In recent years batteries have emerged in the marketplace that take advantage of the unique properties of lithium. Lithium metal is an attractive choice to serve as a battery anode because it is easily oxidized and it produces an exceptionally high amount of electrical charge per unit-weight. The electrolytes used in lithium batteries contain lithium salts dissolved in polar organic solvents. A variety of substances can serve as the battery cathode. They include inorganic solids, liquids, and dissolved gas. The cell potentials of lithium-metal batteries can be calculated from thermodynamic principles. These open-circuit voltages can be compared to the operating voltages of batteries delivering a current. Some lithium batteries employ intercalation compounds as their cathodes. These solids have layered or tunneled crystal structures into which lithium ions insert during the reduction process. When an intercalation cathode is paired with a lithiated-graphite anode, the resulting battery has the advantage of being rechargeable. It is known as a lithium-ion battery because no lithium metal is present.
Students need to be aware of the fact that even our best scientific measurements unavoidably involve some error. To develop this awareness, general chemistry courses introduce the concepts of precision and accuracy. The distinction between the two terms is illustrated in textbooks through the analogy of a target with arrows more or less clustered around the bull's eye. After this brief introduction many texts do not develop the subject further.This paper expands upon the topic of precision and accuracy at a level suitable for general chemistry. It serves as a bridge to the more extensive treatments in analytical chemistry texts and the advanced literature on error analysis. It presents a simple model experiment involving graduated cylinders, a discussion of some complications, and suggestions for classroom implementation. Previous articles in the Journal cover such related topics as significant figures (1-5), propagation of error (6-13), experiments and demonstrations of uncertainty (14-21), and a general review (22). Definition of TermsWe begin by defining the terms central to the theme of this paper. Measurement: the act or process of measuring. The process may be as simple as reading a thermometer or as complex as all the operations required for a chemical analysis. Precision: reproducibility. A measurement is precise if it is close to other values obtained by repeating the determination using the same procedure. Accuracy: correctness. A measurement is accurate if it is close to the true value. Since the true value of a quantity can never be exactly known, an accepted value is commonly used as the test of accuracy. Error: anything that causes a measurement to differ from the true value. The amount by which the measured value differs from the true value is also called the error.
Le Chatelier's principle is a well known generalization stating how changes of condition affect systems at equilibrium (1), In a previous paper I proposed a brief, yet unambiguous way of phrasing it (2):A system at equilibrium resists attempts to change its temperature, pressure, or concentration of a reagent.General chemistry texts often cite the principle when discussing the temperature dependence of solubility. It predicts that solubility will increase with temperature if dissolution absorbs heat and, conversely, that solubility will decrease with temperature if dissolution liberates heat.The validity of the principle when applied to ionic compounds in water has been questioned by Bodner (3). He points out that the enthalpies of solution usually tabulated in reference books refer to infinitely dilute solutions, and he cautions that such values have little relevance to the situation involving a solute in equilibrium with saturated solution. Bodner properly focuses attention on enthalpies of solution at saturation. Even then, his examination of literature data does not confirm the principle for many compounds. He offers several possible explanations for the apparent anomalies. One explanation, which is not explored, refers to the complicating factor that some ionic compounds exist as hydrated solids when equilibrated with saturated solution.Subsequent papers by Fernandez-Prini and by Brice defend the principle with largely theoretical arguments (4). Both authors reiterate that the parameter of most importance is enthalpy of solution at saturation. Furthermore, in the case of ionic compounds in water, they point out that enthalpy of solution varies unpredictably as one proceeds from lower to higher concentration. Except for a few examples, this matter is not pursued in any comprehensive fashion. This paper extends the work of previous authors by conducting a detailed examination of experimental results available in the literature. Le Chatelier's principle is tested, using appropriate thermodynamic data, for predicting the temperature dependence of solubility for ionic compounds in water. Care is taken to identify correctly the actual hydrate solid equilibrated with saturated solution and to base predictions solely upon its enthalpy of solution at saturation.
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