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Equilibrium : CommonIonEffect (9 Variations)
The molar solubility of lead(II) fluoride (PbF_{2}) is
2.1 x 10^{-3} mol/L in pure water at 25^{o}C. What is the molar solubility of lead(II) fluoride in 0.10 M NaF at 25^{o}C? (Assume that the only relevant reaction is the solubility-product equilibrium.)

Cross-Proportions: A Conceptual Method for Developing Quantitative Problem-Solving SkillsElzbieta Cook and Robert L. Cook This paper focuses attention on the cross-proportion (C-P) method of mathematical problem solving, which was once widely used in chemical calculations. We propose that this method regain currency as an alternative to the dimensional analysis (DA) method, particularly in lower-level chemistry courses. In recent years, the DA method has emerged as the only problem solving mechanism offered to high-school and general chemistry students in contemporary textbooks, replacing more conceptual methods, C-P included. Cook, Elzbieta; Cook, Robert L. J. Chem. Educ.2005, 82, 1187.

Learning Theories |

Stoichiometry |

Chemometrics |

Student-Centered Learning

Encouraging Meaningful Quantitative Problem SolvingJeff Cohen, Meghan Kennedy-Justice, Sunny Pai, Carmen Torres, Rick Toomey, Ed DePierro, and Fred Garafalo This paper describes the efforts of a group of teachers to help college freshman chemistry students and high school science students to improve their problem-solving skills. The presentation includes several sets of questions intended to elucidate ideas and to involve the reader in the process of reflecting upon his or her own problem-solving strategies. Cohen, Jeff; Kennedy-Justice, Meghan; Pai, Sunny; Torres, Carmen; Toomey, Rick; DePierro, Ed; Garafalo, Fred. J. Chem. Educ.2000, 77, 1166.

Mathematics / Symbolic Mathematics |

Chemometrics

MathBrowser: Web-Enabled Mathematical Software with Application to the Chemistry Curriculum, v 1.0Jack G. Goldsmith MathBrowser, a freeware web-enabled derivative of the MathCad mathematical software (MathSoft Inc., Cambridge, MA), is designed to reconcile the problem of how to distribute mathematically rich information over the WWW and to maintain interactivity for the end user. Goldsmith, Jack G. J. Chem. Educ.1997, 74, 1164.

Visualizing Numerical Methods (2)William F. Coleman These movies are designed to help students visualize various numerical approaches to evaluating functions or solving equations. The methods themselves may be familiar to students from their mathematics courses, but they may have forgotten the material or never made the connection between a statement such as "the derivative of a curve at a given point is the slope of the line tangent to the curve at that point" and the way that one might evaluate such a derivative. All of the movies have VCR-style controls that enable the student to step through them one frame at a time and to move backwards as well as forwards.

Chemometrics

A Method of Visual Interactive RegressionMichelle S. Kim, Maureen Burkart, Myung-Hoon Kim Over the past decade many colleges and universities have placed increased emphasis on having students develop statistical and data analysis skills in a range of disciplines. Some institutions now require that all students complete at least one course with a strong component of data analysis, whether the data are from chemical experiments, the census, or some other source. As chemists, one of our concerns should be to ensure that students view data analysis as an integral part of any quantitative experiment, and, as far as possible, do not treat this process as a black box. The authors of A Method of Visual Interactive Regression, a spreadsheet application, have developed a visual approach to linear least-squares curve fitting that drives home the idea of minimizing the sum of the squares of the deviations in order to find the best fit to a set of data that are being described by a linear relationship. For many students these visualizations are likely to persist a great deal longer than the mathematical derivations of the equation for the slope and the intercept. The visualizations will provide a useful connection between a set of equations and the buttons on a calculator or the insertion of a trendline in a spreadsheet.