboxylic acids and ultimately to polynuclear hydrocarbons. This general scheme of synthesis of substituted hydrocarbons through the use of succinic anhydride is sometimes called the Haworth reaction. Thus a-tetralone (see below) may be reduced by the Clemmensen method to tetralin (tetrahydronaphthalene) and the latter converted into naphthalene either catal3d.ically or by means of sulphur or selenium (compare Section, VI,33). 

Furthei-more, the cyclization of the iododiene 225 affords the si.x-membered product 228. In this case too, complete inversion of the alkene stereochemistry is observed. The (Z)-allylic alcohol 229 is not the product. Therefore, the cyclization cannot be explained by a simple endo mode cyclization to form 229. This cyclization is explained by a sequence of (i) e.vo-mode carbopallada-tion to form the intermediate 226, (ii) cydopropanation to form 227. and (iii) cyclopropylcarbinyl to homoallyl rearrangement to afford the (F3-allylic alcohol 228[166]. (For further examples of cydopropanation and endo versus e o cyclization. see Section 1.1.2.2.)... 

It has already been noted (p. 195) that some Type I isotherms exhibit a kind of hysteresis which persists to the lowest pressures (cf. Fig. 4.2) some adsorbate is retained even after prolonged outgassing ( lO Torr) at the temperature of the isotherm determination, and can only be removed if the pumping is carried out at an elevated temperature. Further examples are shown in Fig. 4.25, as well as in Fig. 4.23. 

The values of d and n are given in Table 3 typical values for can be found in Table 4. The exponent of 0.5 on the Schmidt number (l-L /PiLj) supports the penetration theory. Further examples of empirical correlations provide partial experimental confirmation of equation 78 (3,64—68). The correlation reflecting what is probably the most comprehensive experimental basis, the Monsanto Model, also falls in this category (68,69). It is based on 545 observations from 13 different sources and may be summarized as... 

Sohd rocket propellants represent a very special case of a particulate composite ia which inorganic propellant particles, about 75% by volume, are bound ia an organic matrix such as polyurethane. An essential requirement is that the composite be uniform to promote a steady burning reaction (1). Further examples of particulate composites are those with metal matrices and iaclude cermets, which consist of ceramic particles ia a metal matrix, and dispersion hardened alloys, ia which the particles may be metal oxides or intermetallic compounds with smaller diameters and lower volume fractions than those ia cermets (1). The general nature of particulate reinforcement is such that the resulting composite material is macroscopicaHy isotropic. 

Fusion/Hydroxylation. The conversion of arylsulfonic acids to the corresponding hydroxy compound is normally effected by heating with caustic soda (caustic fusion). The primary examples are P-naphthol in the naphthalene series and resorcinol in the benzene series further examples are m- am in oph en o1 from metanilic acid and diethyl-y -arninophenol from /V,/V-diethy1metani1ic acid. In the naphthalene series the hydroxy group is much... 

Details of bond lengths and bond angles for all the X-ray structures of heterocyclic compounds through 1970 are listed in Physical Methods in Heterocyclic Chemistry , volume 5. This compilation contains many examples for five-membered rings containing two heteroatoms, particularly pyrazoles, imidazoles, Isoxazoles, oxazoles, isothlazoles, thlazoles, 1,2-dlthloles and 1,3-dlthloles. Further examples of more recent measurements on these heterocyclic compounds can be found in the monograph chapters. 

It was reported only recently that A-methyl transfer from an oxaziridine to an amine occurs with formation of an N—N bond (79JA6671). N—N bond forming reactions with A-unsubstituted oxaziridines had been found immediately after discovery of this class of compound (64CB2521) and have led to simple hydrazine syntheses (79AHC(24)63). Secondary amines like diethylamine or morpholine are A-aminated by (52) in the course of some minutes at room temperature with yields exceeding 90% (77JPR195). Further examples are the amination of aniline to phenylhydrazine, and of the Schiff base (96) to the diaziridine (97). 

A further example employing displacement of a suitably activated hydroxyl group rather than halogen is also shown in Scheme 10. The use of titanium trichloride in the final step... 

As further examples of some important polyatomic molecules. 

Figure 3-28 shows, as an example, results obtained from an intensive measurement of a short section of pipe which could be very strongly polarized to increase the sensitivity of defect location. From Eq. (3-51 a) Tq = 4 mm at = 0.1 V. In the results in Fig. 3-29, rg = 9 cm at AU = 0.1 V. These results are clear indications of water traps resulting from a poor coating [46]. Further examples are shown in Section 3.7. 

An example of the first route is given in the preparation of nylon 66, which is made by reaction of hexamethylenediamine with adipie acid. The first 6 indicates the number of carbon atoms in the diamine and the second the number of carbon atoms in the acid. Thus, as a further example, nylon 6.10 is made by reacting hexamethylenediamine with sebacic acid (HOOC (CH2)s"COOH). (In this context the numbers 10,11 and 12 are considered as single numbers the need to use two digits results simply from the limitations of the decimal system.)... 

This is also a further example of a spiro-polymer as well as being of the inorganic backbone type. 

A further example where quantitative surface composition analysis is possible for a non-trivial surface is shown in Fig. 3.58, where for the systems Ta -i- O and Nb -i- O adsorption the ion signal from the metal is shown as a function of the ion signal from O. In this binary example Eq. (3.43) are valid for the concentration ... 

My ehosen examples inelude rapid solidifieation, where the extremity is in eooling rate nanostruetured materials, where the extremity is in respeet of extremely small grains surface seienee, where the extremity needed for the field to develop was ultrahigh vaeuum, and the development of vacuum quality is traced thin films of various kinds, where the extremity is in one minute dimension and quasierystals, where the extremity is in the form of symmetry. Various further examples could readily have been ehosen, but this chapter is to remain relatively short. 

Further examples of these synthetically useful reactions can be foimd in Chapter 9 of Part B. 

Studies of chiral substrates have also demonstrated that chirality is maintained in the reaction. Further examples of the synthetic application of the Claisen rearrangement are discussed in Section 6.5 of Part B. 

Further examples of synthesis using [2,3] sigmatropic reactions are given in Section 6.6 of Part B. 

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