Le Chatelier's Principle Research Articles

LeChatelier dynamics†

Dynamics of the relaxation of a perturbed thermodynamic system to equilibrium is determined by the generalised eigenvalue equation . Here S αβ is a matrix of linear response coefficients and is a matrix of kinetic coefficients. We describe LeChatelier's Principle and both its static and dynamical symmetries, and treat cases in which there are multiple relaxation channels. The treatment simplifies when the relaxation channels have widely separated time scales. † Note: This paper is part of the Levine special issue published in Volume 106 (2–4) of the journal.

Modeling of hydrodynamic cavitation reactors based on orifice plates considering hydrodynamics and chemical reactions occurring in bubble

In the present work, a model has been developed for predicting the cavitational intensity in a hydrodynamic cavitation reactor based on the use of orifice plates considering the hydrodynamic conditions and the different chemical reactions taking place inside the cavity. The model is based on a set of ordinary differential equations and considers the bubble hydrodynamics and heat exchange including the phase change. It also accounts for the chemical reactions of the various gaseous species in the air–water system and diffusion/dissolution of the reaction products from the cavity. Weber number criterion has been incorporated for the stability of the growing bubble. During rapid bubble collapse a large amount of water vapor is trapped inside the bubble, resulting in an increased heat capacity and endothermic chemical reactions leading to lower temperatures at the end of the collapsing event. Analyzing the reaction thermodynamics within the dense, collapsed bubble, it can be said that the effect of excluded volume of the non-ideal gas results in pronounced suppression of the molecule-producing endothermic reactions using Le-Chatelier's principle. Design correlation in terms of cavitational intensity (in terms of collapse pressure and temperatures) and cavitational yield (in terms of OH radicals) aims at understanding the design information related to the dependency of the cavitational intensity and the radical yield on the operating parameters in the case of the hydrodynamic cavitation.

Conceitos de química dos ingressantes nos cursos de graduação do Instituto de Química da Universidade de São Paulo

A diagnostic instrument was developed to evaluate the basic chemistry concepts held by freshmen students of the three Chemistry undergraduate courses offered by the University of Sao Paulo. The instrument minimizes the use of algorithms or memorization by students and values high-order cognitive skills. Analysis of the students' performances reveals systematic use of displacement as an algorithm and a mechanical use of Le Chatelier's Principle. Failure in comprehending the chemical equation and chemical language drives students to alternative models for chemical reactions in aqueous solution. For instance, reaction would occur between ionic pairs and/or between species situated in separate compartments.

Nearly Isostructural Polymorphs of Ethynylbenzene: Resolution of ⋮CH···π(arene) and Cooperative ⋮CH···π(C⋮C) Interactions by Pressure Freezing

In ethynylbenzene, elevated pressure favors cooperative ⋮CH···π(C⋮C) hydrogen bonds compared to ⋮CH···π(arene) and leads to the ordered polymorph nearly isostructural form with the crystals frozen by cooling. The high-pressure polymorph is more resistant to polymerization than the liquid and, in this respect, is a manifestation of Le Chatelier principle explained at the microscopic level for this compound. A new type of the polymorphic relation has been described.

Mixed sites and promoter segregation: A DFT study of the manifestation of Le Chatelier's principle for the Co(Ni)MoS active phase in reaction conditions

The phase diagrams and equilibrium 2D-morphologies of Co(Ni)MoS nano-crystallites with various promoter contents are determined by periodic DFT calculations coupled to a thermodynamic model. The edge energies of the crystallite depend on two key parameters: the chemical potential of sulfur (Δ μ S), representing the sulfo-reductive conditions of the gas phase, and the number and distribution of promoter atoms at the edges. High values of Δ μ S, corresponding to strongly sulfiding conditions, stabilize edges with a full promoter content. At very low values of Δ μ S, i.e. strongly reductive environment, the mixed Co(Ni)MoS active phase is destabilized with respect to MoS 2 due to the total segregation of promoter atoms to the edges. For intermediate Δ μ S, including industrial HDS conditions, it is found that the M-edge is partially decorated by Co and Ni, and that the S-edge is partially decorated by Ni. The existence of mixed Co–Mo or Ni–Mo edge sites is thus thermodynamically possible. The Gibbs–Curie–Wulff equilibrium morphologies depend on the type of promoter. These quantitative DFT results are consistent with Le Chatelier's principle and are crucial to understand the thermodynamic balance between the active phase and the reaction conditions impacting the nature of active edge sites.

Kinetic Analysis of Volatile Formation in Milk Subjected to Pressure‐Assisted Thermal Treatments

Volatile formation in milk subjected to pressure-assisted thermal processing (PATP) was investigated from a reaction kinetic analysis point of view to illustrate the advantages of this technology. The concentration of 27 volatiles of different chemical class in milk subjected to pressure, temperature, and time treatments was fitted to zero-, 1st-, and 2nd-order chemical reaction models. Temperature and pressure effects on rate constants were analyzed to obtain activation energy (E(a)) and activation volume (deltaV*) values. Hexanal, heptanal, octanal, nonanal, and decanal followed 1st-order kinetics with rate constants characterized by E(a) values decreasing with pressure reflecting negative deltaV* values. Formation of 2-methylpropanal, 2,3-butanedione, and hydrogen sulfide followed zero-order kinetics with rate constants increasing with temperature but with unclear pressure effects. E(a) values for 2-methylpropanal and 2,3-butanedione increased with pressure, that is, deltaV* > 0, whereas values for hydrogen sulfide remained constant, that is, deltaV* = 0. The concentration of all other volatiles, including methanethiol, remained unchanged in pressure-treated samples, suggesting large negative deltaV* values. The concentration of methyl ketones, including 2-pentanone, 2-hexanone, 2-heptanone, 2-octanone, 2-nonanone, 2-decanone, and 2-undecanone, was independent of pressure and pressure-holding time. PATP promoted the formation of few compounds, had no effect on some, and inhibited the formation of volatiles reported to be factors of the consumer rejection of "cooked" milk flavor. The kinetic behavior observed suggested that new reaction formation mechanisms were not likely involved in volatile formation in PATP milk. The application of the Le Chatelier principle frequently used to explain the high quality of pressure-treated foods, often with no supporting experimental evidence, was not necessary.

Economics of the Mortgage and Mortgage Institutions: Differences between Civil Law and Common Law Approaches

We examine the history of U.S. mortgage as a means of illustrating the influence of different aspects of the U.S. common law system on financial development. We hypothesize that the value of common law to financial development is with respect to the flexibility that the system provides market participants as they attempt to respond to shocks. This is in contrast to civil law, which tends to specify particular contracts as admissible. The model is an application of the Le Chatelier Principle, which suggests that adding constraints to system makes it's responses less elastic. We consider a special case of restrictions on mortgage type (fixed vs adjustable rate) to illustrate the principle.

The scope of the LeChatelier Principle

LeChatelier [Comptes Rendus 99 (1884) 786; Ann. Mines 13 (2) (1888) 157] showed that a physical system's “adjustment” to a disturbance to its equilibrium tended to be smaller as constraints were added to the adjustment process. Samuelson [Foundations of Economic Analysis, Harvard University Press, Cambridge, 1947] applied this result to economics in the context of the comparative statics of the actions of individual agents characterized as the solutions to optimization problems; and later (1960), extended the application of the Principle to a stable, multi-market equilibrium and the case of all commodities gross substitutes [e.g., L. Metzler, Stability of multiple markets: the hicks conditions. Econometrica 13 (1945) 277–292]. Refinements and alternative routes of derivation have appeared in the literature since then, e.g., Silberberg [The LeChatelier Principle as a corollary to a generalized envelope theorem, J. Econ. Theory 3 (1971) 146–155; A revision of comparative statics methodology in economics, or, how to do comparative statics on the back of an envelope, J. Econ. Theory 7 (1974) 159–172], Milgrom and Roberts [The LeChatelier Principle, Am. Econ. Rev. 86 (1996) 173–179], W. Suen, E. Silberberg, P. Tseng [The LeChatelier Principle: the long and the short of it, Econ. Theory 16 (2000) 471–476], and Chavas [A global analysis of constrained behavior: the LeChatelier Principle ‘in the large’, South. Econ. J. 72 (3) (2006) 627–644]. In this paper, we expand the scope of the Principle in various ways keyed to Samuelson's proposed means of testing comparative statics results (optimization, stability, and qualitative analysis). In the optimization framework, we show that the converse LeChatelier Principle also can be found in constrained optimization problems and for not initially “conjugate” sensitivities. We then show how the Principle and its converse can be found through the qualitative analysis of any linear system. In these terms, the Principle and its converse also may be found in the same system at the same time with respect to the imposition of the same constraint. Based upon this, we expand the cases for which the Principle can be found based upon the stability hypothesis.

The Comparative Statics of Constrained Optimization Problems

This paper develops and applies some new results in the theory of monotone comparative statics. Let f be a real-valued function defined on R l and consider the problem of maximizing f(x) when x is constrained to lie in some subset C of R'. We develop a natural way to order the constraint sets C and find the corresponding restrictions on the objective function f that guarantee that optimal solutions increase with the constraint set. We apply our techniques to problems in consumer, producer, and portfolio theory. We also use them to generalize Rybcsynski's theorem and the LeChatelier principle.

A thermodynamic theory of economics

An analogy between thermodynamic and economic theories is developed further, following a previous paper published by the author in 1982. Economic equivalents are set out concerning the ideal gas equation, pressure, temperature, entropy, 1st and 2nd Laws of Thermodynamics and the Le Chatelier Principle. Links to utility, the Law of Diminishing Marginal Utility and the Cobb Douglas function are developed. A trade cycle is constructed, based on the Joule Cycle, with equations for cycle efficiency, growth and entropy gain. A thermodynamic model of a money system is developed. Aspects concerning the measurement of economic value in thermodynamic terms are discussed.

Weak polyelectrolytes tethered to surfaces: Effect of geometry, acid–base equilibrium and electrical permittivity

AbstractThe structural and thermodynamical properties of weak polyelectrolytes end‐tethered to surfaces of arbitrary geometry are studied using a molecular theory. The theory is based on writing down the free energy functional of the system including all the basic interactions and the explicit acid–base equilibrium for the chargeable groups of the polymer. The theory explicitly includes the size, shape, conformations, and charge distribution of all the molecular species. The electrostatic interactions include a density‐dependent dielectric function, modeled with the Maxwell–Garnett mixing formula, to account for the composition‐dependent permittivity. The minimization of the free energy leads to the distribution of all molecular species and their dependence on bulk pH and salt concentration. We apply the theory to polymer chains end‐tethered to planar, cylindrical, and spherical surfaces. The radius of the curved surfaces is small to enhance the curvature effect. We find that when the grafting surfaces are uncharged, the approximation of a constant dielectric function works very well for both structural and thermodynamic properties. The structure of weak polyelectrolytes tethered on cylindrical and spherical surfaces is different from that of polymers tethered on planar surfaces due to the available volume as a function of the distance from the surface. Specifically, the degree of dissociation increases with increasing curvature of the surface. This is a manifestation of the coupling between the local density of protons, counterions, and polymer segments. The results can be interpreted in terms of the local Le Chatelier principle for the acid–base equilibrium, with proper account of the three local contributions: counterions, protons, and chargeable groups. We find that one can achieve local changes of pH between one to two units within 1–2 nm. The thickness of the tethered layers as a function of bulk pH shows a large increase when the pH is equal to the bulk pK. However, the variation with salt concentration is different for the different geometries. The largest swelling is found for cylindrical surfaces. The predictions from scaling theories of a maximum in the thickness of the film as a function of salt concentration is found for planar films, but not for curved surfaces. Finally, the interactions between cylinders with tethered polyelectrolytes is very different from the equivalent planar surfaces. These results are important for the interpretation of force measurements with nanoscale AFM tips. The implications of the results for the rational design of responsive tethered polymer layers is discussed together with the limitations of the theoretical approach. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2638–2662, 2006

The “Le Chatelier's Principle”-Governed Response of Actin Filaments to Osmotic Stress

Actin filaments inhibit osmotic stress-driven water flow across a semipermeable membrane in proportion to the filament concentration (Ito, T.; Zaner, K. S.; Stossel, T. P. Biophys. J. 1987, 51, 745). When the filaments are cross-linked by F-actin binding protein, filamin A, this flow is stopped completely (Ito, T.; Suzuki, A.; Stossel, T. P. Biophys. J. 1992, 61, 1301). No conventional theory accurately accounts for these results. Here, this response is analyzed by formulating the entropy of the system under osmotic stress. Results demonstrate that the response of the actin filaments to osmotic stress is governed by the Le Chatelier's principle, which states that an external interaction that disturbs the equilibrium brings about processes in the body that tend to reduce the effects of this interaction. In the present case, disrupting equilibrium by osmotic stress brings about a reaction that decreases the chemical potential of water in the F-actin solution, reducing the effect of the applied osmotic disturbance. This decrease in the chemical potential of the water in the F-actin solution is caused by an increase in the chemical potential of F-actin, which is induced by isothermal absorption of heat by F-actin aided by work done by osmotic stress. As a result, F-actin has an inhibitory effect on the osmotic stress-driven water flow, and can even completely stop the flow when it is cross-linked. This is the first report demonstrating that the Le Chatelier's principle applies to the reaction of biopolymers against equilibrium disturbances such as osmotic stress.

Undergraduate Pre-Service Teachers' Understandings and Misconceptions of Phase Equilibrium

This study aimed to reveal pre-service chemistry teachers' misunderstandings in phase equilibrium. An open-ended test was developed in the light of the findings obtained from the related literature, interviews with instructors and investigation of physical chemistry course examination papers belonging to the last three educational years. The instrument was administered to 59 pre-service chemistry teachers in the Faculty of Education in a public university in Turkey. Eighteen misunderstandings were identified through analysis of the answers. The results indicated that some misunderstandings originated from a misuse of Le Chatelier's principle and the ideal gas law. Other reasons for the misunderstandings were incorrect interpretation of graphs and inappropriate generalizations of facts or formulae.

Equilibrium econophysics: A unified formalism for neoclassical economics and equilibrium thermodynamics

We develop a unified conceptual and mathematical structure for equilibrium econophysics, i.e., the use of concepts and tools of equilibrium thermodynamics in neoclassical microeconomics and vice versa. Within this conceptual structure the results obtained in microeconomic theory are: (1) the definition of irreversibility in economic behavior; (2) the clarification that the Engel curve and the offer curve are not descriptions of real processes dictated by the maximization of utility at constant endowment; (3) the derivation of a relation between elasticities proving that economic elasticities are not all independent; (4) the proof that Giffen goods do not exist in a stable equilibrium; (5) the derivation that ‘economic integrability’ is equivalent to the generalized Le Chatelier principle and (6) the definition of a first order phase transition, i.e., a transition between separate points in the utility function. In thermodynamics the results obtained are: (1) a relation between the non-dimensional isothermal and adiabatic compressibilities and the increase or decrease in the thermodynamic potentials; (2) the distinction between mathematical integrability and optimization behavior and (3) the generalization of the Clapeyron equation.

Response Reactions: Equilibrium Coupling

It is pointed out and illustrated in the present paper that if a homogeneous multiple equilibrium system containing k components and q species is composed of the reactants actually taken and their reactions contain only k + 1 species, then we have a unique representation with (q - k) stoichiometrically independent reactions (SIRs). We define these as coupling reactions. All the other possible combinations with k + 1 species are the coupled reactions that are in equilibrium when the (q - k) SIRs are in equilibrium. The response of the equilibrium state for perturbation is determined by the coupling and coupled equilibria. Depending on the circumstances and the actual thermodynamic data, the effect of coupled equilibria may overtake the effect of the coupling ones, leading to phenomena that are in apparent contradiction with Le Chatelier's principle.

Room temperature hydrogen response kinetics of nano–micro-integrated doped tin oxide sensor

The nano–micro-integrated sensor has been fabricated by sol–gel depositing the nanocrystalline indium oxide (In 2O 3)-doped tin oxide (SnO 2) thin film on microelectromechanical systems (MEMS) device having interdigitated electrode configurations with two different electrode spacing (10 μm and 20 μm) and two different number of fingers (8 and 20). The present nano–micro-integrated sensor exhibits high H 2 sensitivity range ( S = 3–10 5) for the H 2 concentration within the range of 100–15,000 ppm at room temperature. It has been demonstrated that, the room temperature response kinetics of the present nano–micro-integrated sensor is a function of finger spacing, H 2 concentration and air-pressure, but independent of number of fingers. Such dependence has been explained on the basis of Le Chatelier's principle applied to the associated H 2 sensing mechanism and the role of above parameters in shifting the dynamic equilibrium of the involved surface reactions under the described test conditions. A new definition of the response time has been proposed, which is not only suitable for the theoretical analysis but also for the practical applications, where a gas-leak detection alarm is required to be triggered.

Coping with uncertainty and stress: a parallel computation approach

This paper is concerned with computations whose characteristics are akin to certain unique phenomena that occur in different domains of science. We are particularly interested in systems whose parameters are altered unpredictably whenever one of these parameters is measured or modified. Examples of such computational environments include those in which Heisenberg's uncertainty principle of quantum physics is witnessed, or those in which Le Chatelier's principle of chemical systems under stress manifests itself. A study of these systems uncovers computations that are inherently parallel in the strong sense, meaning that they are efficiently executed in parallel, but impossible to carry out sequentially.

A Global Analysis of Constrained Behavior: The LeChatelier Principle “in the Large”

New global results are obtained on the LeChatelier‐Samuelson principle reflecting the properties of constrained behavior. Relying on the saddle point characterization of the Lagrangean, simple yet powerful LeChatelier results are derived and investigated under general conditions. The results do not require differentiability assumptions or unique solution, and they hold for discrete changes. The usefulness of the approach is illustrated in several applications, showing how the analysis generates insights into global economic adjustments.

A Global Analysis of Constrained Behavior: The LeChatelier Principle "In the Large"

New global results are obtained on the LeChatelier-Samuelson principle reflecting the properties of constrained behavior. Relying on the saddle point characterization of the Lagrangean, simple yet powerful LeChatelier results are derived and investigated under general conditions. The results do not require differentiability assumptions or unique solution, and they hold for discrete changes. The usefulness of the approach is illustrated in several applications, showing how the analysis generates insights into global economic adjustments.

Anion hopping of (and on) functional oligoarginines: from chloroform to cells.

Rapid progress in the understanding of counteranions as either activators or inactivators of guanidinium-rich macromolecules is summarized. From phase transfer of polyarginine into chloroform to the cytosolic delivery of green-fluorescent proteins or apoptosis-inducing peptides with cell-penetrating peptides, counteranions emerge consistently as the origin of function. A unified view of this "demystified arginine magic" is proposed, focusing on the manipulation of the underlying anion hopping of and on these sticky molecular chameleons according to the principle of Le Chatelier.