Order footnote

Bubble-point and dew-point pressures are calculated using a first-order iteration procedure described by the footnote to Equation (7-25). 

Purification of the Methylamine HCI is in order now, so transfer all of the crude product to a 500mL flask and add either 250mL of absolute Ethanol (see end of FAQ for preparing this) or, ideally, n-Butyl Alcohol (see Footnote 4). Heat at reflux with a Calcium Chloride guard tube for 30 minutes. Allow the undissolved solids to settle (Ammonium Chloride) then decant the clear solution and cool quickly to precipitate out Methylamine HCI. Filter rapidly on the vacuum Buchner funnel and transfer crystals to a dessicator (see Footnote 3). Repeat the reflux-settle-cool-filter process four... 

Hylleraas mentioned the possibility of using the (2/-f 2) order functions in a footnote in ref. 14, but he did not give any explicit formulas or numerical results. 

Rate coefficients have been determined for protodeboronation of benzene- and thiophene-boronic acids in a range of aqueous perchloric acid mixtures at temperatures between 25 and 90 °C630. First-order rate coefficients are given in Table 204, but not all of the rates were measured at the acidities indicated (see Table footnote), but were corrected to these making use of the linear relationship which was found, in preliminary experiments, to exist between log rate and H0. Similarly, the relative reactivities to thiophene-2-, thiophene-3-, and benzene-boronic acid (8.5 x 10s, 7.1 x 103, and 1.0, respectively) were obtained at an H0... 

The reaction is in methanol, like iododestannylation, first-order in each reagent. The second-order rate coefficient at 23 °C was reported as 20,900 and thus the reaction occurs very much more readily than cleavage of the corresponding tin compound, which repeats the pattern observed in acid-cleavage reactions (see p. 342). The magnitude of the rate coefficient may be subject to the same error that appears to be present in the measurement of the corresponding tin compound (see footnote to Table 264) since the rates were determined under the same conditions. 

Some functionalized thiophenes have been investigated in order to assess the scope of ylide-derived chemistry. As already mentioned, 2-(hydroxymethyl)thiophene still gives the S-ylide upon Rh2(OAe)4-catalyzed reaction with dimethyl diazomalonate 146 but O/H insertion instead of ylide formation seems to have been observed by other workers (Footnote 4 in Ref. 2S4)). From the room temperature reaction of 2-(aminomethyl)thiophene and dimethyl diazomalonate, however, salt 271 was isolated quite unexpectedly 254). Rh2(OAc)4, perhaps deactivated by the substrate, is useless in terms of the anticipated earbenoid reactions. Formation of a diazo-malonic ester amide and amine-catalyzed cyclization to a 5-hydroxytriazole seem to take place instead. 

Figure 4.3 Comparison of cjc 0 for various orders of reaction in a BR or PFR (for conditions, see footnote to Table 4.1)...

The competition between the OsvCl6 reaction with a neutral compound (A) and a negatively charged one (A-), respectively, which is the experimental situation in some of the spin trapping reactions mentioned above, was analysed by the Marcus treatment for some model cases in dichloromethane or acetonitrile. These data are shown in Table 7, giving the details of the calculations in order to illustrate the use of equations (20) and (21) and the importance of the electrostatic factors, particularly in dichloromethane. The assumptions behind the calculations are given in the table heading and footnotes. 

As a footnote to these observations, we also have to mention that frequently structural distortions (axial ratio and/or inter-axial angle variations) accompany the formation of derivative structures, especially because of the ordered distribution of atoms of different sizes or of vacant sites. 

Pines and Herling 83) dehydrated the title alcohols over alumina B (Footnotes, Table V). The dehydration was made at 350° and the contact time was adjusted in order to obtain 50-60% styrenes. The dehydration was accompanied by a 6% of the phenyl and 9% of the tolyl migration from carbon atom 2 to carbon atom 1 and can be explained as follows ... 

Ultrapure Th metal has been processed at the Ames Laboratory by solid-state electrotransport under very low pressures (on the order of 0.3 nPa), which has produced the purest Th metal known, that with a resistivity ratio of 4200 for doubly refined metal (99-101). This resistivity ratio of 4200 translates into probably <50 ppm total impurities in the metal (see footnote 1) (87-90, 104). Single crystals measuring 0.25 cm in diameter by 1.1 cm in length with resistivity ratios of 1700-1800 have also been grown (55). 

In this paper the rate expressions have all been corrected for nitrogen evolution from the azo initiator, oxygen absorption by initiator radicals, and oxygen evolution in termination. It is assumed that the initiator which decomposes without starting oxidation chains does not react with oxygen (21). This correction involves the addition of (l-e)Ri/2e to the measured rate, where e is the efficiency of chain initiation, found to be 0.5 at 30 °C. and 0.6 at 56 °C. The rate constant for Reaction 7 has been written as 4ktCT in order that the three termination constants may be comparable (26, footnote 27).]... 

In cases wherein empirical relationships can be established between data in water and in water-organic mixtures, we have used them in order to calculate the pK values given in the tables. The appropriate equations are given as footnotes to these tables. 

The nuclear size correction of order Za) m in muonic hydrogen in the external field approximation is given by (6.13). Unlike ordinary hydrogen, in muonic hydrogen it makes a difference if we use mj or mmf in this expression (compare footnote after (6.13)). We will use the factor mj as obtained in [53]... 

Footnote to Table 3 a- Decreasing order of heat release... 

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