What can student-generated diagrams tell us about their understanding of chemical equations?

Chemical equations are representations that use symbols to summarise the net changes occurring in a reaction whereas depictions such as drawings of the submicroscopic level provide representations of the chemical transformations. While the ability to balance and interpret chemical equations is key to understanding many concepts in chemistry, many undergraduate chemistry students struggle to master these skills. The equations contain a great deal of implicit information and novices may not be able to make the connection between the equation and the actual chemical transformations that are occurring. This paper reports on a study which used submicroscopic diagrams to probe students' understanding of chemical equations. Assessment tasks required students to interpret diagrams, construct diagrams and to relate diagrams to symbolic representations. The analysis showed that some students have misconceptions about the molecular nature and chemical formulae and could not distinguish between coefficients and subscripts when representing chemical formulae. While students were generally able to balance a chemical equation presented as a set of diagrams, a significant number could not generate the balanced equation based on a diagram of the progress of a reaction, The study has demonstrated the use of student-generated diagrams to provide insight into students' understandings of chemical equations.

Student-generated submicro diagrams : a useful tool for teaching and learning chemical equations and stoichiometry

This paper reports on a pedagogical approach to the teaching of chemical equations introduced to first year university students with little previous chemical knowledge. During the instruction period students had to interpret and construct diagrams of reactions at the submicro level, and relate them to chemical equations at the symbolic level with the aim of improving their conceptual understanding of chemical equations and stoichiometry. Students received instruction in symbol conventions, practice through graded tutorial tasks, and feedback on their efforts over the semester. Analysis of the student responses to formative test and summative exam items over consecutive years indicates that there was a consistent improvement in the abilities of the various cohorts to answer stoichiometry questions correctly. The responses provide evidence for diagrams of the submicro level being used as tools for reasoning in solving chemical problems, to recognise misconceptions of chemical formulae and to recognise the value of using various multiple representations of chemical reactions connecting the submicro and symbolic levels of representation. The student-generated submicro diagrams serve as a visualisation tool for teaching and learning abstract concepts in solving stoichiometric problems. We argue that the use of diagrams of the submicro level provides a more complete picture of the reaction, rather than a net summary of a chemical equation, leading to a deeper conceptual understanding.

A dictionary of chemical equations.

Mode of access: Internet.

The descent of Morgan in Australia: kinship representation from the Australian colonies

Morgan had two extraordinary disciples in Lorimer Fison and Alfred Howitt in Australia. They were inspired by Morgan’s kinship schedule and were profoundly engaged in the method and theory of the collection of kinship data and its interpretation. Fison began using the schedule in Fiji in 1869. Soon after his first contact with Howitt, in 1873, they changed the method of collection of kinship terminologies. This paper traces the shift from tabulated kinship lists to family trees and the use of sticks to represent relationships (nearly twenty years before Rivers’ celebrated ‘genealogical method’), as well as efforts to find new means of representing kinship through experimentation with ‘ graphic formulae’ inspired by chemical equations. These innovations first occurred through the gathering of kinship data about the Kŭnai of Gippsland, Victoria, and crucially involved close collaboration between Howitt and his Kŭnai consultant Tulaba. What was revealed in this process was an indigenous kinship system quite different from that found in other parts of colonial Australia known at the time. Fison and Howitt explained this system as transitional between two stages in terms of Morgan’s evolutionary scheme, but at the same time challenged the assumption that the general scheme could be applied to Australia. While the details of Morgan’s evolutionary stages have faded from view, the methods of collection, representation, transmission, comparison and interpretation of kinship data are still live issues in anthropology today. The kind of kinship system discovered in Gippsland involved neutralisation of the cross-parallel distinctions, distinctions that are otherwise typical of Australia. Such neutralisation can now be shown to occur elsewhere in Australia. There does indeed seem to have been a transition from a Dravidianate system with cross-parallel distinctions to ‘overlays’ of cross-parallel neutralisation, and finally a complete loss in some generations of such distinctions in the terminology. These discoveries open up possibilities of rebuilding a diachronic theory of kinship change and evolution, incorporating some of the insights of Fison and Howitt, though without their specific hypotheses, either of local developments in Gippsland or the grand scheme of Morgan.

Suicide nucleophilic attack: Reactions of benzohydroxamate anion with bis(2,4-dinitrophenyl) phosphate

(Chemical Equation Presented) The reaction between the benzohydroxamate anion (BHO-) and bis(2,4-dinitrophenyl)phosphate (BDNPP) has been examined kinetically, and the products were characterized by mass and NMR spectroscopy. The nucleophilic attack of BHO- follows two reaction paths: (i) at phosphorus, giving an unstable intermediate that undergoes a Lossen rearrangement to phenyl isocyanate, aniline, diphenylurea, and O-phenylcarbamyl benzohydroxamate; and (ii) on the aromatic carbon, giving an intermediate that was detected but slowly decomposes to aniline and 2,4-dinitrophenol. Thus, the benzohydroxamate anion can be considered a self-destructive molecular scissor since it reacts and loses its nucleophilic ability. © 2009 American Chemical Society.

Analysis of elements at DSDP Holes 70-506 and 70-509B

Sediments in the area of the Galapagos hydrothermal mounds are divided into two major categories. The first group, pelagic sediments, are nannofossil oozes with varying amounts of siliceous microfossils. The second group are hydrothermal sediments consisting of manganese-oxide crust fragments and green nontronitic clay granules. Hydrothermal sediments occur only in the upper half to two-thirds of the cores and are interbedded and mixed with pelagic sediments. Petrologic evidence indicates that hydrothermal nontronite forms as both a primary precipitate and as a replacement mineral of pre-existing pelagic sediment and hydrothermal manganese-oxide crust fragments. In addition, physical evidence supports chemical equations indicating that the pelagic sediments are being dissolved by hydrothermal solutions. The formation of hydrothermal nontronite is not merely confined to the surface of mounds, but also occurs at depth within their immediate area; hydrothermal nontronite is very likely forming today. Geologically speaking, the mounds and their hydrothermal sediments form almost instantaneously. The Galapagos mounds area is a unique one in the ocean basins, where pelagic sediments can be diagenetically transformed, dissolved, and replaced, possibly within a matter of years.

Evaluation of NRC, UC Davis and ADAS approaches to estimate the metabolizable energy values of feeds at maintenance energy intake from equations utilizing chemical assays and in vitro determinations

Feed samples received by commercial analytical laboratories are often undefined or mixed varieties of forages, originate from various agronomic or geographical areas of the world, are mixtures (e.g., total mixed rations) and are often described incompletely or not at all. Six unified single equation approaches to predict the metabolizable energy (ME) value of feeds determined in sheep fed at maintenance ME intake were evaluated utilizing 78 individual feeds representing 17 different forages, grains, protein meals and by-product feedstuffs. The predictive approaches evaluated were two each from National Research Council [National Research Council (NRC), Nutrient Requirements of Dairy Cattle, seventh revised ed. National Academy Press, Washington, DC, USA, 2001], University of California at Davis (UC Davis) and ADAS (Stratford, UK). Slopes and intercepts for the two ADAS approaches that utilized in vitro digestibility of organic matter and either measured gross energy (GE), or a prediction of GE from component assays, and one UC Davis approach, based upon in vitro gas production and some component assays, differed from both unity and zero, respectively, while this was not the case for the two NRC and one UC Davis approach. However, within these latter three approaches, the goodness of fit (r(2)) increased from the NRC approach utilizing lignin (0.61) to the NRC approach utilizing 48 h in vitro digestion of neutral detergent fibre (NDF:0.72) and to the UC Davis approach utilizing a 30 h in vitro digestion of NDF (0.84). The reason for the difference between the precision of the NRC procedures was the failure of assayed lignin values to accurately predict 48 h in vitro digestion of NDF. However, differences among the six predictive approaches in the number of supporting assays, and their costs, as well as that the NRC approach is actually three related equations requiring categorical description of feeds (making them unsuitable for mixed feeds) while the ADAS and UC Davis approaches are single equations, suggests that the procedure of choice will vary dependent Upon local conditions, specific objectives and the feedstuffs to be evaluated. In contrast to the evaluation of the procedures among feedstuffs, no procedure was able to consistently discriminate the ME values of individual feeds within feedstuffs determined in vivo, suggesting that the quest for an accurate and precise ME predictive approach among and within feeds, may remain to be identified. (C) 2004 Elsevier B.V. All rights reserved.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w caus

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.