Mathematica ® computer program package

Mathematical methods are discussed in references 21-27 (some of these are "golden oldies"). Integrals, series, and other tables can be found in [28-33]. Of course, much labor can now be saved by using the computer program package Mathematica. 

In this exercise, the fractional conversion XA for the 4-min isothermal batch operation is 77.1%. Obviously, the required answer is obtained through trial-and-error. Equation 5-45 can be incorporated into a computer program or mathematical package such as Mathcad, Maple, Polymath, or Mathematica. 

A number of standard computer programs easily handle problems of this type such as spreadsheet packages, Matlab, Mathcad, Polymath, and so on as well as symbolic manipulators such as Mathematica, Maple, Derive, etc. Most statistic packages and equation solvers will also solve linear equations and have a simple user interface. 

The first entry is for the species with the fewest hydrogen atoms. Only species of interest in the range pH 5 to 9 are included. No complex ions are included in this table. The advantage of this table is that, with Mathematica in a personal computer, it is not necessary to copy these numbers to make a calculation. Programs for making these calculations are also included in the package. 

A second option is to use existing packages for numerical methods. The software libraries by IMSL and NAG have a wide variety of state-of-the-art numerical integrators. These libraries are well documented, reliable, and flexible, and can be found at most university computing centers or networks. The packages Matlab, Mathematica, and Maple are more interactive and also have programs for solving ordinary differential equations. 

Before closing this section it should be mentioned that most of the methods discussed above can be solved using commercially available programs such as symbolic computation (Mathematica, Maple, or Mathcad 3.0), equation solvers (TK Solver Plus or Mathcad 3.0), spreadsheets (e.g., Lotus 123, Quattro Pro, Microsoft Excel, or Wingz), simulators (Extend or Stella), or Microsoft FORTRAN 5.0. For example, one can introduce the idea of molecular mechanics on model systems using a spreadsheet. Actual applications of molecular mechanics are much better carried out on a software package designed for that purpose, however. 

Some computer exercises will be discussed briefly in this section. They serve as laboratory exercises for the second semester of physical chemistry sequence when quantum chemistry is taught. These computer exercises are also used in the lecture demonstration format. Sometimes they are given as extended problem assignments. Four software packages are used to various degrees in these exercises BASIC programs, spreadsheet templates, Mathematica, and Mathcad. 

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