Equation warning

If Dirac was warning us that solution of the equations of quantum mechanics was going to be horrendous for everyday chemical problems, then history has proved him right. Fifty years on from there, Enrico dementi (1973) saw things differently ... 

We use the international Hazard road sign A to warn that a skeletal equation is not balanced. Then we balance hydrogen and oxygen atoms ... 

One word of warning when using the van t Hoff equation for reactions involving gases, the equilibrium constants must be K, not K(.. If we want a new value for Kc for a gas-phase reaction, we convert from K(. into K at the initial temperature (by using Eq. 12), use the van t Hoff equation to calculate the value of K at the new temperature, and then convert that K into the new Kc by using Eq. 12 at the new temperature. 

We have not yet introduced the influence of the presence of point charges on the lipophilicity of a chemical. Nevertheless, Sections 12.1.1.2 and 12.1.1.3 do warn that the lipophilic behavior of an ionized molecule might be very different from that of its parent neutral compound. Indeed, in order to investigate the balance of forces governing the lipophiUcity of ionized species we must do without Abraham s equations, since they do not exist when ions are considered. Recently, Abraham et al. also demonstrated what had long been perceived intuitively - descriptors for ions are not the same as those for nonelectrolytes [12]. 

In the following, definitions of essential analytical terms are compiled, if possible on the basis of international agreements. Attached are sparse references and cross-references. The symbols, being used here, means —> see also (cross-references to terms, additional references as well as paragraphs, chapters, equations and figures of this book), and X is a warning notice. 

In the particular case dealt with now (fully labile complexation), due to the linearity of a combined diffusion equation for DmCm + DmlL ml, the flux in equation (65) can still be seen as the sum of the independent diffusional fluxes of metal and complex, each contribution depending on the difference between the surface and bulk concentration value of each species. But equation (66) warns against using just a rescaling factor for the total metal or for the free metal alone. In general, if the diffusion is coupled with some nonlinear process, the resulting flux is not proportional to bulk-to-surface differences, and this complicates the use of mass transfer coefficients (see ref. [II] or Chapter 3 in this volume). 

Although equations (22) and (23) look compellingly similar, the reader is warned against undue generalization The fourth cumulant does not follow the same pattern. 

The synthesis of thiophenol 326 according to equation 78 is assumed to proceed via an intermediate organolithium compound 325. There is a warning against trying to purify intermediate 325 and similar metallated compounds due to a danger of explosion . ... 

Equations used to calculate percent yield or dilution ratios A list of disposable equipment (e.g., rubber gloves, Bunsen burners) Step-by-step instructions of the procedure Warnings to other scientists about unusual hazards Quantitative statements of reaction times and temperatures Descriptions of the physical appearances of synthesis products IR or NMR data confirming product purity Statistical packages used (including the name of the software) Reports of other software used to keep track of data (e.g., Excel)... 

The prediction of such a curve for a specific system has defied mathematical analysis, except in the region of low inertial effects. Recourse must be made to the time-honored method of graphical empirical correlation. Klee and Treybal (K3) arrived at two equations, one for the region below the peak diameter and one for that above the peak. They warn that these are simply good approximations, and that their dimensionless-group equations describe their data and those of other authors fairly accurately. The field liquid in all systems used was one of low viscosity. 

In this example, 30 calibration factors have to be quantified by the calibration procedure, which requires 30 independent equations and, therefore, 10 calibration samples (gives 3 equations per sample). Martens warned against pitfalls by using MLR. There is, for example, no check whether the general model is adequate to describe the unknown samples. The calculated concentrations may be in error because the sample contains other impurities than present in the calibration samples, or because some... 

Finally, a word of warning because the order of operations in a product is important (the one to the right always being carried out first), one must be careful when manipulating equations involving symmetry operations, for example, if PQ = R then we can write TPQ = TR (combining T on the left of both sides) or PQT = RT... 

Warning. The idea of using a nonlinear Fokker-Planck equation as a general framework for describing fluctuating systems has attracted many authors. Detailed balance, in its extended form, was a useful aid, but the link with the deterministic equation caused difficulties. It may therefore be helpful to emphasize three caveats. 

In equation (4.7) the initial time is no longer mentioned, and it therefore applies to all distributions, regardless of the time the shutter opened, provided that occurred more than tc earlier than t. This proviso means that (4.7) is not a master equation (see the Warning in V.l). Yet it may be approximately treated as such if p does not change much during tc. 

N-Chloropiperidine is trimerized on heating with alcoholic potassium hydroxide. The initial stage is the loss of hydrogen chloride to give the intermediate (155), and mixed products are produced (Scheme 93) (59HC(13)1, p. 446). Recently, Warning and Mitzlaff have found a selective synthesis of a-tripiperideine from l-formyl-2-methoxypiperidine (equation... 

Warning. If the azide group is coordinated in step c without an accompanying oxidation-reduction reaction, the resulting red azide complex is dangerously explosive. Equations e and f represent this process ... 

---