This unit explores the problem solving process. We will see that there are organized ways to approach and solve problems. Applied mathematics forms

Transcription

1 PART I. MATHEMATICS This unit explores the problem solving process. We will see that there are organized ways to approach and solve problems. Applied mathematics forms the basis of physical sciences. When you finish this unit you should have a general perspective on problem solving methods, understand what an algorithm is and how it is constructed, and be able to solve problems involving conversion of units and basic algebra. A fundamental concept for this unit is that systematic procedures, called algorithms form the basis of organized activities, including scientific problem solving. This will be illustrated with examples taken from measurement manipulations and mathematics.

2 PART II. PHYSICS Physics deals with measurements and models of natural objects. Physics and chemistry overlap at the molecular level in their approach to understanding and predicting behavior. But chemistry is preceeded by physics both historically as well as conceptually. In this sense chemistry owes more to physics than physics owes to chemistry. In many respects physics forms a foundation for chemistry as mathematics forms a foundation for all science. Thus an understanding of certain areas of mathematics and physics is essential to understanding chemistry.

3 PART III. ATOMS This unit deals with two of the fundamental concepts in chemistry, the atomic theory and the chemical periodic table. When you finish this unit you will understand what atoms, ions, elements and isotopes are, and how their properties are measured and explained in terms of fundamental subatomic particles. Youwill also begin to learn the language of chemistry through the symbolism used to represent atoms, isotopes and ions. The foundation concepts for this unit are that, except under relatively extreme energy conditions, all matter is composed of fundamental components, called atoms, of which there are a finite number (about 100) of different types, called elements, that atoms, in turn, are composed of more fundamental particles, of which there are a finite number (3 dominant) of different types, and that the behavior of matter is described accurately by wave mechanics. These concepts will be applied to the analysis and behavior of elemental matter. The notions related to atomic behavior were first discovered through experimentation and applied as heuristics to explain and predict. Now they are understood through more fundamental principles that provide theoretical justification for the algorithms of atomic science. The long history of the analysis of matter achieved three landmarks with John Dalton s atomic theory at the beginning of the Nineteenth Century, Ernest Rutherford s nuclear theory at the beginning of the Twentieth, and Erwin Schr"odinger s wave theory of These models of the structure of matter will form the subject of this unit.

4 PART IV. MOLECULES Atoms stick together in fixed numbers to form molecules. Chemical formulas use element symbols, parentheses and subscripts to represent element composition, (e.g. H 2 O for water). The elements in a chemical formula may be ordered and grouped to reflect the way atoms are bound together. Graphical pictures called structural formulas show the relative positions of atoms and the chemical bonds holding the atoms together (e.g. H O H). It is literally true for complex substances that a picture can be worth a thousand words. In this unit we will see how molecular formulas are derived from experiment and theory, investigate the forces that hold atoms together in molecules, and discuss how molecular substances are named. When you have finished this unit you should know how to deduce and name chemical formulas and explain properties of the molecules which they represent. The foundation concepts for this unit are that molecules are collections of atoms held together by chemical bonds described by the Schro"dinger wave mechanical equation. These principles will be used to determine the number and nature of the bonds in molecules.

5 PART V. ENSEMBLES Atoms are bound into molecules by the interactions of the electrons of the atoms. Groups of molecules can bind together through residual interactions of the electrons as well. 1 In this unit we will see how toidentify and solve problems related to the phases of matter under various external conditions. When you finish this unit you should be able to determine the phases of a substance, answer a variety of questions about the phases of gases and structure of solids, convert between various solution concentration units and determine sizes of atoms and molecules in gases and crystals. The foundation concept for this unit is that the stability of molecules and groups of molecules is determined by the competition between the strength of the attractions and the dissipative forces of the thermal energy of the system due to molecular collisions. 1 It is necessary in these discussions to use the broad definition of molecules as consisting of single atoms, neutral or ionized, or collections of atoms, possibly ionized (polyatomic ions), but stabilized by chemical bonds.

6 PART VI. DYNAMICS This unit deals with the fundamental chemical event, the chemical reaction. Three key questions regarding chemical reactions are: where are the reactants going, how fast do they get there, and what paths do they take? These questions began to be addressed quantitatively in the Nineteenth Century, with progress in understanding chemical behavior continuing to this day. When you finish this unit, you should be able to balance achemical reaction and apply the laws of stoichiometry, equilibrium and kinetics to analyze and predict amounts of products produced. The foundation concept for this unit is that chemical reactions result from the rearrangement of the atoms of reactant molecules to the atoms of product molecules, following paths described by the laws of thermodynamics, kinetics and ultimately, wave mechanics.