P/t, values

Calculated from P T values tabulated in Rabinovich (ed.), Thetmophysical Fropetiies of Neon, Argon, Krypton and Xenon, Standard Press, Moscow, 1976. This book was published in English translation by Hemisphere, New York, 1988 (604 pp.). 

P/T-value (precision to tolerance ratio), addresses what portion of the specification is taken up by the measurement error. The % P/T-value is an important metric for the method capability towards application in release testing against specifications. 

P(t ) values simulated based on these functions are plotted in Figure 2(a) for both the and Tj states. It can be found from Figure 2(a) that the P(t ) curve calculated based on the mechanism [C] tends to increase with increasing delay time, while the corresponding values... 

Additive effects can be seen in the symmetrical biscycloalkyl[fc,e]pyridines (23-26) with dicyclobutyl[b,e]pyridine (26) showing a remarkable p f value of 4.4, four pK units lower than the least strained analogue, dicyclohexyl[b,e]pyridine (23) (8.09). Similarly, the p T values of unsymmetrical biscycloalkyUb.cTjpyridines (28-31) are consistent with the effect of [b]-annelation dominating over that of the [d]-annelation. ... 

Tabulating absorption coefficients c (p,T) for a range of (p,T) values for each absorber g... 

Then, in 1973, Streitwieser reported that the polyarylmethane exchange rates measured in cyclohexylamine-cyclohexylamide correlate with equilibrium p/T values with a = 0.31.79 Apparently, when the proton is removed by cyclo-hexylamide, the polyarylmethanes have early transition states, just as the fluorenes did for proton removal by the weaker base methoxide.80 A short extrapolation of the Bronsted correlation led to a pKa for toluene of 40.9, about seven units higher than the value assigned in the MSAD scale. Furthermore, if we... 

Figure 8.22. Equilibrium curves for the reaction CaC03 + SiC>2 —> CaSiC>3 + Si02 at a CO2 pressure of 1 atm and at a CO2 pressure equal to total pressure on the system. At P-T values between the two CO2 pressure extremes, caicite and quartz are stable. Heavy solid line is experimentally determined and dashed lines are extrapolated or theoretical. (After Barth, 1962.)...

The pAT-behaviour of 1-, 2- and 9-anthroic acids in the excited state was studied by Vander Donckt and Porter (1968a). Directly determined p/ (T )-values were found to lie nearer to the p/ (S1)-values calculated using the Forster cycle than to pA (S0). In a study of the fluorescence of 1- and 2-anthroic acids over a wide acidity range (Schulman et al., 1973a), it appeared that the deprotonation reactions did not come to equilibrium in the excited state. For protonation of the carboxyl group only 1-anthroic acid showed an excited state reaction and, as expected, it became more basic in the Si state. Fluorescence lifetime measurements on the prototropic species derived from 1- and 2-anthroic acids help in understanding the failure to reach equilibrium ... 

H, Eq. (1.15.17) is then employed again to trace out the general dependence of T on P. Note that, on account of Eq. (1.15.1), the slope of this curve furnishes a value of for each specified set of (P, T) values. The maximum of the slope for each H curve thus determines the largest accessible value of the Joule-Thomson coefficient for a given set of conditions. 

Obviously the diagrams for fresh water and for seawater are generally similar but differ in certain details, for example, the buffer intensity at high pH, point z. Because of the ionic strength effects, the operational acidity constants are larger for seawater than for fresh waters that is, the p/T values and thus the pH at the equivalence point—especially at the equivalence point y— are lower for seawater than for fresh water. Seawater contains, in addition to dissolved CO2, boric acid, H3BO3 (representative concentration of total boi on = 4.1 X 10 M). Its presence does not contribute markedly to the buffering of seawater. At the pH of seawater (pH = 8.1), its buffer intensity is near the minimum. 

Excitation into the T, state changes the pK value in the same direction as excitation into the S, state, but much less, and the p (T,) value tends to be closer to p/k(So) than to p/k(S ) ... 

Crarn had developed an acidity scale based on the ion pair acidity and used this and other measures (such as the acidity function technique) in compiling his so-called MS AD acidity scale, named after W. K. McEwen, A. Streitwieser, D. E. Applequist and R. E. Dessy. The scale used 9-phenylfluorene (pifa = 18.5) as its standard and is considered at least approximately to refer to the dilute aqueous solution as the standard state. On this scale ethylene is assigned a p T value 0.5 units lower than benzene however, in another early compilation ethylene is 1 pif unit higher than benzene. In an updated MS AD scale, ethylene was found to be 1 p f unit less acidic than benzene . ... 

Streitwieser and Boerth studied the kinetic acidities of cycloalkenes with lithium cyclo-hexylamide (LiCHA) in cyclohexylamine for comparison with those of benzene and toluene. The relative rates of deprotonation and the corresponding equilibrium p T values are tabulated in Table l2. These proton transfer transition states are stabilized by conjugation of the reacting C—H bond with the double bond. 

One can detect from this figure that (7) dependence covers more than three orders of p(T) value. From the straight line slope it is possible to determine To 4 107 K value. No doubt, this is a variable range hopping process, which occurs in a narrow band of the order of kT width in the Fermi level vicinity. There were provided special calculations for To value [8,11,13] based on the percolation approach. Those calculations give the similar result, which is... 

As more detailed studies of excited state p/T-values accumulate and our understanding of acidic and basic solutions deepens, it should become possible to discover local effects which will explain consistently both the trends in the appropriate acidity scales and the spectral effects (absorption-fluorescence spacings) related to departures from the simple Forster calculation of the pK shift upon excitation. 

Supercritical carbon dioxide (SCCO2) has been used as the reaction medium for hydroformylation reactions. The most attractive feature of SCFs is that its properties (density, polarity, viscosity, diffusivity, etc.) can be varied over a wide range by small changes in P/T values. 

For all dibasic acids pKi > p/ i. This is because it is more difficult to remove the second proton from the negatively charged anion produced in the first dissociation. However, the difference between the two p/T values decreases as the value of n increases, a consequence of... 

In Section 3.5, it was stated that aliphatic aminoacids and aminophenols showed strongly contrasting behaviour when studied over a range of pH. Both show acidic and basic behaviour and, for both, the titration curves show two p T values and two end-points. 

Reaction of the pentadentate bispidine-based systems with H2O2 in methanol at low-temperature yields a purple solution of the low-spin iron(III) end-on hydroperoxo complexes that of the isomer with an in-plane coordination of the hydroperoxide is, as expected, considerably more stable than that with an axially coordinated substrate. Deprotonation to the end-on high-spin peroxo complex (seven-coordinate) is reversible for the more stable isomer, with a p T value of... 

Treatment of any of these compounds with strong base produces an anion (or a lithium derivative if BuLi is used) on what was the methyl group. How does the sulfur stabilize the anion This question has been the subject of many debates and we have not got space to go into the details of all of them. There are at least two factors involved, and the first is evident from this chart of p T values for protons next to sulfone, sulfoxide and sulfide functional groups. 

There has been very little new information on xenic and perxenic acids and their salts since the late 1960s. More recent information includes study of the spectra and protol3dic properties of aqueous perxenic acid in the pH range -0.2 to 13, which yielded p T values at 25°C as follows ... 

The solvent term [H2O] varies by a negligible amount in such reactions and is incorporated in the constants K, and K, . If the concentrations are expressed in mol dm" , and have the same units. Table 3.3 lists p/T, values for some typical compounds. The behaviour of the conjugate base may be represented in line with equation (3.15). 

The pA" of several common amines used in synthesis have been determined in THF at 25°C. All will be used as bases in reactions used later in this book. 4-Al,Al-Dimethylaminopyridine (DMAP, 16), proton sponge (17), quinuclidine, (18), DBU (l,8-diazabicyclo-[5.4.0]-undec-7-ene, 19), and diazabicyclo-[2.2.2]octane (DABCO, 20) are shown, along with triethylamine, tributylamine, and tribenzylamine for comparison. The p/T values for these compounds are shown in THF, DMSO, and acetonitrile in Table 2.4.27 These values were determined from proton-transfer ion pairs of the type BH" " with acidic indicator hydrocarbons in THF. The values obtained in THF differ substantially from the ionic pKa values for NH+ in DMSO or acetonitrile. Streitwieser and co-workers27 states that "at the present time amines cannot be placed quantitatively on any of the ion pair acidity scales currently in use for neutral acids in THF". The realization that it may be necessary to use different bases in different solvents, despite the fact that all are considered to be good bases in organic reactions, makes it clear why a quantitative comparison of bases would be useful. 

MHL shows p/T values which depend strongly on the charge of the metal ion. In the specific cases of platinum(II) and palladium(II) it was possible to detect other species with more protons, i.e. MHjL and MH3L". Depending on the stability of the complex, these can also be formed with other cations. 

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