Thesis (Ph. D.)--Columbia University, 1923. / Vita. "Reprinted from the Journal of biological chemistry, vol. LVI, no. 2, June 1923." Bibliography: p. 591.

Thèse--Faculté des sciences de Paris, 1900. / Includes bibliographical references.

In a large class of multi-unit auctions of identical objects that includes the uniform-price, as-bid (or discriminatory), and Vickrey auctions, a Bayesian Nash equilibrium exists in monotone pure strategies whenever there is a finite price / quantity grid and each bidder's interim expected payoff function satisfies single-crossing in own bid and type. A stronger condition, non-decreasing differences in own bid and type, is satisfied in this class of auctions given (a) independent types and (b) risk-neutral bidders with marginal values that are (c) non-decreasing in own type and have (d) non-increasing differences in own type and others' quantities. A key observation behind this analysis is that each bidder's valuation for what he wins is always modular in own bid in any multi-unit auction in which the allocation is determined by market-clearing. This paper also provides the first proof of pure strategy equilibrium existence in the uniform-price auction when bidders have multi-unit demand and values that are not private.

Thesis (Ph.D.)--Boston University / The work described here in this dissertation was undertaken to investigate the isotope effect on an equilibrium which is closely related to the assumed equilibria between reactants and transition states in solvolytic reactions and aromatic substitution. Earlier studies of the ion-forming equilibria of triphenylchloromethane and many of its o-, m-, and p-substituted derivatives together with data on the dissociation equilibria of many ionophores have provided a convenient means of evaluating substituent effects on the ionization equilibrium: Ar3CCl ↔ SO2 Ar3C+Cl- (1). The similarity of substituent effects in this system to those observed in solvolytic reactions (2,3) and electrophilic substitution reactions (4) has been elegantly demonstrated by Brown and Okamoto (5). Lewis and Boozer (6) suggest that β-deuterium isotope effects observed in the solvolysis of secondary alkyl halides and tosylates are dependent in part on the requirements of the developing carbonium ion for internal electron supply at the transition state. Studies of the ionization equilibrium above provide a measure of substituent effects where full carbonium character is unequivocally developed. [TRUNCATED]

[No abstract available] / Science, Faculty of / Chemistry, Department of / Graduate

A modified version of an apparatus by Sage and Lacey for phase equilibrium measurements at elevated temperatures and pressures has been designed and built. Assembly and detail drawings of the apparatus, and a detailed description for its use have been included. The vapor pressure of methanol has been measured at temperatures from 100°C to 225°C, and the vapor pressures of benzene and of toluene have been measured at temperatures from 125°C. to 250°C. Good agreement with literature values was found for the vapor pressures of each of these materials. Vapor-liquid equilibrium composition and pressure data have been measured for the benzene-toluene system at 200°C and compared to values reported for this system by v. Huhn and by Griswold, Andres, and Klein . Activity coefficients calculated for the liquid phase from the experimental data show that the liquid mixture forms a Lewis and Randall perfect solution. Isothermal vapor-liquid equilibrium composition and pressure data for the methanol-toluene system have been measured at 25-degree intervals from 125°C. to 250°C. An azeotrope was found for the system at temperatures of 125°, 150°, and 175°C, and it was estimated that this azeotrope disappears at 193.4°C. Activity coefficients have been calculated from the experimental data using several approximate methods, and tested for thermodynamic consistency using the test proposed by Redlich and Kister . Coefficients calculated using the method proposed by Black were the only ones which showed good thermodynamic consistency when tested in this way, and these have been correlated with a Redlich and Kister four-constant equation. The failure of activity coefficients calculated by approximate methods other than Black's to show good thermodynamic consistency indicates that the solution theories on which these methods are based are invalid for a non-ideal system of the type studied. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

Equipment and methods used to measure vapor-liquid equilibriums at pressures above one atmosphere are reviewed, and the methods of treating the results obtained from such equipment are also discussed. An apparatus suitable for the study of vapor-liquid equilibrium at pressures up to 3000 pounds per square inch and temperatures up to 550°F. has been designed. Provision is made in the apparatus for measuring the volume of each of the two phases and for removing samples of the individual phases at constant temperature and pressure. Recommendations for the calibration and use of the apparatus and for the purification of the solvents to be studied are given. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

In the main part of this work, an equilibrium in anion exchange between HC1 gas and vacuum-sublimed KBr powder has been studied from 0° to 87°C. For total amounts of exchange corresponding to less than one surface layer, the equilibrium isotherms could be represented by a very simple empirical equation of the form, 1/R[subscript p]X = 1/R[subscript p]X[subscript m] + 1/K'Xm', --------------------------------(1) where X = amount exchanged normalized to BET surface, Xm and Xm' are paramaters of exchange capacity with the same dimensions as X, K' = a dimensionless parameter related in some way to an equilibrium constant for exchange, and R[subscript p] = P[subscript HBr]/P[subscript HCI] in the gas phase at equilibrium. If Xm were independent of temperature and equal to unity or some whole number of layers, eq. (1) with Xm = Xm' would correspond to an ideal chemical equilibrium expression, K = R[subscript p] [x/(Xm - X)] --------------------------------(2). In practice Xm was found to be temperature-dependent (Xm[symbol omitted]exp(-4,600/RT)) and ranged 0.5 at 9.4°C to 3 at 87°C (rather scattered experimental points render the 0°C value uncertain). The quantity designated (K'Xm') in eq. (1) is obtained experimentally as a single constant, and its separation Into an equilibrium constant and an exchange capacity parameters depends on the interpretation of the results. (K' Xm') has approximately the same temperature dependence as Xm , but it is not clear in the first instance whether this is to be ascribed to K' or to Xm'. Various models are examined which may give rise to the above experimental results. Among them; (a) one in which co-operative interactions of first and second anion neighbours in a single layer are treated by a modified form of the quasi-chemical approximation seems to be able to explain isotherms for 0° and 9.4°C, (b) another in which three layers are taken into account in a simple manner is capable of explaining isotherms for 500 to 87°C. This latter is capable of explaining results at all temperatures if the correlation of BET surface with exchange capacity of one layer is assumed to be in error by a factor of ∼ 2 and the experimental isotherm for 0°C is discarded on the basis that plots according to eq. (1) are scattered. Alternatively, some combination of the models used in (a) and (b) would probably also account for the complete set of results. In part II of this work, the system in which the reaction 2IBr = I₂ + Br₂ and gas chromatographic separation of IBr, I₂ and Br₂ occur simultaneously on the column has been studied experimentally. Various methods of matching the experimental data by computation are discussed, and a computational method based on a "plate theory" model is found satisfactory. / Science, Faculty of / Chemistry, Department of / Graduate

A rather general expression for the excess Gibbs free energy of a nonionic liquid mixture has been developed in this thesis and the expression has been tested on nine binary mixtures exhibiting a considerable range of nonideal behavior in both vapor-liquid and liquid-liquid equilibria. The basis for the formulation is that of the constant coordination number quasichemical mixture theory of Guggenheim, suitably modified to account for the major effects arising from the nonconstant coordination number situation inherent in a mixture of unequally sized constituents. The development of the geometric aspects of the theory is considerably based on the ideas of Hogendijk for mixtures of random-packed spheres. The generalization of the theory to multicomponent systems is based on the work of Barker on associated mixtures. Because the expression handles a nonconstant coordination number system, it has for brevity been termed the NCZ equation. Although in many cases the proposed equation performed no better than those already available for certain systems, no existing theory was able to deal with all of the nine binaries on which the NCZ expression has been so far tested. The proposed method of formulating the excess Gibbs function has brought to the fore the need for physical chemical measurement of data of a kind not presently available on a large scale, despite the fact that the required parameters are in themselves standard thermodynamic quantities, such as the pure-component free energy of a liquid. The present extension of quasichemical theory is seen as an indication of the basic viability of the quasichemical type of approach for the prediction of the excess properties of liquid mixtures. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

The detection of trace explosives in the subsurface is an active area of research for landmine detection. Understanding the air-water flow and heat transport phenomena in the subsurface plays an important role in improving chemical vapor detection. Implementing a finite element method that accurately captures water vapor transport in the vadose zone is still an open question. A non-equilibrium, pressure-pressure formulation has been implemented based on Smits, et al [22]. This implementation consists of four equations: a wetting phase (water) mass balance equation, a non-wetting phase (air) mass balance equation, a water vapor transport equation, and a heat transport equation. This work will compare two implementations, a fully coupled approach and an operator splitting approach for the water vapor and heat transport equations. The formulation of the methods will be presented and the methods will be tested using collected data from physical experiments.