Refutations

To clarify the different roles played by the Helmholtz and Gibbs free energies of ionic solutions, it is relevant to reconsider the derivation of these thermodynamic quantities in the original Debye-Hiickel theory [1—4], 

In their investigation of dilute solutions of simple ions, Debye and Hiickel regarded the jth small ion as a spherical particle with radius a such that the small ion has an electric charge zf at its spherical center and the dielectric constant e inside the sphere. In this case, the total electrostatic energy of the system is obtained as 

When kzi is sufficiently small, this function is written in series expansion form as 

Taking the difference between the Gibbs and Helmholtz free energies, we obtain the equation of state for the osmotic pressure of the small-ion gas as follows  

To take derivatives of F with respect to N, and Zn and to sum up the component chemical potentials without contradiction to the constraint condition [8, 9], we introduce the following differential operator DNZ as 

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Oxygen Difluoride as a Source of the OF Radical. The existence of the OF radical [12061 -70-0] was first reported in 1934 (27). This work was later refuted (28). The OF radical was produced by photolysis of OF2 in a nitrogen or argon matrix at 4 K. The existence of the OF species was deduced from a study of the kinetics of decomposition of OF2 and the kinetics of the photochemical reaction (25,26) ... 

Early structures, proposals and refutations included benzoazetenone, cyclobutadienes (B-65MI41600) Or an oxarirane (04CB966, 26LA(437)162, B-35MI41600), and these references should be consulted for this early work. 

A number of other suggestions for formation of azetes seem most unlikely or have been definitely refuted (B-50MI50900, 76TL3931, 78TL1543). 

If the null hypothesis is assumed to be true, say, in the case of a two-sided test, form 1, then the distribution of the test statistic t is known. Given a random sample, one can predict how far its sample value of t might be expected to deviate from zero (the midvalue of t) by chance alone. If the sample value oft does, in fact, deviate too far from zero, then this is defined to be sufficient evidence to refute the assumption of the null hypothesis. It is consequently rejected, and the converse or alternative hypothesis is accepted. 

Wilde, G. J. S. (1984). Evidence Refuting the Theory of Risk Homeostasis A Rejoinder to Frank P. McKenna. Ergonomics 25, 879-890. 

Experimentalists have proposed that oxygen should bind to the 6-6 bond. Does your calculation support or refute this Can you justify any inconsistencies ... 

Based on its structure and valence electron count, draw a Lewis structure or series of Lewis structures for diborane Examine the bond density surface. Does it substantiate 01 refute your speculation ... 

Unsaturated y-lactones, c.g., a- (23) and / -angelica lactone (24), are well known. Compounds 23 and 24 are both converted by alkaline catalysts into an equilibrium mixture in which 23 predominates, the amount of the hydroxy form (25) present at equilibrium being exceedingly small. True a-hydroxy furans are unknown, and, although the preparation of both a- and / -bydroxyfurans has been reported, these claims have often been refuted (see, e.g., reference 14). 

Niederschlagbarkeit, /. precipitability. niederschlagen, v.t. precipitate deposit condense beat down, quell, refute, depress. —... 

There are no objective tests which will enable one to tell at what point mishandling in storage took place. The packer who fails to keep a record of the quality and condition of his product as it is placed in storage, of the storage conditions, and of product condition as it is loaded for shipment is exposing himself to unnecessary risk. Without such records he may find himself unable to refute unjust or misdirected claims initiated by the buyer. 

Paper nine is another one that appeared in American Scientist. In it I took a philosophical look at two important ideas that contributed to the evolution of the periodic system. These two ideas are Prout s hypothesis and the notion of triads, which was the subject of paper eight. Both hypotheses are interesting because they were extremely productive even though they both turned out to be refuted some time later. The fact that this should happen lends some support to the views of Karl Popper who always claimed that refutability was the all important aspect of good hypotheses and theories and not whether they turn out to be correct or not.23 For Popper, all that we really have is tentative theories and not theories that last forever. 

As in the case of triads attempts to confirm ur refute Proofs hypothesis contributed to renewed efforts on the part of chemists to measure atomic weights However, although lltese Ideas Wert fruitful tn some ways, they were also found wanting as more Ac-... 

Tammann has, by a large amount of experimental evidence, apparently refuted the hypothesis of a critical point of fusion— against which of course there is no a priori objection. In some cases (e.g., with ice) new crystalline modifications appear when the temperature and pressure are modified, and in all cases the pair of relations L = 0, Ar = 0 (cf. 89) were never simultaneously satisfied. 

Equilibrium phosphate concentration theory refutes the concept of blanket control determined by boiler pressure and operates each boiler system on a case-by-case basis. It seeks to strenuously avoid hideout-related problems and the subsequent risks of misdiagnosis. Operators are encouraged to explore the maximum operating tolerances before phosphate destabilization takes effect and hideout results, and to ensure... 

This color change was first observed by Duffin and Kendall (1954). A first structural interpretation (Baigrie et al., 1979) was later refuted by Gorelik et al. (1980). 

Ultraviolet spectra of diazonium salt solutions were recorded for the first time by Hantzsch and Lifschitz as early as 1912. However, electron spectra did not provide significant information on the structure of diazonium ions, either at that time or later. For example, Anderson and coworkers (Anderson and Steedly, 1954 Anderson and Manning, 1955), compared spectra of 4-amino-benzenediazonium salts with those of diphenylquinomethane (4.18). Their conclusion that the structures of these compounds are analogous is basically correct, but the arguments given by Anderson can easily be refuted, as shown by Sorriso (1978, p. 102). 

All the same, lasting credit is due to Hantzsch for refuting the proposals, made so often since 1894, to interpret the isomerism of diazo derivatives using other than stereochemical arguments. For his purpose Hantzsch used the methods of physical chemistry, such as conductivity measurements and spectroscopy, at a time when these were most unusual in the organic field. 

In Section 8.3 the mechanism of heterolytic dediazoniation of arenediazonium ions was discussed, and it was shown that the hypothesis of Crossley et al. (1940) that the aryl cation is the characteristic metastable intermediate in those reactions was not consistent with some experimental facts found in 1952 by Lewis and Hinds. Nevertheless, these facts did not have significant influence on the scientific community, which continued to accept the original and apparently convincing hypothesis of the rate-limiting formation of an aryl cation as an intermediate as correct . The incom-patabilities of various mechanistic hypotheses with experimental facts were, however, discussed in some detail only two decades later (Zollinger, 1973 a). Another year passed before I performed a crucial experiment that refuted a number of hypotheses (Bergstrom et al., 1974, 1976). ... 

Popper s theory has been criticized by Thomas Kuhn (1962, 1969), who asserts that the development of science proceeds in revolutions hypotheses and theories are not refuted and replaced by new ones instead the scientific community will accept a new, more convincing, or better presented hypothesis without the old one having been disproved. 

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