The Dissociation Equilibrium of Hydrogen and its Adsorption on Tungsten

1936 ◽  
Vol 32 (1) ◽  
pp. 152-157 ◽  
Author(s):  
J. K. Roberts
Keyword(s):  
Adsorption Isotherm ◽  
Statistical Method ◽  
Gas Phase ◽  
Approximation Formula ◽  
Dissociation Equilibrium ◽  
First Approximation ◽  
Adsorbed Atoms ◽  
Detailed Interpretation ◽  
Rate Of Evaporation ◽  
Detailed Balancing

The various processes occurring at the surface when hydrogen is adsorbed on tungsten are considered together with the dissociation equilibrium of hydrogen in the gas phase. The form of the adsorption isotherm is deduced from the principle of detailed balancing and is in agreement with that obtained by Fowler using a statistical method. A detailed interpretation of the experimental results now available shows that either (a) measurements of the rate of removal of the adsorbed film of oxygen on tungsten do not measure the rate of evaporation of oxygen atoms or (b) it is not possible to obtain a general first approximation formula giving the rate of evaporation of adsorbed atoms in terms of the heat of desorption. The desorption of hydrogen from tungsten is discussed and it is shown that the agreement between the temperature at which the film evaporates at an appreciable rate and that deduced from a desorption formula of the type mentioned in (b) assuming that the hydrogen evaporates as atoms must at present be regarded as a coincidence.

A further note on the measurement of the affinity of a dye (Azure A) for histological substrates

1965 ◽  
Vol s3-106 (76) ◽  
pp. 299-306
Author(s):  
D. J. GOLDSTEIN
Keyword(s):  
Adsorption Isotherm ◽  
Goblet Cell ◽  
Binding Sites ◽  
Langmuir Isotherm ◽  
Langmuir Adsorption Isotherm ◽  
Intestinal Epithelial ◽  
Langmuir Adsorption ◽  
Azure A ◽  
First Approximation ◽  
The Ideal

If two histological sections, of thickness nµ and 2nµ, and having the same apparent intensity of staining, are at equilibrium with dyebaths of concentration B1 and B2 respectively, the affinity of the histological substrate for the dye is, under denned conditions, given by the expression ΔF° = - RT In I/B, where B is either (i) B2 if the thinner section is stained to saturation, or (ii) B1 if B1 = 3B2. The affinity tends to be greater when measured in a weaker dyebath, as implied in method (ii). Evidence is presented suggesting that the uptake of the basic dye Azure A by pancreatic basal chromidial substance, goblet cell mucin and intestinal epithelial cytoplasm follows a Langmuir adsorption isotherm to a first approximation, in that, at low dyebath concentrations, the uptake of dye is proportional to the concentration of dyebath with which the substrate is in equilibrium, while in strong dyebaths the uptake approaches a plateau. A deviation from the ideal Langmuir isotherm in dyebaths of moderate concentration, observed in epithelial cytoplasm and to a lesser extent in pancreatic basal chromidial substance, may have been due to interaction between neighbouring dye-binding sites, or to the presence in a single area of sites with different affinities for the dye.

scholarly journals The reflection of vapour molecules at a liquid surface

1931 ◽  
Vol 131 (818) ◽  
pp. 554-564 ◽  
Keyword(s):  
Kinetic Theory ◽  
Vapour Pressure ◽  
Liquid Surface ◽  
Unit Area ◽  
Kinetic Theory Of Gases ◽  
Perfect Gas ◽  
Saturated Vapour Pressure ◽  
Saturated Vapour ◽  
First Approximation ◽  
Rate Of Evaporation

The rate of evaporation of a liquid may be calculated from the kinetic theory of gases if it be assumed that all vapour molecules which strike the surface enter the liquid and that, as a first approximation, the vapour behaves as a perfect gas. Under these circumstances, it follows from the kinetic theory of gases that m = mass of molecules leaving unit area per minute = mass of molecules striking unit area per minute from the saturated vapour = 14·63 P s /√T s gram/sq. cm. /min., where P s is the saturated vapour pressure in millimetres of mercury at the surface temperature T s ° A.

Statistical theory of adsorption with interaction between the adsorbed atoms

1936 ◽  
Vol 32 (3) ◽  
pp. 471-476 ◽  
Author(s):  
R. Peierls
Keyword(s):  
Statistical Theory ◽  
Adsorption Isotherm ◽  
Statistical Problem ◽  
Physical Problem ◽  
Adsorbed Atoms

In a recent paper, Fowler discusses the adsorption isotherm for a monatomic layer, assuming an interaction between neighbouring atoms in this layer. In this paper we do not intend to give a contribution to the physical problem, but merely to show how the statistical problem involved can be solved by a method due to Bethe.

scholarly journals Secondary aerosol formation from atmospheric reactions of aliphatic amines

2007 ◽  
Vol 7 (9) ◽  
pp. 2313-2337 ◽  
Author(s):  
S. M. Murphy ◽  
A. Sorooshian ◽  
J. H. Kroll ◽  
N. L. Ng ◽  
P. Chhabra ◽  
...  
Keyword(s):  
Nitric Acid ◽  
Equilibrium Constant ◽  
Gas Phase ◽  
Organic Aerosol ◽  
Aliphatic Amines ◽  
Aerosol Formation ◽  
Atmospheric Reactions ◽  
Dissociation Equilibrium Constant ◽  
Dissociation Equilibrium ◽  
Nitrate Salts

Abstract. Although aliphatic amines have been detected in both urban and rural atmospheric aerosols, little is known about the chemistry leading to particle formation or the potential aerosol yields from reactions of gas-phase amines. We present here the first systematic study of aerosol formation from the atmospheric reactions of amines. Based on laboratory chamber experiments and theoretical calculations, we evaluate aerosol formation from reaction of OH, ozone, and nitric acid with trimethylamine, methylamine, triethylamine, diethylamine, ethylamine, and ethanolamine. Entropies of formation for alkylammonium nitrate salts are estimated by molecular dynamics calculations enabling us to estimate equilibrium constants for the reactions of amines with nitric acid. Though subject to significant uncertainty, the calculated dissociation equilibrium constant for diethylammonium nitrate is found to be sufficiently small to allow for its atmospheric formation, even in the presence of ammonia which competes for available nitric acid. Experimental chamber studies indicate that the dissociation equilibrium constant for triethylammonium nitrate is of the same order of magnitude as that for ammonium nitrate. All amines studied form aerosol when photooxidized in the presence of NOx with the majority of the aerosol mass present at the peak of aerosol growth consisting of aminium (R3NH+) nitrate salts, which repartition back to the gas phase as the parent amine is consumed. Only the two tertiary amines studied, trimethylamine and triethylamine, are found to form significant non-salt organic aerosol when oxidized by OH or ozone; calculated organic mass yields for the experiments conducted are similar for ozonolysis (15% and 5% respectively) and photooxidation (23% and 8% respectively). The non-salt organic aerosol formed appears to be more stable than the nitrate salts and does not quickly repartition back to the gas phase.

The adsorption of dipoles

1940 ◽  
Vol 36 (1) ◽  
pp. 69-78 ◽  
Author(s):  
A. R. Miller
Keyword(s):  
Adsorption Isotherm ◽  
Statistical Method ◽  
Electrostatic Interactions ◽  
Opposite Sign ◽  
Van Der Waals ◽  
Statistical Treatment ◽  
Van Der Waals Forces ◽  
Considerable Effect ◽  
Heat Of Adsorption ◽  
General Shape

In the present paper Bethe's approximation is applied to the statistical treatment of the adsorption of dipoles considering (a) the electrostatic forces alone, and (b) the electrostatic and van der Waals forces jointly. In each case formulae are obtained for the adsorption isotherm and for the variation of the heat of adsorption with the fraction of surface covered. In case (a) the heat curves are compared with those obtained by Wang who used a different approximation to take into account the electrostatic interactions due to particles adsorbed on outer sites. The curves are of the same general shape; sources of differences in them are discussed. In case (b) the results are compared with those obtained by Roberts using a different method. This treatment confirms his result that the electrostatic and van der Waals forces give contributions to the variation of the heat of adsorption which are of opposite sign and almost counterbalance one another, so that the resultant variation in the heat of adsorption is very much less than would be expected from a consideration of forces of one type only. This comparison shows further that the distribution of particles on the surface, which is taken into account in the statistical method used in this paper, has a considerable effect on the variation of the heat of adsorption.

CORRELATION IDENTITIES FOR NEAREST-PARTICLE SYSTEMS AND THEIR APPLICATIONS TO ONE-DIMENSIONAL CONTACT PROCESS

1991 ◽  
Vol 05 (02) ◽  
pp. 151-159 ◽  
Author(s):  
NORIO KONNO ◽  
MAKOTO KATORI
Keyword(s):  
Order Parameter ◽  
Particle System ◽  
Contact Process ◽  
Critical Value ◽  
Particle Systems ◽  
Approximation Formula ◽  
One Dimensional ◽  
Renewal Measure ◽  
First Approximation ◽  
The One

A series of identities of correlation functions K(n1, n2, …, nN) are given in the nearest-particle system. The above correlation identities are applied to the one-dimensional contact process. The decoupling induced by a renewal measure yields the first approximation: [Formula: see text] for the critical value and [Formula: see text] for the order parameter, which makes a rigorous bound as proved by Holley and Liggett. Furthermore, introducing a new decoupling procedure, improved estimations of [Formula: see text] and [Formula: see text] are calculated.

The equilibrium of atoms and ions adsorbed on a metal surface

1933 ◽  
Vol 29 (1) ◽  
pp. 161-164 ◽  
Author(s):  
R. C. Evans
Keyword(s):  
Metal Surface ◽  
Alkali Metals ◽  
Present Note ◽  
Surface Concentration ◽  
Hot Metal ◽  
Equilibrium Conditions ◽  
Adsorbed Atoms ◽  
Rate Of Evaporation

The theory of the evaporation of adsorbed atoms and ions of the alkali metals from a hot metal surface has been developed from somewhat different viewpoints by Langmuir and Kingdon and by Becker. These two treatments, which yield essentially the same results, are applicable only when equilibrium conditions obtain on the surface, so that the surface concentration is not changing. It is the purpose of the present note to extend Becker's treatment to take account of the rate of attainment of equilibrium on the surface, in order to lead to an interpretation of some experiments on the rate of evaporation of the alkali metals adsorbed on hot tungsten.

PYROLYSIS STUDIES: X. RATES OF THE THERMAL DECOMPOSITION OF ortho-SUBSTITUTED ETHYL BENZOATES IN THE GAS PHASE

1964 ◽  
Vol 42 (2) ◽  
pp. 294-297 ◽  
Author(s):  
Grant Gill Smith ◽  
David F. Brown
Keyword(s):  
Thermal Decomposition ◽  
Benzoic Acid ◽  
Gas Phase ◽  
Steric Effects ◽  
First Approximation ◽  
Chromatographic Measurement

Eight ortho-substituted ethyl benzoates (with substituents varying from o-NH2 to o-NO2) have been partially pyrolyzed to ethylene and the corresponding benzoic acid. By gas chromatographic measurement of the amount of ethylene produced, the relative rates of the thermal decomposition of the various ethers have been determined. There are minor steric effects (primary or secondary) in the reaction and direct field influences are negligible. The varying reactivity, therefore, is attributed to changes in polar effects of the substituent. This reaction appears to be a useful method of determining, quantitatively, to a good first approximation, polar effects of ortho substituents.

Superlattice formation of the type AB in an adsorbed layer

1939 ◽  
Vol 35 (1) ◽  
pp. 70-83 ◽  
Author(s):  
T. S. Chang
Keyword(s):  
Free Energy ◽  
Interaction Potential ◽  
Adsorbed Layer ◽  
Rate Of Change ◽  
Nearest Neighbours ◽  
Adsorbed Atoms ◽  
The One ◽  
Type Ab ◽  
A Site ◽  
Detailed Balancing

The possibility, pointed out in a previous paper, of superlattice formation in an adsorbed layer when the adsorbed atoms tend to repulse each other is developed in detail. Both Bragg and Williams's approximation and Bethe's approximation are used, but restricted to superlattices of the type AB. In a range of θ, the fraction of surface covered, a superlattice is found to be possible. Bragg and Williams's approximation shows further that the state with the lowest free energy is the one with a superlattice when the latter is possible. Rough kinetic expressions are also given. The equations derived from the principle necessary to preserve equilibrium are found to reduce to those of detailed balancing, and they also agree with the formula obtained statistically. As expected, all the corresponding results obtained from the two methods become the same when the number of nearest neighbours of a site approaches infinity, provided that the product of this number and the interaction potential of two adsorbed atoms occupying two neighbouring sites remains finite.The only significant result is the large value of the slope of isotherms (the rate of change of the pressure with respect to the fraction of adsorption) when there is a nearly complete superlattice.

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