Using All Four Factors

Now that we have seen all four factors individually, we need to see how to put them all together. When analyzing a reaction, we need to look at all four factors and make a determination of which mechanism, SnI or Sn2, is predominating. It may not be just one mechanism in every case. Sometimes both mechanisms occur and it is difficult to predict which one predominates. Nevertheless, it is a lot more common to see situations that are obviously leaning toward one mechanism over the other. For example, it is clear that a reaction will be Sn2 if we have a primary substrate with a strong nucleophile in a polar aprotic solvent. On the flipside, a reaction will clearly be SnI if we have a tertiary substrate with a weak nucleophile and an excellent leaving group. 

Your job is to look at all of the factors and make an informed decision. Let s put everything we saw into one chart. Review the chart. If there are any parts that do not make sense, you should return to the section on that factor and review the concepts. 

EXERCISE 9.29 For the reaction below, look at all of the reagents and conditions, and determine if the reaction will proceed via an Sn2 or an SnI, or both or neither. 

Answer The substrate is primary, which immediately tells us that it needs to be Sn2. On top of that, we see that we have a strong nucleophile, which also favors Sn2. The LG is good, which doesn t tell us much. The solvent is not indicated. So, taking everything into account, we predict that the reaction follows an Sn2 mechanism. 

23—Both Moderate—Both Good—Both (but more Sn2)  

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Compare the stability of these two bases using all four factors. 

ASSESSING RELATIVE STABILITY USING ALL FOUR FACTORS... 

STEP 2 Compare the stability of these conjugate bases using all four factors, in this order ... 

An analysis of variance (ANOVA) would typically be conducted because we can estimate the interaction of all four factors and also use the two-level factorial designs with centre points to reduce the number of experimental runs. 

The most widely used and best known resistance furnaces are iadirect-heat resistance furnaces or electric resistor furnaces. They are categorized by a combination of four factors batch or continuous protective atmosphere or air atmosphere method of heat transfer and operating temperature. The primary method of heat transfer ia an electric furnace is usually a function of the operating temperature range. The three methods of heat transfer are radiation, convection, and conduction. Radiation and convection apply to all of the furnaces described. Conductive heat transfer is limited to special types of furnaces. 

Ethylene Oxide Catalysts. Of all the factors that influence the utihty of the direct oxidation process for ethylene oxide, the catalyst used is of the greatest importance. It is for this reason that catalyst preparation and research have been considerable since the reaction was discovered. There are four basic components in commercial ethylene oxide catalysts the active catalyst metal the bulk support catalyst promoters that increase selectivity and/or activity and improve catalyst life and inhibitors or anticatalysts that suppress the formation of carbon dioxide and water without appreciably reducing the rate of formation of ethylene oxide (105). 

Those basic matrix selection factors are used as bases for comparing the four principal types of matrix materials, namely polymers, metals, carbons, and ceramics, listed in Table 7-1. Obviously, no single matrix material is best for all selection factors. However, if high temperatures and other extreme environmental conditions are not an issue, polymer-matrix materials are the most suitable constituents, and that is why so many current applications involve polymer matrices. In fact, those applications are the easiest and most straightforward for composite materials. Ceramic-matrix or carbon-matrix materials must be used in high-temperature applications or under severe environmental conditions. Metal-matrix materials are generally more suitable than polymers for moderately high-temperature applications or for modest environmental conditions other than elevated temperature. 

In Ugi four-component reactions (for mechanism, see Section 1.4.4.1.) all four components may potentially serve as the stereodifferentiating tool65. However, neither the isocyanide component nor the carboxylic acid have pronounced effects on the overall stereodiscrimination60 66. As a consequence, the factors influencing the stereochemical course of Ugi reactions arc similar to those in Strecker syntheses. The use of chiral aldehydes is commonly found in substrate-controlled syntheses whereas the asymmetric synthesis of new enantiomerically pure compounds via Ugi s method is restricted to the application of optically active amines as the chiral auxiliary group. 

Equations of state that are cubic in volume are often employed, since they, at least qualitatively, reproduce the dependence of the compressibility factor on p and T. Four commonly used cubic equations of state are the van der Waals, Redlich-Kwong, Soave, and Peng-Robinson. All four can be expressed in a reduced form that eliminates the constants a and b. However, the reduced equations for the last two still include the acentric factor u> that is specific for the substance. In writing the reduced equations, coefficients can be combined to simplify the expression. For example, the reduced form of the Redlich-Kwong equation is... 

Table XIV lists comparative SD and /values for fittings of all the sets of Table Xlll with each of the scales of Table V, the FandR values of Swain, and with the single substituent parameter treatment, po y These statistics, coupled with structural considerations, we believe support the usefulness and uniqueness of a scale of limited generality. In general, the / values of Table XIV for the Or scale are smaller than those of the other scales by factors of from 2 to 10. The root-mean-square F values for the other scales are from 2.25 (< j (BA)) to 3 to 4 (S L,, cr (yv)) times that for. Because this analysis has demonstrated that Swain s F and R are generally inferior for the discriminating data for all four types, there appears little to encourage proliferation of these parameters.

Cellulase and all chemicals used in this work were obtained from Sigma. Hydrolysis experiments were conducted by adding a fixed amount of 2 x 2 mm oflSce paper to flasks containing cellulase in 0.05 M acetate buffer (pH = 4.8). The flasks were placed in an incubator-shaker maintained at 50 °C and 100 rpm. A Box-Behnken design was used to assess the influence of four factors on the extent of sugar production. The four factors examined were (i) reaction time (h), (ii) enzyme to paper mass ratio (%), (iii) amount of surfactant added (Tween 80, g/L), and (iv) paper pretreatment condition (phosphoric add concentration, g/L), as shown in Table 1. Each factor is coded according to the equation... 

Several additional, non-microstructural, inputs are required for the fracture model (i) Particle critical stress intensity factor, KIc. Here, the value determined in a previous study (Klc = 0.285 MPa in )[3] was adopted for all four graphites studied. This value is significantly less than the bulk Klc of graphites (typically -0.8-1.2 MPa rn). However, as discussed in the previous section, when considering fracture occurring in volumes commensurate in size with the process zone a reduced value of Klc is appropriate (ii) the specimen volume, taken to be the stressed volume of the ASTM tensile test specimens specimen used to determine the tensile strength distributions and (iii) the specimen breadth, b, of a square section specimen. For cylindrical specimens, such as those used here, an equivalent breadth is calculated such that the specimen cross sectional area is identical, i.e.,... 

The adjustable parameters were a, y, and rQ. The best-fit friction factors y for the 43-bp fragment are the same on all four time spans, as shown in Figure 4.9. The best-fit y values are similarly independent of time span for the 69-bp fragment.(109) The hydrodynamic radius a for azimuthal rotation was calculated from the measured friction factor for uniform azimuthal rotation of the entire filament, f = (N+ 1 )y, using the formula of Tirado and Garcia de la Torre,(129)/ii = 3Mlrjna2L(l +<5,), where t is the solvent viscosity, and dM is an end-plate correction, which they tabulate. The same value... 

In the earliest work, Krouse and Thode (1962) found the Se isotope fractionation factor Sse(iv)-se(o) to bc 10%o ( l%o) with hydroxylamine (NH2OH) as the reductant. Rees and Thode (1966) obtained a larger value, 12.8%o, for reduction by ascorbic acid. Webster (1972) later obtained 10%o for NHjOH reduction. Rashid and Krouse (1985) completed a more detailed study, and found that the fractionation factor varied with time over the course of the experiments. They explained the variations observed among the experiments in all four studies using a model in which reduction consists of two steps. With the rate constant of the second step two orders of magnitude smaller than the first, and kinetic isotope effects of 4.8%o and 13.2%o for the hrst and second steps, respectively, all the data (Table 3) were fit. Thus, kinetic isotope effects of apparently simple abiotic reactions can depend on reaction conditions. 

One approach is to mesh all investigation and root cause analysis activities under one management system for investigation. Such a system must address all four business drivers (1) process and personnel safety, (2) environmental responsibility, (3) quality, and (4) profitability. This approach works well since techniques used for data collection, causal factor analysis, and root cause analysis can be the same regardless of the type of incident. Many companies realize that root causes of a quality or reliability incident may become the root cause of a safety or process safety incident in the future and vice versa. 

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