This chapter introduces probability theory—the mathematical theory of statistics—that gives the theoretical models and analytical tools for the organization, interpretation, and analysis of statistical data. Probability theory is applied in chemistry for the description of the collective behaviour of very large numbers of particles in statistical mechanics, the quantum mechanical descriptions of changes of state and of rate processes, the physical interpretation of wave functions, and the enumeration of the ways of assembling basic chemical units to form large molecules. The chapter starts with a brief discussion on descriptive statistics. Then it tackles frequency and probability, as well as the combinations of probabilities. Furthermore, the discussion covers the binomial distribution. It describes permutations and combinations, as well as continuous distributions, then explains the Gaussian distribution. Lastly, it discusses the method of least squares.
Chapter
Probability and statistics
Book
Peter Atkins, Julio de Paula, and Ronald Friedman
Physical Chemistry starts off by looking at the foundations of the subject and provides the reader with some mathematical background. It then looks at quantum mechanics, taking into consideration the quantum mechanics of motion, molecular structure, and molecular symmetry. It then considers Fourier transforms, molecular spectroscopy, magnetic resonance, statistical thermodynamics, probability theory, the first law of thermodynamics, and multivariate calculus. The final part of the book examines physical equilibria, chemical equilibria, molecular motion, chemical kinetics, reaction dynamics, and processes in fluid systems and solid states.
