Problem two

The problem with the fiowsheet shown in Fig. 10.5 is that the ferric chloride catalyst is carried from the reactor with the product. This is separated by washing. If a reactor design can be found that prevents the ferric chloride leaving the reactor, the effluent problems created by the washing and neutralization are avoided. Because the ferric chloride is nonvolatile, one way to do this would be to allow the heat of reaction to raise the reaction mixture to the boiling point and remove the product as a vapor, leaving the ferric chloride in the reactor. Unfortunately, if the reaction mixture is allowed to boil, there are two problems ... 

The introduction of low quantities of surfactants (50 to 125 ppm) helps solve these two problems. The surfactant molecule has a lipophilic organic tail and a polar head that is adsorbed selectively on the metal walls of the admission system. These products have a double action ... 

There are two problems to consider when calculating 3D pharmacophores. First, unless the molecules are all completely rigid, one must take account of their conformational properties The second problem is to determine which combinations of pharmacophoric groups are common to the molecules and can be positioned in a similar orientation in space. More than one pharmacophore may be possible indeed, some algorithms can generate hundreds of possible pharmacophores, which must then be evaluated to determine which best fits the data. It is important to realise that all of these approaches to finding 3D pharmacophores assume that all of the molecules bind in a common manner to the macromolecule. 

Solve the same two problems with Mathcad. Is there a noticeable difference between the two sets Mathcad uses a variant on the Gaussian substitution method called LU Factorization (Kreyzig, 1988). 

Using the. results (roiri the previous two problems, evaluate the integrals in the answer to Problem 5 and find t as a dosed algebraic expression for the Gaussian trial runetion. 

Physicochemical studies on aminothiazoles are mainly centered on two problems the position of imino-amino protomeric equilibrium and IsRR substitution effects on the thiazole nucleus. 

Next we consider a substitution for the mean-square end-to-end distance r. At first glance this seems easy, since Eq. (1.62) gives r = nlo. There are two problems associated with the use of this substitution ... 

The considered problem is formulated as a variational inequality. In general, the equations (3.140)-(3.142) hold in the sense of distributions. In addition to (3.143), complementary boundary conditions will be fulfilled on F, X (0,T). The exact form of these conditions is given at the end of the section. The assumption as to sufficient solution regularity requires the variational inequality to be a corollary of (3.140)-(3.142), the initial and all boundary conditions. The relationship between these two problem formulations is discussed in Section 3.4.4. We prove an existence of the solution in Section 3.4.2. In Section 3.4.3 the main result of the section concerned with the cracks of minimal opening is established. 

There are two problems in the manufacture of PS removal of the heat of polymeriza tion (ca 700 kj /kg (300 Btu/lb)) of styrene polymerized and the simultaneous handling of a partially converted polymer symp with a viscosity of ca 10 mPa(=cP). The latter problem strongly aggravates the former. A wide variety of solutions to these problems have been reported for the four mechanisms described earlier, ie, free radical, anionic, cationic, and Ziegler, several processes can be used. Table 6 summarizes the processes which have been used to implement each mechanism for Hquid-phase systems. Free-radical polymerization of styrenic systems, primarily in solution, is of principal commercial interest. Details of suspension processes, which are declining in importance, are available (208,209), as are descriptions of emulsion processes (210) and summaries of the historical development of styrene polymerization processes (208,211,212). 

Potentiometric Titrations. If one wishes to analyze electroactive analytes that are not ions or for which ion-selective electrodes are not available, two problems arise. First, the working electrodes, such as silver, platinum, mercury, etc, are not selective. Second, metallic electrodes may exhibit mixed potentials, which may arise from a variety of causes. For example, silver may exchange electrons with redox couples in solution, sense Ag" via electron exchange with the external circuit, or tarnish to produce pH-sensitive oxide sites or Ag2S sites that are sensitive to sulfide and haUde. On the other... 

The last two problems have been realized only recently, and additional progress in these research directions may be expected in the near future. At present it is clear that with the standard geometry approximation all time step limitations below 10 fs can be overcome rather easily. This time step increase gives a substantial net increase in performance compared to conventional MD. The possibility of larger step sizes now looks problematic, although it has been demonstrated for small molecules. Larger steps should be possible, however, with constraints beyond the standard geometry approximation. 

Viable methods of producing the metals from oxide ores have to siumount two problems. In the first place, reduction with carbon is not possible because of the formation of intractable carbides (p. 299), and even reduction with Na, Ca or Mg is unlikely to remove all the oxygen. In addition, the metals are extremely reactive at high temperatures and, unless prepared in the absence of air, will certainly be contaminated with oxygen and nitrogen. 

The molecular mechanics calculations discussed so far have been concerned with predictions of the possible equilibrium geometries of molecules in vacuo and at OK. Because of the classical treatment, there is no zero-point energy (which is a pure quantum-mechanical effect), and so the molecules are completely at rest at 0 K. There are therefore two problems that I have carefully avoided. First of all, I have not treated dynamical processes. Neither have I mentioned the effect of temperature, and for that matter, how do molecules know the temperature Secondly, very few scientists are interested in isolated molecules in the gas phase. Chemical reactions usually take place in solution and so we should ask how to tackle the solvent. We will pick up these problems in future chapters. 

For the rest of the chapter, I am going to be concerned with two problems ... 

Two problems in the calculation of interfacial energies in crystals have been addressed, namely how to obtain the chemical potentials and how to define the terminating planes on the atomic scale for the purposes of calculating the excess free energy. 

There are occasions when a contractor will apply for an interim payment based on plant obtained by him for the contract and stored by him on his premises. This is a difficult situation, and should be approached with care. Two problems can arise ... 

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