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A fast and generally applicable alternative solution to the problem of determining the useful shelf life of medicinal solutions is described. It illustrates the power and convenience of the combination of numerical simulation and nonlinear least squares with a practical pharmaceutical application of chemical kinetics and thermodynamics, validated by comparison with literature data. (Contains 4 tables and 9 figures.)

How useful are the standard deviations per se, and how reliable are results derived from several least-squares coefficients and their associated standard deviations? When the output parameters obtained from a least-squares analysis are mutually independent, as is often assumed, they are reliable estimators of imprecision and so are the functions derived from them. But when these parameters have strong mutual dependencies, as is the rule rather than the exception in chemical data analysis, a more sophisticated approach to the statistical imprecision is required than is described in most chemistry textbooks. For the analysis of data from a typical kinetic experiment in physical chemistry, this is illustrated numerically as well as graphically. (Contains 2 tables and 13 figures.)

A recent article by McCarty and Vitz "demonstrating that it is not true that pH = -log[H+]" is examined critically. Then, the focus shifts to underlying problems with the IUPAC definition of pH. It is shown how the potentiometric method can provide "estimates" of both the IUPAC-defined hydrogen activity "and" the hydrogen ion concentration, using the same assumptions and with similar inherent uncertainties. Moreover, it is argued that the original Sorensen definition of pH as -log[H[superscript+]] is preferable over the current one.

A 19-year-old undergraduate at the University of Chicago, Kenneth Goode, in 1921 came up with the idea of an electronic pH meter, worked out some of its initial problems, and set in motion an international scientific effort that culminated in the current, wide availability of electronic pH meters. Except for the replacement of vacuum tubes by solid-state electronics, modern pH meters closely follow his original designs. (Contains 10 figures.)

The different methods used for computing labile metal-ligand complexes, which are suitable for an iterative computer solution, are illustrated. The ligand function has allowed students to relegate otherwise tedious iterations to a computer, while retaining complete control over what is calculated.

The numerical analysis of a NIST reference data set on a spreadsheet is illustrated in detail. We describe several interesting features, such as an efficient way of centering when fitting data to a high-order polynomial, and a little-known aspect of the imprecision of the imprecision. We also discuss a powerful alternative to standard matrix inversion, an extended set of add-in matrix functions for Excel, and software for making spreadsheet calculations with extended number length. [DOI: 10.1119/1.2721585]

The study on the ionic activity coefficient should be introduced at freshmen level so that the students can understand each and every aspect of physical chemistry and inorganic chemistry. The way in which ionic activity coefficient could make learning chemistry simple and easy is discussed.

The ionic activity effect on the rate of chemical reaction is expected to be weaker as the rate of chemical reaction is expressed in terms of concentration. The reasons for the ionic activity effect not following the well-known chemical reaction Principle are discussed.

A simple method to deconvolve spectra combines aspects of nonlinear least-squares curve fitting and Fourier transformation to reduce the effects of noise. The method fits data to smooth analytical functions, then deconvolves the latter analytically. For example, when the data can be written as a sum of Gaussians [g.sub.r] = [a.sub.r]exp[ - [(x - [c.sub.r]).sup.2]/2[b.sup.2.sub.r], and the transfer function as a single Gaussian [g.sub.t], then the deconvolved signal is the corresponding sum of Gaussians [g.sub.s], with [c.sub.s] = [c.sub.r], [b.sup.2.sub.s] = [b.sup.2.sub.r] - [b.sup.2.sub.t], and [a.sub.s] = [a.sub.r][b.sub.r]/[b.sub.s]. [DOI: 10.1119/1.1666896]

A harmonic analysis of the tides combines astronomical data, Fourier transformation, and nonlinear least-squares analysis. Fourier transformation is used to display the power spectrum of the initial data and, during the subsequent refinement stages of the analysis, of the remaining residuals. Because only a relatively small sample is used, the frequency resolution of the Fourier transformation is insufficient to determine the precise frequencies involved, which are instead taken from astronomical data. The actual fitting of successive terms, in order of decreasing importance, is accomplished with nonlinear least squares. Because both Fourier transformation and nonlinear least-squares fitting are readily automated on a spreadsheet, the amount of computational effort required for this analysis is minimal.

Stochastics are the basis of chemical dynamics. Atoms ions and molecules do not solve differential equations. They adhere to simple statistical laws of probability. Chemical laws can often be expressed in very simple mathematical terms. This causes students to ask why the expressions are so simple. Experimental observations directly show the stochasticity of nature. Topics include radioactive disintegration, opening/closing of an ion-conducting channel, enzyme kinetics and the reason for so few stochastic observations being made in chemistry.

A general computer simulator can be used to teach chemistry students about acid-base titrations. An similar algorithm might be used for expert systems. General equations based on well, known principles, for instance the Guldberg-Waage law of chemical equilibrium and conservation of mass and charge, can be used to calculate titration progress curves. The titration curve is essentially inverted to make it amenable to closed-form mathematical description.

A simple, general mathematical relation for the progress curve of a redox titration has been developed. Using the relationship it is possible to provide explicit expressions and a rational framework for the quantitative explanation of redox buffer action. If there is no redox equilibrium the buffering action may be slow. Time scale may cause buffer strength to be less than the computation would indicate. The traditional acid-base titration curve provides pH as a function of the volume of titrant added and the buffer value is a quantity related to titrations.

Students of chemistry can understand differential equations without solving them, which can be helpful when they are trying to learn about behavior of charged particles, perhaps colloidal particles or ions, and the Poisson-Boltzmann differential equation comes up in connection with Coulombic interactions. Attention gets off of understanding what the equation is all about and onto the mathematical operations for the students who are not so mathematically inclined. A more intuitive approach can be used and students can then go on learning chemistry.

The indium thiocyanate electrochemical oscillator was examined in an experiment and by digital simulation based on independently determined rate variables. Digital simulation results showed that the characteristic features of the oscillations can be reproduced in the absence of additional model assumptions. The indium reaction in aqueous thiocyanate mixture can also be analyzed without the need for external resistance. In addition, measurements can be made on well-defined, easily renewable and highly reproducible mercury electrodes.

Asimple explicit closed-form expression can be found for all titration curves without approximations or segmentation by considering the curve as a function of the concentration monitored. This expression can be used in simple acid-base titrations as well as complexometric and redox titrations. One limitation is that exact results are only obtained when formal equilibrium parameters are used instead of thermodynamic parameters. However, the advantages are numerous and include producing detailed numerical information from the titration curve.

Nonlinear fits of standard curves are discussed with description of a simple route to uncertainties in unknowns. Determining an unknown concentration using a standard calibration curve may be complicated by the need to find the associated uncertainty. It is important to be aware of the problem of neglecting covariance in such a calculation. A nonlinear least-squares procedure that makes a direct estimation of the concentration uncertainty without the need for covariance possible is illustrated.

The naming of scientific things and phenomena is usually somewhat arbitrary. The environment in which it takes place is often polarized by personal ambitions and in some cases group prejudices. Name-giving is one way used to assign credit for an accomplishment. Several examples of misnomers and misattribution are discussed. Topics include electrode kinetics, enzyme kinetics, data smoothing, continuous variation, the double layer, and mass action.

A distinguish between two linear correlation coefficients, r and r2, is discussed. One coefficient is readily available but typically of very limited usefulness in chemistry, and the other one is used for some chemical calculations.