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The densities of the molten alkali fluoroborates were each measured over a temperature interval of approximately 150°C using a dilatometric method. The molar volumes and expansivities derived from these measurements exhibit the order predicted from the periodic table. At equal corresponding temperatures, molar volumes of molten alkali fluoroborates were found to be slightly larger than the molar volumes of molten alkali iodides. For LiBF4, RbBF4, and CsBF4, melting points and solid-state transition temperatures were determined. At the solid-state transition temperature, volume changes are predicted on the basis of analogous behavior of MBF4 and MClO4. The indices of refraction of the crystalline compounds were also measured; an electronic polarization averaging 2.77 Å3 for BF4− was calculated from these measurements. The polarization of BF4− appears to decrease with increasing alkali cation size.

Over the past several years I have taught approximately 1000 students in college general chemistry courses ranging from general chemistry for nurses to honors general chemistrv. While teachine these eeneral chemistrv courses. I have noted several typesof comhon learning difficulties or errors. All of these errors seem to have arisen from difficulties in assimilating or integrating knowledge.There have recently been suggestions1 that learning difficulties in courses such as general chemistry may result from differences between the instructor's framework of prior experience and knowledge and the analogous framework of the average student. While teaching a topic, the instructor may iuadv&ently assume too much experience and knowledge on the part of the students.I t is also possible that some of the students' difficulties arise from failing to integrate knowledge such as information in two seoarate chaoters of a eeneral chemistrv text. Such integration should indeed be the students' responsibility; however, many students are not capable of it. The instructor, in theend, may have to integrateconceptsin lectureand, along with that, build a conceptual framework for the students. Students construct their own knowledge or frameumork of knowledge, hut it is the instructor's responsibility to aid and guide the students in that construction.With these thoughts in mind, I decided to pursue the sourres or root rauses of student errorsand learningdifficulties. Determination of the source or rause of each error was carried out through personal interviews of the students. Occasionally, written responses on examinations gave the evidence. Correction or orevention of each error or learnine difficulty was done through modifications of subsequeni instruction. The modifications were specifically designed to resolve what were found to he problems or deficiencies of the students' learning or conceptual framework. Yet, as we will soon see, all of the modifications were actually of a general nature. We will now examine a numher of errors that I have found to be typical and give the source or causes and how the problem was corrected.The formula weight of KzCrz07 was calculated using only the formula 0209-. Almost without exception, students indicated that thev did not see the ooint of the two ootassium ions. "Those potassium ions are spectator ions, right?The hook does not eive the notassium ions in the net ionic -equation. Dichromate ion is the oxidizing agent," the students would sav. I t seemed that the students failed to retain the significance of a rompound being electrirally neutral, and thus did not think of the fact that one would never find in the stockroom a bottle containing only dichromate ions. This was so in spite of the fact that electrical neutrality was emphasized eariy in the course as a guide to writing the correct formula of an ionic compound. The same concept was emphasized as an aid in the determination of oxidation numbers. The students could write correct formulas of ionic compounds and determine oxidation numbers,...