Physical Chemistry

Concepts and Theory

Kenneth S Schmitz

• Éditeur: Elsevier
• Année: 2016
• ISBN:
  9780128006009
• Sujet: Physical Sciences
• Sous-sujet: Physical & Theoretical Chemistry

Physical Chemistry: Concepts and Theory provides a comprehensive overview of physical and theoretical chemistry while focusing on the basic principles that unite the sub-disciplines of the field. With an emphasis on multidisciplinary, as well as interdisciplinary applications, the book extensively reviews fundamental principles and presents recent research to help the reader make logical connections between the theory and application of physical chemistry concepts.

Also available from the author: Physical Chemistry: Multidisciplinary Applications (ISBN 9780128005132).

• Describes how materials behave and chemical reactions occur at the molecular and atomic levels
• Uses theoretical constructs and mathematical computations to explain chemical properties and describe behavior of molecular and condensed matter
• Demonstrates the connection between math and chemistry and how to use math as a powerful tool to predict the properties of chemicals
• Emphasizes the intersection of chemistry, math, and physics and the resulting applications across many disciplines of science

Chapter 1

Overview

Abstract

The objectives of Physical Chemistry: Concepts and Theory are presented. The book is organized in accordance with the mathematics used: continuum for thermodynamics; discrete for quantum theory; statistics and probabilities for statistical mechanics; and the mathematics for potential-driven changes at short and long times for kinetics. The Reader is presented with material developed from the fundamental mathematical form of differential equations rather than integrated expressions to provide a better understanding of the interrelationships between subfields within the area of physical chemistry. This approach reveals how experimental conditions and a judicious choice of theoretical expressions can reduce the equations to a suitable form for the system at hand.

The introduction of how mathematics describes the world we experience is at three levels: Nature is Patterns, Nature is Numbers, and Nature is Recursion Relationships. Many objects in Nature are related to the Golden Ratio, such as apple seeds, spiral galaxies, and mollusk shells. Numbers give a quantitative description of Nature and the power of prediction. The complexity of Nature is embraced in the relationships between the numbers as manifested in recursion relationships, in which a few numbers can be used to generate a more complete description of Nature.

The study of prime numbers is an example of how a scientific study on a system evolves through the use of mathematical models. It is through mathematics that information is gained about a system, which leads to a simple understanding as reflected in movies and television series such as Star Trek.

Keywords

Classical thermodynamics; Fibonacci numbers; Fibonacci sequence; Golden Ratio; Golden Rectangle; Golden Triangle; Kinetics; Mathematics; Prime numbers; Quantum mechanics; Scientific fact; Scientific hypothesis; Scientific law; Scientific theory; Statistical mechanics

1.0. Introduction

“Let no one who is not a mathematician read my works”

Leonardo da Vinci (1452–1519), opening of Trattato della pittura (Treatise on painting)

Leonardo da Vinci is considered to be a true polymath, known for his paintings, sculptures, architectural achievements, inventions, science, music, mathematics, engineering, literature, anatomy, geology, astronomy, botany, and the list goes on. A familiar example is da Vinci's drawing of “Vitruvian Man” in which the human form is drawn inside a square and an inscribed circle. Medical students should be familiar with this drawing as it appears on the cover of many books on anatomy. The inspiration of this drawing was the Roman artist–architect Vitruvius who, in the 2nd century CE, formulated a theory on architecture based on the proportions in the human body that are associated with the Golden Ratio that has a value of approximately 1.618. Two examples are (1) the ratio of the length of the elbow-to-outstretched fingers (EF) to the length of the elbow-to-wrist (EW), viz, EF/EW and (2) the ratio of the distance from the chin-to-top of the head (CH) and the distance from the chin-to-top of eyes (CE), viz, CH/CE. The body abounds with such pairs of lengths. The outstretched arms and legs along with the head of the Vitruvian Man form a pentagon, which is also associated with the Golden Ratio. The human form is thus associated with geometric objects.

Geometry has played a major role in the evolution of civilizations. The pyramids of Egypt are the first of the Seven Wonders of the Ancient World. The Egyptian scholar Imhotep is given the honor of being the architect of the “step pyramid” of Sakkara (c.2950 BCE). These step structures are so familiar that even their silhouettes are recognizable by those who never saw a “real-life” pyramid. The pyramid may be characterized by its height, length of the base, and angle of inclination. However, there is nothing in Nature that demands that the pyramids be of a certain shape and size. The p...