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Students can study the dissolution of carbon dioxide in water, an environmentally important process, using a simple and inexpensive setup. No vacuum line is needed and the procedure is straightforward. Students become acquainted with the concept of relaxation to equilibrium. They also learn about kinetic treatment of reversible reactions, special problems of interphase transfer and the concept of mass accommodation coefficients. The mechanism of interphase transfer is not entirely understood, which makes the experiment of interest as well.

The Gibbs function can only be applied to chemical systems and subsystems that have uniform temperature and pressure and retain the initial values in the final state. This limitation, though recognized by Willard Gibbs, is rarely indicated in chemistry and thermodynamics textbooks but limits the function to only isotropic solids. Placing the boundaries on the inner rather than outer surfaces of closed containers can resolve the difficulties for teachers.

A thermodynamics problem proposed in two chemistry textbooks concerning an irreversible process taking place in a rigid container produced two paradoxical solutions. However, both textbooks took Gibbs free energy (G) into account when it is not useful to measure or calculate G's change if the pressure distribution on the container's inner surface changes during the process. Therefore, the lack of constant pressure in the subsystem provides no criterion for G's changes so the change in G can equal zero without violating thermodynamic rules.

We have studied the behavior of phase response curves of different oscillatory states in a Belousov–Zhabotinsky reaction by using the amplified Oregonator model. As perturbants we have used bromide ion and silver ion. In case of oxidation spikes, the effect of bromide ion is a phase delay as reported previously. However, when the oscillations stay a considerable time in the oxidized state, bromide ion can cause significant phase advances, whenever the perturbation exceeds a lower critical bromide ion concentration. We are able to model recent experiments performed by Marek and co-workers, which have been claimed to give poor agreements with Oregonator-type of models. We have also compared the effect of a low (104 M-1 s-1) or high (109 M-1 s-1) silver bromide precipitation rate constant on phase response curves when silver ion perturbs oxidation spikes. We find that best agreements with experiments are obtained when the low silver bromide precipitation rate constant is used. The computations exhibit virtually identical behavior whether the rate constant values due to Field, Körös, and Noyes, or to Field and Försterling are used to parametrize the oxybromine chemistry. [ABSTRACT FROM AUTHOR]

A model based on five independent composition variables has been tested by simulating the complex bursting patterns observed experimentally for a Belousov–Zhabotinsky system in a flow reactor. If the system is in a region of constraint space where all stationary states are locally unstable, and if malonic acid concentration in the feed is decreased at constant flow of bromide ion, simple limit-cycle oscillations persist until the system reaches the Hopf bifurcation which generates a stable stationary state with low concentration of bromide ion. If bromide ion concentration in the feed is increased at constant flow of malonic acid, more and more small-amplitude oscillations are interspersed between trains of fewer and fewer large-amplitude excursions until a Hopf bifurcation leads to a stable stationary state with a high concentration of bromide ion. Patterns may be quite complex but usually repeat regularly. If a firing number is defined as ΣS/(ΣS+ΣL), where the summations represent the numbers of small- and large-amplitude oscillations in a complete pattern, then this firing number increases monotonically with increasing bromide ion in the feed. Narrow regions of chaotic mixing of patterns are also observed. The computations agree spectacularly with the careful experimental observations of Maselko and Swinney. Two separate curves are generated by the Hopf bifurcations which limit local stabilities of stationary states containing low and high concentrations of bromide ion, and the intersection of these curves provides a rationale for the ‘‘cross-shaped phase diagrams’’ which define regions of bistability and of oscillations in constraint spaces for such systems. [ABSTRACT FROM AUTHOR]

A stiffly-coupled Oregonator model based on the two independent variables Y and Z has been examined in detail with the use of the stoichiometric factor as a single disposable parameter. The trajectories and periods of the stable limit cycles can be generated with unanticipated accuracy from simple linear differential equations. Transitions between stable limit cycles and stable steady states takes place by means of subcritical Hopf bifurcations. Unstable limit cycles and thresholds of excitability can be recovered by integrating the equations of motion backward in time; such procedures cannot be applied so easily for models based on more than two independent variables. We have examined claims of experimental evidence for saddle-node infinite period (SNIPER) bifurcations and have concluded that all currently available evidence is equivocal. Until unambiguous criteria can be established for identifying SNIPER bifurcations in real systems, and until chemical mechanisms have been proposed which generate such bifurcations, observations should be interpreted by existing models based on Hopf bifurcations. Experimental behaviors are listed which can and cannot be simulated in terms of two independent composition variables. [ABSTRACT FROM AUTHOR]

When a chemical reaction is carried out in a continuously stirred tank reactor, the behavior may be significantly affected by the efficiency with which the entering chemicals are mixed with the main contents of the reactor. We have developed a model for this effect which assumes that a feed of premixed chemicals remains for a while in totally segregated packets before they are rapidly and perfectly mixed with the rest of the system. The time of this initial segregation is affected by the efficiency of stirring in the reactor. The model has been tested by computations on a mechanism developed by Roelofs et al. for a reaction which would oscillate even in a closed system. It has also been tested by computations on the rapid autocatalytic oxidation of cerous ion by bromate in the presence of a small amount of bromide. The results are qualitatively consistent with effects observed experimentally and in computations with other models including a somewhat similar one by Kumpinsky and Epstein. More quantitative tests should recognize the difference whether two streams of chemicals enter the reactor independently or are premixed before they do so. [ABSTRACT FROM AUTHOR]

The original Oregonator model of five irreversible steps and one stoichiometric parameter has been amplified to seven irreversible steps. The amplified model simulates excitability of a reduced steady state induced by silver ions and of an oxidized steady state induced by bromide ions. It also simulates how oscillations during a single run might change from reduction pulses to oxidation pulses. Finally, it simulates a temporary bistability persisting for over two hours in a closed system. If independent measurements determine the rate of enolization of the organic substrate and the rate of reaction of that substrate with the oxidized form of the catalyst, this model may be able to simulate semiquantitatively a large fraction of reported behaviors of catalyzed homogeneous Belousov–Zhabotinsky systems. It will not model systems in which Br2 accumulates or in which there are high-frequency small-amplitude oscillations around an oxidized steady state. Procedures are suggested for simulating such behaviors. [ABSTRACT FROM AUTHOR]

Asexual seed production (agamospermy) via gametophytic apomixis in flowering plants typically involves the formation of an unreduced megagametophyte (via apospory or diplospory) and the parthenogenetic development of the unreduced egg cell into an embryo. Agamospermy is almost exclusively restricted to polyploids. In this study, the genetic basis of agamospermy was investigated in a segregating population of 130 [F.sub.1]'s from a cross between triploid (2n = 27) agamospermous Erigeron annuus and sexual diploid (2n = 18) E. strigosus. Correlations between markers and phenotypes and linkage analysis were performed on 387 segregating amplified fragment length polymorphisms (AFLPs). Results show that four closely linked markers with polysomic inheritance are significantly associated with parthenogenesis and that 11 cosegregating markers with univalent inheritance are completely associated with diplospory. This indicates that diplospory and parthenogenesis are unlinked and inherited independently. Further, the absence of agamospermy in diploid [F.sub.1]'s appears to be best explained by a combination of recessive-lethal gametophytic selection against the parthenogenetic locus and univalent inheritance of the region bearing diplospory. These results may have major implications for attempts to manipulate agamospermy for agricultural purposes and for interpreting the evolution of the trait.