The pKBH+ calculation of strong bases: A revision of various methods

1987 ◽  
Vol 52 (2) ◽  
pp. 299-307 ◽  
Author(s):  
Begoña García ◽  
José M. Leal
Keyword(s):  
Perchloric Acid ◽  
Infinite Dilution ◽  
Polynomial Function ◽  
Acid Base ◽  
Third Order ◽  
Acid Media ◽  
The Third ◽  
Aniline Derivatives ◽  
New Methods

The pKBH+ values have been obtained for seventeen acid-base equilibriums corresponding to thirteen aniline derivatives in dilute perchloric acid media in the pH region at 25 °C using the spectrophotometric technique. By revising the method of extrapolation to infinite dilution it was possible to introduce new methods for calculating pKBH+ values of strong bases by means of the functions logI = f(pH) and pKap = f(pH). The equation - logfBH+/fB = f(pH) - has been proved to conform to a polynomial function of the third order and is applicable to each compound.

Acid–base behaviour of the ferrocyanide ion in perchloric acid media potentiometric and spectrophotometric study

1987 ◽  
Vol 65 (3) ◽  
pp. 583-589 ◽  
Author(s):  
Pedro L. Domingo ◽  
Begoña Garcia ◽  
Jose M. Leal
Keyword(s):  
Perchloric Acid ◽  
Spectrophotometric Study ◽  
Separate Study ◽  
Acid Base ◽  
Acid Media ◽  
Protonation Equilibria ◽  
The Third ◽  
Brønsted Base

Ferrocyanide ion behaves as a tetravalent Brønsted base and can react with four protons, forming ferrocyanic acid. By potentiometric and spectrophotometric techniques it is shown that the first two protonation equilibria overlap, as do the third and fourth equilibria. The two techniques yield identical results when processed with the inclusion of non-ideality terms. The method of "separation of equilibria" is proposed to allow separate study of each of the overlapping equilibria. Values of pK1 = −2.54 ± 0.10, pK2 = −1.08 ± 0.03, pK3 = 2.65 ± 0.02, and pK4 = 4.19 ± 0.02 were obtained.

Acid–base behaviour of the ferricyanide ion in perchloric acid media. Spectrophotometric and kinetic study

1990 ◽  
Vol 68 (2) ◽  
pp. 228-235 ◽  
Author(s):  
Pedro L. Domingo ◽  
Begoña García ◽  
José M. Leal
Keyword(s):  
Kinetic Study ◽  
Perchloric Acid ◽  
Decomposition Reaction ◽  
Acid Base ◽  
Acid Media ◽  
Protonation Equilibria ◽  
Aqueous Perchloric Acid ◽  
Protonated Species ◽  
Heterolytic Dissociation ◽  
Homolytic Dissociation

A wide study was carried out of the acid–base behaviour of ferricyanide ions in aqueous perchloric acid media in the range 0.1–11.5 M. This study shows that protonation and decomposition of the ferricyanide ions occur simultaneously. The three successive protonation equilibria were found in the acidity ranges 0.1–4.0, 3.5–8.5, and 7.0–11.5 M HClO4, respectively. A kinetic study was also made of the decomposition reaction at 60 °C. The kinetic data are explained by considering a reaction mechanism involving homolytic and heterolytic dissociation steps. The homolytic and heterolytic rate constants corresponding to each of the four protonated species were determined, along with the acid–base protonation constants, pK1 = −6.25 ± 0.10; pK2 = −3.23 ± 0.03; and pK3 = −0.60 ± 0.02. Keywords: acid–base behaviour, protonated species, decomposition, homolytic dissociation, heterolytic dissociation.

scholarly journals Separation of Long-Crested Nonlinear Bichromatic Waves into Incident and Reflected Components

2019 ◽  
Vol 7 (2) ◽  
pp. 39 ◽  
Author(s):  
Thomas Lykke Andersen ◽  
Mads R. Eldrup ◽  
Maria Clavero
Keyword(s):  
Physical Model ◽  
Nonlinear Waves ◽  
New Method ◽  
Regular Waves ◽  
Third Order ◽  
Reflected Waves ◽  
The Third ◽  
New Methods ◽  
Linear Waves ◽  
Physical Model Tests

Methods for the separation of long-crested linear waves into incident and reflected waves have existed for more than 40 years. The present paper presents a new method for the separation of nonlinear bichromatic long-crested waves into incident and reflected components, as well as into free and bound components. The new method is an extension of a recently proposed method for the separation of nonlinear regular waves. The new methods include both bound and free higher harmonics, which is important for nonlinear waves. The applied separation method covers interactions to the third order, but can easily be extended to a higher orders. Synthetic tests, as well as physical model tests, showed that the method accurately predict the bound amplitudes and incident and reflected surface elevations of nonlinear bichromatic waves. The new method is important in order to be able to describe the detailed characteristics of nonlinear bichromatic waves and their reflection.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

scholarly journals Ultrafast Third-Order Nonlinear Optical Response Excited by fs Laser Pulses at 1550 nm in GaN Crystals

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3194
Author(s):  
Adrian Petris ◽  
Petronela Gheorghe ◽  
Tudor Braniste ◽  
Ion Tiginyanu
Keyword(s):  
Harmonic Generation ◽  
Nonlinear Optical ◽  
Laser Pulses ◽  
Third Harmonic Generation ◽  
High Repetition Rate ◽  
Third Order ◽  
Third Harmonic ◽  
The Third ◽  
High Repetition ◽  
Gan Crystal

The ultrafast third-order optical nonlinearity of c-plane GaN crystal, excited by ultrashort (fs) high-repetition-rate laser pulses at 1550 nm, wavelength important for optical communications, is investigated for the first time by optical third-harmonic generation in non-phase-matching conditions. As the thermo-optic effect that can arise in the sample by cumulative thermal effects induced by high-repetition-rate laser pulses cannot be responsible for the third-harmonic generation, the ultrafast nonlinear optical effect of solely electronic origin is the only one involved in this process. The third-order nonlinear optical susceptibility of GaN crystal responsible for the third-harmonic generation process, an important indicative parameter for the potential use of this material in ultrafast photonic functionalities, is determined.

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