Le Chatelier's Principle Research Articles

Seeing the Physics of Chemistry

S tark Design's 3-D Molecular Dynamics (3DMD) program uses state-of-the-art interactive visualization software to simulate atomic motion. Although the target audience is the typical college undergraduate student, the software is also useful for advanced physical chemistry and graduate students. The four main modules of the program are Introductory Topics, Gas Behavior, Condensed Phases, and Advanced Topics, which covers most of the basic chemical principles. These include Dalton's law of partial pressure, diffusion, Maxwell-Boltzmann speed distribution, pressure/temperature and pressure/volume relationships, LeChatelier's principle, collision frequency, mean free path, pressure fluctuations, and the time average of kinetic energy. To view one of the concepts, a student picks a module and specific experiment from the home screen. For example, to study diffusion, the Gas Behavior module is chosen and diffusion is selected from the list of choices. A box appears that is divided into two compartments by a barrier (see figure). The opening between the chambers can be resized as desired. Next, the user selects atoms (helium, krypton, argon, and neon are the only choices) and introduces a specified number of each type into the system. The size of each atom is a function of its Van der Waals radius. By adjusting the temperature and time periods per screen update (with sliding switches), the atomic motion may be increased or slowed. This allows one to view the effect each parameter has on ultimately reaching equilibrium across the opening. In the Condensed Phases module, molecules actually “form” and “degrade” as the temperature changes. These processes may be hastened, or retarded, by the inclusion or exclusion of user-specified interatomic forces. While all this is happening, users can switch between two views—atoms as spheres or the classical view of atoms as circles with attached vectors. In addition to the molecular animations, two graphs are also visible for the diffusion module. The topmost graph displays the average position of an ensemble of atoms in the box in real time, and the bottom graph describes the relation between the atomic velocity and the square root of the ratio of the mass of a helium atom to the mass of any of the other three. The clever use of visualizations, combined with relevant graph plots, is a feature of all of the modules. Unfortunately, in the present version only Macintosh users can print screen views. A short, clearly written manual describing each module accompanies the CD-ROM. The manual is largely free of mathematics, except as necessary to support the program's atomic illustration functions. 3-D Molecular Dynamics succeeds in teaching basic physical-chemical principles with clever visualizations. The addition of other atoms and even small molecules would be a welcome addition to future editions. The program comes in both Macintosh and Windows formats. 3-D Molecular Dynamics version 2.5 Stark Design, Inc. Morristown, NJ. $180 877-384-8021

Adsorption isotherms ofm-xylene on activated carbon: measurements and correlation with different models

In this study, adsorption isotherms of m -xylene on activated carbon were measured by time integration of the breakthrough curves at T= (298.15, 308.15, 318.15, and 333.15) K using home-made apparatus developed for this purpose. At the temperature 333.15 K, isotherms were also measured using a microbalance in order to check the accuracy of the proposed apparatus. As expected, in keeping with the principle of Le Chatelier, the m -xylene loadings were observed to decrease with increasing temperature. Activated carbon was used as the adsorbent because it typically exhibits high adsorption capacities and shows potential as an adsorbent to effectively remove volatile organic compounds (VOCs) such as m -xylene. In a second step, the experimental data obtained were correlated with different existing adsorption isotherm models such as the Langmuir model, the Freundlich model, and the Dubinin equation. The Langmuir model was found to be well adapted to describe the adsorption of m -xylene onto activated carbon.

Identification and Analysis of Student Conceptions Used to Solve Chemical Equilibrium Problems

This study identified and quantified chemistry conceptions students use when solving chemical equilibrium problems requiring application of Le Chatelier's principle, and explored the feasibility of designing a paper and pencil test to accomplish these purposes. A 10-item pencil and paper, two-tier diagnostic instrument, the Test to Identify Student Conceptualizations (TISC), was developed and administered to 95 second-semester university general chemistry students after they received regular course instruction concerning equilibrium in homogeneous aqueous, heterogeneous aqueous, and homogeneous gaseous systems. To validate TISC, nine students from a stratified random sample were selected for interviews incorporating comparable chemistry problems. The probability that TISC correctly identified an answer given by a student in the interview was p = .64, whereas the probability that TISC correctly identified a reason given by a student in the interview was p = .49. Eleven prevalent incorrect student conceptions about chemical equilibrium were identified by TISC. Students consistently selected correct answers more frequently (53% of the time) than they provided correct reasons (33% of the time). The level of association between student answers and their respective reasons on each TISC item was quantified using conditional probabilities calculated from logistic regression coefficients. The Kuder-Richardson 20 reliability for TISC was .79. © 2000 John Wiley & Sons, Inc. J Res Sci Teach 37: 160–176, 2000

LeChatelier Effects for the Competitive Firm under Price Uncertainty

The intuition that constrained choices are less elastic as well as suboptimal is confirmed by LeChatelier's principle in economic models of optimizing behavior for environments with no uncertainty. For a competitive entrepreneurial firm facing output price uncertainty, risk preferences interact with possibilities for substituting between capital and labor in production to determine the presence or absence of LeChatelier effects for labor demanded. LeChatelier's principle holds without qualification for output supplied in the neighborhood of any long‐run equilibrium with respect to both monotone likelihood ratio improvements in the price distribution and increases in risk aversion. Global LeChatelier predictions, however, are unattainable.

Functional fixedness and functional reduction as common sense reasonings in chemical equilibrium and in geometry and polarity of molecules

Many of the learning difficulties in the specific domain of chemistry are found not only in the ideas already possessed by students but in the strategic and procedural knowledge that is characteristic of everyday thinking. These defects in procedural knowledge have been described as functional fixedness and functional reduction. This article assesses the procedural difficulties of students (grade 12 and first and third year of university) based on common sense reasoning in two areas of chemistry: chemical equilibrium and geometry and polarity of molecules. In the first area, the theme of external factors affecting equilibria (temperature and concentration change) was selected because the explanations given by the students could be analyzed easily. The existence of a functional fixedness where Le Chatelier's principle was almost exclusively applied by rote could be observed, with this being the cause of the incorrect responses given to the proposed items. Functional fixedness of the Lewis structure also led to an incorrect prediction of molecular geometry. When molecular geometry was correctly determined by the students, it seemed that other methodological or procedural difficulties appeared when the task was to determine molecular polarity. The students showed a tendency, in many cases, to reduce the factors affecting molecular polarity in two possible ways: (a) assuming that polarity depends only on shape (“geometric functional reduction”) or (b) assuming that molecular polarity depends only on the polarity of bonds (“bonding functional reduction”). © 2000 John Wiley & Sons, Inc. Sci Ed 84:545–565, 2000.

An error correction almost ideal demand system for meat in Greece

AbstractThis paper represents a dynamic specification of the Almost Ideal Demand System (AIDS) based on recent developments on cointegration techniques and error correction models. Based on Greek meat consumption data over the period 1958–1993, it was found that the proposed formulation performs well on both theoretical and statistical grounds, as the theoretical properties of homogeneity and symmetry are supported by the data and the LeChatelier principle holds. Regardless of the time horizon, beef and chicken may be considered as luxuries while mutton‐lamb and pork as necessities. In the short‐run, beef was found to have price elastic demand, pork an almost unitary elasticity, whereas mutton‐lamb, chicken and sausages had inelastic demands; in the long‐run, beef, and pork were found to have a demand elasticity greater than one, whereas mutton‐lamb, chicken, and sausages still had inelastic demands. All meat items are found to be substitutes to each other except chicken and mutton‐lamb, and pork and chicken.

LeChatelier Effects for the Competitive Firm under Price Uncertainty

LeChatelier effects confirm the intuition that constrained decisions are not only suboptimal but also restrained in the sense of being less elastic. Samuelson (1947) introduced this idea into economics and showed that it blends neatly with economic models of decision making under certainty, being particularly well suited to the competitive firm. As emphasized by Silberberg (1971), linearity of the objective function combines with convexity in the constraint, imposed by the production technology, to yield envelope results at the first order, and LeChatelier effects at the second, as powerful consequences of the maximization hypothesis. The envelope results of primary interest in producer theory, Shephard's Lemma for cost functions and Hotelling's Lemma for profit functions, are equality relations reflecting the firstorder stationarity of an optimum. LeChatelier effects, in contrast, are inequality relations reflecting the restrained nature of short-run responses compared with long-run, less constrained responses. Thus, the quantities of labor demanded and output supplied are more elastic with respect to wage rate and output price changes in the long run than in the short run. These LeChatelier predictions pertain to a firm that has fully adjusted to an exogenous set of factor and output prices and thus apply only in the neighborhood of a long-run equilibrium configuration for the firm. However, they apply equally well whether capital and labor are substitute or complementary factors of production. Milgrom and Roberts (1996) have established a global LeChatelier principle under the assumption that capital and labor are always substitutes, or always complements, in production, a stipulation that is necessarily true for the infinitesimal changes contemplated in the local LeChatelier predictions. When the firm makes decisions while facing uncertainty about output price, risk preferences influence behavior if the uncertainty cannot be fully diversified through futures contracts or the sale of ownership shares, as in the case of closely held family businesses, such as some of those

"Conceptual Questions" on LeChatelier's Principle

Three conceptual questions presented are designed to assess the student's ability to conceptualize chemical equilibrium and to predict the effect of changes made to a system at equilibrium, using...

Political, Economic and Military Evolution of Instability, North Korea, 1945-1998

Korea since 1945 revives Le Chatelier's principle: if conditions in a system initially at equilibrium are changed. the instability will shift towards renewed equilibrium. Here we examine the nature or changing conditions in the years since the origin of the 'mental blockade' of the years 1953 until 1972. when the two Koreas began discreet. preliminary negotiations. Reviwed are North Korea's quest for nuclear energy and the efforts of other interested parties to limit the concomitant acquisition of sufficient plutonium that would facilitate the manufacture and deployment of nuclear arms. Borrowing an analytical template from Fisher and Brown. we trace the slow return of equilibrium within a political stand-off (Fisher and Brown. 1989). [This paper should be read in parallel columns]

Pressure Transients in Gas Phase Adsorptive Reactors

The role of pressure and flow transients caused by strong adsorption on the behavior of gas phase adsorptive reactors was studied using a staged model. The general gas phase reaction A + B ⇌ C is considered for two cases: (1) the product C is adsorbed and (2) both reactants A and B are adsorbed. Strong adsorption of one or more components causes a decrease in the pressure(s) in the stage(s). The pressure decrease causes variations in the inlet and outlet flow rates and in the case of multiple stages, it causes variations in the flows between tanks. In accordance with Le Chatelier's principle, the pressure decrease aids or inhibits product formation depending on whether there is an increase or decrease in total moles by reaction. Reactant flow into the section where adsorption occurs increases because of increased pressure drop behind the adsorption front. However, the residence time of the reactants behind the adsorption front is lower because of the higher velocity. The flow variations can aid or hinder product formation depending on the specific conditions. Thus, the adsorption-caused pressure variations directly modify reaction rates and product concentrations and, also indirectly, by causing flow variations which affect reaction rates and product concentrations. This study highlights the need to include pressure variations when modeling gas phase adsorptive reactors if adsorption is strong irrespective of the net change in the total moles by reaction. It also demonstrates a method to incorporate axial pressure drop in staged models.

The use of ion-exchange resins for the recovery of valuable species from slurries of sparingly soluble solids

An example of an industrial process which recovers valuable species by shifting the solid/liquid dissociation equilibrium condition is the extraction of rare earths from low-grade kaolinite ore by percolation leaching. Valuable species can be recovered from such sparingly soluble solids which slightly dissociate to give traces of the valuable ions in solution, using ion-exchange resins in a slurry mixture. A dissociation equilibrium exists between the dissolved ions in solution and the solid ore. If the dissolved ions are removed from solution by ion-exchange, thus continually displacing the solid/liquid dissociation equilibritrin condition, further dissolution of the solid is required according to Le Chatelier's principle so as to restore the equilibrium concentration of the valuable species in solution. It is possible to recover valuable metals from sparingly soluble solids, such as metal sulphates, by contacting a slurry of the solid with an ion-exchange resin. As a result of the ion-exchange that takes place, electrolyte solutions are created which facilitate the dissolution process and hence the overall extraction process by changing the activities of the species in solution. Complete dissolution of the solid, hence complete liberation of the valuable metal species, can be achieved provided that a sufficient amount of ion-exchanger is used. The extraction of base metal sulphates was used as a case study.

A quantum molecular similarity analysis of changes in molecular electron density caused by basis set flotation and electric field application

Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed.

Cation disorder and gas phase equilibrium in an YBa 2Cu 3O 7− x superconducting thin film

YBa 2Cu 3O 7− x superconducting thin films have been grown by in situ off-axis rf sputtering with varying oxygen pressure, Ba/Y ratio in a target, and deposition temperature. With decreasing oxygen pressure, increasing Ba/Y ratio, increasing deposition temperature, the critical temperature of the thin films decreased and the c-axis length increased. The property change of films with the variation of deposition variables has been explained by a gas phase equilibrium of the oxidation reaction of Ba and Y. Applying Le Chatelier's principle to the oxidation reaction, we were able to predict the relation of deposition variables and the resultant properties of thin films; the prediction was in good agreement with the experimental results. From the relation between the three deposition variables and gas phase equilibrium, a 3-dimensional processing diagram was introduced. This diagram has shown that the optimum deposition condition of YBa 2Cu 3O 7− x thin films is not a fixed point but can be varied. The gas phase equilibrium can also be applied to the explanation of previous results that good quality films were obtained at low deposition temperature using active species, such as O, O 3, and O 2+.

Polysoaps: Extension and Compression

Intramolecular self-assembly in polysoaps qualitatively modifies their deformation behavior. The modified elasticity reflects the coupling of the chain deformation to the internal degrees of freedom associated with the existence of intrachain micelles. The equilibration of this secondary structure tends to lower the restoring force associated with the deformation in accordance with the LeChatelier principle. The force laws for extension and for confinement into a slit are derived for the case of a linear string of spherical intrachain micelles. In both situations the chain behaves as a string of stars for weak deformations. Force laws characteristic of simple linear chains are obtained for strong deformations. Novel force laws, reflecting strong coupling to the secondary structure, are obtained at the intermediate regime. For intermediate extensions, the tension in the chain, f, is independent of R, the end to end distance, up to logarithmic corrections, i.e., f ∼ Ro ln g(R), where g(R) is a slowly increa...

The Theory of Thermodynamics for Chemical Reactions in Dispersed Heterogeneous Systems

In this paper, the expressions of Gibbs energy change, enthalpy change, entropy change, and equilibrium constant for chemical reactions in dispersed heterogeneous systems are derived using classical thermodynamics theory. The thermodynamical relations for the same reaction system between the dispersed and the block state are also derived. The effects of degree of dispersion on thermodynamical properties, reaction directions, and chemical equilibria are discussed. The results show that the present equation of thermodynamics for chemical reactions is only a special case of the above-mentioned formulas and that the effect of the dispersity of a heterogeneous system on the chemical reaction obeys the Le Chatelier principle of movement of equilibria.

Decreasing electrical conductivity of irrigation water by dilution

Although 750 μ mho/cm is the limit for the electrical conductivity (EC) in the “Standard of Taiwan Irrigation Water Quality,”; the EC of irrigation water is usually over limit, resulted from the pollution dumped into the rivers, streams, and creeks. It will be a damage to agricultural crop using polluted irrigation water. The basic principle of dilution can neutralize high EC of polluted water using pure or low EC water. With the increasing quantity of clean water, the polluted water will drop its EC to a certain extent. Therefore, the purpose of this study is to determine the relationship between dilute water quantity and its EC. As results shown in this study, pure water or water of low EC mixing with water of high EC can be a basic principle for diluting. The practical principle can be used in the farms and the results meet the irrigation water standard. Moreover, the better quality of dilute water is, the less its quantity is; the worse the quality the more the quantity is. Furthermore, the electrolyte effect and the principle of Le Chatelier in aquatic chemistry are resulted in solubility of salt and EC of mixed water solution increase. All the precipitation, coagulation, and flocculation will decrease free ions’ content and EC in mixed water solution.

Technological progress and optimal factor demand

This paper analyzes the employment and investment demands of the competitive firm when technological progress embodied in new investment goods is a source of productivity improvements. It is shown that technological progress reduces the implicit cost of capital services as well as its sensitivity to variations in the price system. Several versions of LeChatelier's principle are established showing how technological progress modifies the price sensitivity of the factor demands. Rapid technological progress makes the factor demands less sensitive to price variations. However employment demand becomes less (more) sensitive to interest rate changes when capital and labor are complements (substitutes).

On the extension of polysoaps: The Gaussian approximation

AbstractPolysoaps are linear hydrophilic chains that incorporate, at intervals, covalently bound amphiphilic monomers. In water, the amphiphilic monomers self assemble into intrachain micelles thus endowing the chain with a secondary structure. The relaxation of the secondary structure upon deformation qualitatively modifies the elastic behaviour of polysoaps in accordance with the LeChatelier principle. For long polysoaps a regime in which the tension in the chain, f, is independent of the end to end distance R, f ˜ R° is predicted. The extension of long polysoaps is analysed for the particularly simple case when the backbone obeys Gaussian statistics and excluded volume interactions are neglected.

Molecular dynamics and reaction kinetics during the network structure formation of a diepoxide and diamine mixture under high pressures using dielectric measurements

The dielectric relaxation behaviour of a stoichiometric mixture of ethylene diamine and a diepoxide in which addition reactions produce a polymeric network structure has been studied at isobaric conditions of pressure from 1 to 206 bar and several temperatures from 296 to 314 K. The changes occur faster at high pressure, and the curves of the relative permittivity and loss against the polymerization time, which resemble the corresponding dielectric spectra, shift to a shorter time. This effect is due to an increase in the rate of reaction, and attributed to the mass-controlled reaction kinetics in the region of the polymerization, because the rate of reaction is expected to be slowed by application of pressure when the reaction is in the diffusion-controlled region. The rapid increase in the relaxation time with the polymerization time at high pressures is a consequence of: (a) the acceleration of the reaction kinetics, (b) an increase in the equilibrium constant of the polymerization according to Le Chatelier's principle and (c) a decrease in the configurational entropy. An attempt is made to resolve the magnitude of these effects. A formalism for the changes in the relaxation time and dc conductivity, which includes the change in the chemical as well as physical states of the polymerizing liquid, is given, and the decrease in the configurational entropy formulated in terms of the pressure's effect on the relaxation time. The rate of decrease in the static permittivity on polymerization is increased by the pressure. The polymerization characteristics of this network polymer under hydrostatic pressure are compared with those of the linear-chain polymerization of a stoichiometric mixture of a diepoxide with a monoamine.

An Optimum Transportation Program for Northeast China Using Tumen Area Sea Ports: An Assessment of International Cooperation in the Spirit of Le Chatelier Principle

An Optimum Transportation Program for Northeast China Using Tumen Area Sea Ports: An Assessment of International Cooperation in the Spirit of Le Chatelier Principle