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An educational lattice model is proposed for the investigation of the influence of the density and indirectly of thepressure on the chemical equilibrium of the ideal gas phase reaction A???2B. The model can be introduced by a board gamesimulating a stochastic process. This game can also be used to set up a corresponding computer algorithm. The solutions of thismodel by stochastic simulations are compared to the analytical solutions for the equilibrium state and to the numerical solution ofthe corresponding differential equation. It is the aim of this approach to introduce examples of the scientific method of simulation atan early stage of chemical education such as secondary education using a simple model. It furthermore allows students to deepentheir understanding of chemical equilibria and the Le Cha??telier density as well as pressure effect on the equilibrium at that level.

Paper chromatography is a simple and harmless experiment suitable for lower secondary education. Besides the training of subject-specific contents, paper chromatography allows the application of modelling and simulation since the submicroscopic processes can be simplified in a way that they become understandable in lower secondary education. Here, the application of digital tools in addition to the experimental performance of paper chromatography in a compulsory STEM course in grade 6 is reported. Following a series of experiments, chromatography is at first simulated by a board game and then by computer simulations. Such simulation program allows the variation of the parameters in order to explore the model and to introduce the particle concept of matter and molecular interactions. The implementation with a graphical programming environment such as Scratch also allows the programming by pupils in this age group. In this way, it is possible to introduce modelling and simulation in an early stage as important contributions to scientific work in natural sciences.

These days, theoretical methods and simulations are widely spread in chemical science. However, in secondary and introductory chemistry, students learn little or nothing about such approaches. To introduce simulations at this educational level it is necessary to identify suitable chemical problems and simulation methods that allow setting up concise computer codes. In addition, it is useful to implement simulations in topics which are already part of the regular chemistry curricula. Here, we employ the Arrhenius equation in combination with a simple stochastic simulation method to illustrate how computer simulations can be used in chemistry to get insights in the temperature dependence of the reaction rate constant. The basis for the simulation is a board game, which puts the students in the position to elaborate the mathematical equations for the modeling of kinetics themselves in a playful manner. Such simulation allows students to establish a connection between the reacting system and the particle model. Furthermore, freely available educational programming software makes it possible for students to write their own simulation program based on the game within limited time and effort.

Today quantum mechanics plays a significant role in chemistry. Program packages are available that allow quantum mechanical calculations in many areas of chemistry as well as material and engineering science. Doubtless quantum mechanics is part of university education, nevertheless, it is possible to teach the main features in the final year of high school chemistry. Here, one can merely focus on the principles related to topics which are already part of the curricula. The model of a particle in a one dimensional box discussed here is taught in German high school physics with a different focus but on a similar level and hence pupils are in principle not overtaxed by this topic. This model relatively simply allows to present the basic features of quantum mechanics and it is approximately applicable to linear and cyclic pi electron systems. The major approximation is that the potential energy in the box is zero while the potential energy of the atoms in actually given by a periodic Coulomb potential. The approximation employed here aims on the application of the simple model, that itself is solved exactly, to more complex molecules. Deviations in the electron distribution between the box potential and the periodic Coulomb potential are discussed.

Vapor-liquid nucleation in the binary system n-nonane/methane is investigated by molecular dynamics simulation. The supersaturation is achieved by cooling down the system during the expansion in order to closely mimic the real process. Binary clusters formed by nucleation are frequently inhomogeneous objects in which components are not well mixed. By studying high-pressure nucleation and cluster growth in the n-nonane/methane mixture, we demonstrate the role of structuring effects in these processes. At typical simulation conditions-pressure 60 bar, temperature 240 K, and nucleation rate similar to 10(26) cm (3)s (1)-the mole fraction of methane in the critical cluster reaches 80 percent, which is much higher than its equilibrium value in the bulk liquid at the same pressure and temperature. These observations are supported by the recently formulated coarse-grained theory for binary nucleation as well as by the experimental observations. (c) 2014 AIP Publishing LLC.

The poor dissolution behaviour of solid drugs in biological environment leads to a low bioavailability. However, the dissolution rate of such drugs can be enhanced dramatically by reduction of the particle size. At present, supercritical fluid based particle size reduction processes are gaining in importance in pharmaceutical technology. For the design of such particle formation processes and the determination of their best operating conditions the knowledge of phase equilibrium and solute solubility in a supercritical fluid is essential. Today, models based on equations of state, together with different mixing rules, are most widely used to correlate and predict the solubility in supercritical fluids. Therefore the accurate knowledge of the required solute data, such as critical parameters, acentric factor, solid molar volume, and sublimation pressure of the solutes is essential. However, the common, non-equation of state based group-contribution methods are mostly empirical and often lead to inconsistent and unreliable results. Thus, due to the lack of information on these data, density-based models are often used for the correlation of experimental solubility data. In this investigation, the solubility of Salicylic acid, of S-Naproxen, of RS-Ibuprofen and of Phytosterol in CO2 is correlated by different methods: two methods for the pressure-solubility correlation and two methods for the density-solubility correlation. In addition, the influence of solute data predicted by different group-contribution methods is investigated. With the exception of S-Naproxen all systems investigated can be modelled sufficient well with a non-cubic equation of state while a cubic equation of state gives less accurate results. In addition, it is shown that for the solutes investigated, the equation of state based method is very sensitive to the values of the sublimation pressure. (C) 2010 Elsevier B.V. All rights reserved.

The formation of pharmaceutical particles by the rapid expansion of a supercritical solution is investigated by molecular dynamics simulation. As a pharmaceutical model substance naproxen, a pain reliever and anti-inflammatory drug, is used. The expansion process is modeled in the simulation method by stepwise increasing the size of the simulation box. Comparison with an accurate reference equation of state for the pure solvent carbon dioxide shows that the simulation system follows an adiabatic expansion path. The expansion of a solution of naproxen in supercritical carbon dioxide leads to a highly supersaturated system that starts to form particles. The nucleation and growth kinetics of this particle formation process is investigated and the effect on the particle structure is analyzed. (C) 2010 Elsevier B.V. All rights reserved.

While quantum chemistry is the standard model for treating a chemical bond in chemical science for about one hundred years, its application in secondary education is still limited. Especially the introduction of wave properties of matter is often neglected. The complexity of this topic makes it necessary to treat it exemplary. Simple models with infinitely high potential walls and vanishing potential energy inside can serve as suggestion for teachers to teach the subject. The mathematical modeling is restricted to the sinus function and therefore suitable for the upper secondary level. The foundation of bond formation is the interference of electronic wave functions taking place when waves come close as atoms approach. Interference then leads to a redistribution of the charge. In case, this redistribution takes up more space than available before, the kinetic energy decreases. In addition, the redistribution of the charge leads to changes in the potential energy. This is the background for a series of rules and effects in high school chemistry that are often introduced without relation to each other. Even though the topic is rather located in upper secondary education, in middle secondary education the wave property of matter can be introduced phenomenologically equivalent to particle properties in a preparatory manner.

The observation that high school students often do not recognize the contributions of other subjects such as applied mathematics or informatics to chemistry may be countered by introducing appropriate mathematical modelling in chemistry class. It should be focused on topics which are typically part of the regular curricula. Here chemical kinetics is employed within the introduction of the nucleophilic substitution as an example allowing conjunctions to mathematics and informatics. In this context, kinetics is deepened by quantitative considerations as well as simulations. The time laws for the kinetics of first and second order are derived using mathematical methods that are typically included in present mathematics curricula. In addition, two quantitatively analyzable model experiments can be used to allow a playfully understanding of the differential equations and their solutions. Furthermore, these model experiments can be transformed into concise computer algorithms. In this way, students learn the different methods experiment, analytical derivation, and simulation for gaining chemical knowledge.

In high school and beyond students regard the subjects often isolated from each other. In contrast, every subject always requires contributions from other subjects. The subject chemistry requires, besides others, mathematical skills. In order to illustrate the relation between chemistry and applied mathematics the principles of mathematical modelling can already be introduced in high school. Here a practical example is employed to show how it is possible to simulate a standard experiment in high school chemistry, namely the titration of monoprotic strong and weak acids with a strong base. The mathematical derivation is merely based on mathematical skills, which are typically taught in 9th grade. The topic fits well in the chemistry curricula as a deepening. This approach of implementing mathematics in chemistry also aims to counteract the possible estrangement of the high school subject chemistry from the university subject chemistry. The mathematical derivations are detailed with focus on the traceability and should be adjusted for application in high school. The way of deriving the equations also allows to teach general methods of mathematical modelling in natural science.

The observation that high school students often do not recognize the contributions of other subjects such as applied mathematics or informatics to chemistry may be countered by introducing appropriate mathematical modelling in chemistry class. It should be focused on topics which are typically part of the regular curricula. Here chemical kinetics is employed within the introduction of the nucleophilic substitution as an example allowing conjunctions to mathematics and informatics. In this context, kinetics is deepened by quantitative considerations as well as simulations. The time laws for the kinetics of first and second order are derived using mathematical methods that are typically included in present mathematics curricula. In addition, two quantitatively analyzable model experiments can be used to allow a playfully understanding of the differential equations and their solutions. Furthermore, these model experiments can be transformed into concise computer algorithms. In this way, students learn the different methods experiment, analytical derivation, and simulation for gaining chemical knowledge.

In high school and beyond students regard the subjects often isolated from each other. In contrast, every subject always requires contributions from other subjects. The subject chemistry requires, besides others, mathematical skills. In order to illustrate the relation between chemistry and applied mathematics the principles of mathematical modelling can already be introduced in high school. Here a practical example is employed to show how it is possible to simulate a standard experiment in high school chemistry, namely the titration of monoprotic strong and weak acids with a strong base. The mathematical derivation is merely based on mathematical skills, which are typically taught in 9th grade. The topic fits well in the chemistry curricula as a deepening. This approach of implementing mathematics in chemistry also aims to counteract the possible estrangement of the high school subject chemistry from the university subject chemistry. The mathematical derivations are detailed with focus on the traceability and should be adjusted for application in high school. The way of deriving the equations also allows to teach general methods of mathematical modelling in natural science.

While quantum chemistry is the standard model for treating a chemical bond in chemical science for about one hundred years, its application in secondary education is still limited. Especially the introduction of wave properties of matter is often neglected. The complexity of this topic makes it necessary to treat it exemplary. Simple models with infinitely high potential walls and vanishing potential energy inside can serve as suggestion for teachers to teach the subject. The mathematical modeling is restricted to the sinus function and therefore suitable for the upper secondary level. The foundation of bond formation is the interference of electronic wave functions taking place when waves come close as atoms approach. Interference then leads to a redistribution of the charge. In case, this redistribution takes up more space than available before, the kinetic energy decreases. In addition, the redistribution of the charge leads to changes in the potential energy. This is the background for a series of rules and effects in high school chemistry that are often introduced without relation to each other. Even though the topic is rather located in upper secondary education, in middle secondary education the wave property of matter can be introduced phenomenologically equivalent to particle properties in a preparatory manner.