Chemical reactions far from equilibrium can exhibit oscillatory behavior. Full understanding of this phenomenon is outside of the school curriculum. However, the importance of such processes in life sciences and peculiar spatial and temporal patterns accompanying the reactions can attract the attention of IB Diploma science students. They will have studied chemical kinetics and received sufficient background knowledge in ordinary differential equations in order to be able to appreciate how sceptical the scientific community was when chemical oscillations were first reported. In this article, the famous Belousov–Zhabotinsky (BZ) reaction is investigated, which involves oxidation of malonic acid to carbon dioxide by bromate ions in the presence of a transition metal catalyst. Cerium(IV) and Manganese(II) catalysts at different initial concentrations are used with the research goal of determining the influence of the catalyst on the way the oscillatory stage is established and on the properties of oscillations. Convincing evidence of oscillatory behavior is observed and quantified by digital video processing. The BZ reaction mechanism is reviewed on the basis of the Field, Körös, and Noyes (FKN) model in reduced Oregonator form. The resulting system of nonlinear differential rate equations is solved numerically, and a remarkable agreement of the theoretically predicted oscillation period with an experiment for a Cerium(IV) catalyst is achieved.

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实验室中别洛乌索夫-扎博汀斯基反应的化学和数学

远离平衡的化学反应会表现出振荡行为。对这种现象的充分了解不在学校课程范围之内。但是，此类过程在生命科学中的重要性以及伴随反应而来的特殊时空格局会引起IB文凭理科学生的注意。他们将研究化学动力学，并在常微分方程中获得足够的背景知识，以便能够理解第一次报告化学振荡时科学界的怀疑态度。在本文中，研究了著名的Belousov-Zhabotinsky（BZ）反应，该反应涉及在过渡金属催化剂存在下，溴酸根离子将丙二酸氧化为二氧化碳。铈（IV）和锰（II）催化剂的初始浓度不同，其研究目的是确定催化剂对振荡阶段建立方式和振荡性质的影响。令人信服的振荡行为证据可通过数字视频处理来观察和量化。在还原的Oregonator形式的Field，Körös和Noyes（FKN）模型的基础上，对BZ反应机理进行了综述。对所得的非线性微分速率方程组进行了数值求解，并与铈（IV）催化剂的实验在理论上预测的振荡周期达成了显着一致性。令人信服的振荡行为证据可通过数字视频处理来观察和量化。在还原的Oregonator形式的Field，Körös和Noyes（FKN）模型的基础上，对BZ反应机理进行了综述。对所得的非线性微分速率方程组进行了数值求解，并与铈（IV）催化剂的实验在理论上预测的振荡周期达成了显着一致性。令人信服的振荡行为证据可通过数字视频处理来观察和量化。在还原的Oregonator形式的Field，Körös和Noyes（FKN）模型的基础上回顾了BZ反应机理。对所得的非线性微分速率方程组进行了数值求解，并与铈（IV）催化剂的实验在理论上预测的振荡周期达成了显着一致性。