Chemistry and Mathematics

Learning Objectives

• Chemistry

  Aim of the course is to acquire the knowledge of the key concepts of the chemistry. In particular, the course is aimed:

  - to supply a chemical reading key for the understanding of the natural phenomena;

  - to introduce the fundamental knowledge for the study of matter in relation to its composition, structure, reactivity, property;

  - to know the main classes of inorganic molecules;

  - to the identification, writing and naming the main organic molecule classes, including bio-molecules;

  - to the view of simple organic molecules in three dimensions with an emphasis to their stereochemical properties;

  - to understand the structure-property-reactivity relationships of basic organic compounds
  

• Mathematics

  The course intends to provide students the basic math concepts, and will also provide the basics of differential and integral calculus that will be used in specific disciplines. Students will be stimulated in learning math methods and results and developing their ability to use the same for problem solving. There will also be given a concrete idea, through various examples and applications, about the importance of mathematics in applications.

Course Structure

• Chemistry

  Classroom lectrures.

  Classroom Exercises.

• Mathematics

  Traditional (teacher up front) lessons.

Detailed Course Content

• Chemistry

  Introduction. Classification of Matter. The energy. The elements. The properties of matter. Changes of phase. The Metric System and the International System of Units.

  Atoms and Molecules: the Atomic Theory of Matter. Structure of the Atom. Atomic Theory. Key concepts: Protons, electrons and neutrons. The Quantum Theory for Atomic Structure (hints). The uncertainty principle and the Schrödinger equation. The atomic orbitals. Shapes of Orbitals: Graphics of s, p, d and f orbitals. The Aufbau principle. The Pauli exclusion principle and Hund’s Rule.

  Periodic Table of the Elements. Atomic Number and Mass Number of elements. The isotopes. Exploring the Periodic Table. Atomic Structure and Periodicity. Ionization Energy and Electron Affinity.

  Chemical Bonds. Lewis Dot Structures. σ and π bonds. The Electronegativity. Ionic bonds. Covalent Bonds. Chemical Bonding: Approach of Hybridization of Atomic Orbitals. Discussion of the different types of orbital hybridization. The sp, sp² and sp³ hybridization. The Resonance theory. Intermolecular bonding: Van der Waals forces. Hydrogen bond.

  Chemical compounds. Ionic and Covalent Compounds. Formulas and Nomenclature of Ionic and Covalent Compounds. IUPAC Nomenclature. The oxidation number of elements. Binary and ternary compounds: Hydride, Oxides, Peroxides, Hydrogen halides, Oxoacids, Hydroxides, Salts.

  Chemical Reactions. The meaning of a Chemical Equation. Balancing Chemical Equations. Types of Reactions. RedOx Reactions. Stoichiometry of Chemical Reactions. The Mole and the Molecular Mass. Chemical Equilibrium: A Dynamic Concept. Le Chatelier's Principle. Chemical Equilibrium: Equilibrium Constants. The Autoionization of Water. Aqueous Reactions. pH and pOH concepts. Acids & Bases. Solving an acid base problem. Buffer solutions.

  Properties of Solutions (hints). Solutions and Solubility. Concentration of solution. Molarity and Molality. Mole Fraction. Colligative Properties. Vapor-pressure lowering, boiling- point elevation, freezing-point depression and Osmotic Pressure.

  The Chemistry of Carbon. Organic compounds. The origins of Organic Chemistry. Classification of organic compounds. Functional groups. IUPAC Nomenclature. Drawing Three-Dimensional Molecules.

  Stereochemistry. Constitutional Isomerism. Stereoisomerism: Conformational and Configurational Isomerism. Chirality. Optical Activity. Enantiomeric forms. (R) and (S) Nomenclature of Chiral Carbon Atoms. Diastereomers. Meso Compounds. Geometric isomers (geometric Z, E , cis/trans).

  The Study of Chemical Reactions. Reaction Mechanisms. Reactive Intermediates: Carbocations, Carbanions, Free Alkyl radicals. Addition Reactions. Radical Reactions. Substitutions and Elimination Reactions. Acids-Bases and RedOx Reactions in Organic Chemistry. Regioselectivity, Stereoselectivity & Stereospecificity in Organic Synthesis.

  Alkanes. Nomenclature. Physical Properties of Alkanes. Structure and Stereochemistry of Alkanes. Uses and Sources. Radical Halogenation of Alkanes: Mechanism and Stereochemistry.

  Alkenes. Nomenclature. Physical Properties of Alkenes. Geometric isomers (geometric Z, E , cis/trans). Alkadienes. Conjugated Dienes. Polyenes. Terpenes. Sources of Alkens. Synthesis of Alkens (hints). Reactions of Alkens.

  Alkynes. Nomenclature. Acidity of Alkynes. Reactions of Alkynes. Addition of Halogens.

  Cycloalkanes and Cycloalkenes (hints). Cyclohexane conformations.

  Alkyl Halides. Structure and Nomenclature. Reactions of Alkyl Halides: Nucleophilic Substitution (S_N1 and S_N2). Elimination Reactions (E1 and E2). Comparison of the Nucleophilic Substitution and Elimination Reactions. Substitution versus Elimination.

  Alcohols. Structure, Nomenclature and Classification of Alcohols. Physical Properties: Hydrogen bond in Alcohols. Acidity of Alcohols. Reactions of of Alcohols. Dehydration: Formation of Alkenes. Reaction of Alcohols with Hydrohalic Acids. Esterification of Alcohols.

  Ethers, Epoxides and Sulfides (hints). Nomenclature and Physical Properties.

  Aromatic Compounds. The Structure and Properties of Benzene. Aromaticity. Nomenclature of Benzene Derivatives. Reactions of Aromatic Compounds: Electrophilic Aromatic Substitution. Activating and Deactivating Substituents. Ortho-, Meta- or Para- Directing Substituents. Phenols. Acidity of Phenol. Electrophilic Aromatic Substitution. Phenols in Nature.

  Aldehydes and Ketones. Structure of the Carbonyl Group. Nomenclature. Reactions of Aldehydes and Ketones: Nucleophilic Addition. Nucleophilic Addition of Water. Nucleophilic Addition of Alcohols. Reduction of Aldehydes and Ketones. Oxidation of Aldehydes.

  Carboxylic Acids and Carboxylic Acids Derivates. Nomenclature. Structure and Physical Properties. Acidity of Carboxylic Acids. Reactions of Carboxylic Acids. Nucleophilc Acyl Substitution. Carboxylic Acids Derivates: Acid Chlorides, Estsers, Anhydrides, Amides. Reactions of Carboxylic Acids Derivates.

  Amines. Nomenclatures. Structure and Physical Properties. Basicity of Amines.

  Carbohydrates. Introduction. Classification and Nomenclature of Carbohydrates. Monosaccharides. Classification of Monosaccharides. The D and L Configurations of Sugars. Fischer’s Proof of the Configuration of Glucose. Cyclic Structures of Monosaccharides. Drawing Cyclic Monosaccharides: The Haworth Projection and Chair Conformations. Disaccharides: Maltose, Sucrose and Lactose. Polysaccharides: Cellulose, Starch and Glycogen.

  Amino Acids, Peptides and Proteins. Structure and Sterochemistry of the Amino Acids. Amino Acids in Nature: the α-Amino Acids. Isoelectric Points of the Amino Acids. Peptide Bond. Peptides and Proteins. Levels of Protein Structure.

  Lipids (hints). Lipids. Triglycerides and Oils. Soaps and Detergents. Phospholipids and Steroids.

• Mathematics
  • Sets. Operations between Sets. Relations. N, Z, Q, R.
  • Matrices. Determinant of a matrix. Reduced matrices. Rank of an array. Product columns. Inverse matrix.
  • Linear systems. Cramer's theorem. Rouche-Capelli Theorem.
  • Analytical geometry in the plain. Points. Distances, line equations, angular coefficient, properties, parallelism, perpendicularity.
  • Circumference. Intersection between a straight and a circumference.
  • Ellipse. Parabola. Hyperbole.
  • Functions. Domain of a function. Monotonous functions.
  • Limits of functions. Theorems.
  • Derivative of a function and its geometric meaning. Elementary Derivatives. Deriving rules: sum of functions, function products, composite functions.
  • Maximum and minumum of a function. Theorems.
  • Asymptotes.
  • Primitive of a function. Indefinite integral. Defined Integral.

Textbook Information

• Chemistry

  ESERCIZIARI

  - P. D'Arrigo, A. Famulari, C. Gambarotti, M. Scotti “Chimica: Esercizi e Casi Pratici” – EdiSES

  - P.M. Lausarot – G.A. Vaglio - “Stechiometria per la chimica generale” - PICCIN

  - Nicotra, Cipolla “Eserciziario di Chimica Organica” – EdiSES

  - D. Sica “Esercizi di Chimica Organica” - EdiSES

  - Brown, Lemay, Bursten, Murphy, Woodward, “Fondamenti di chimica” – EdiSES (disponibilità e-book personalizzato) (I PARTE PROGRAMMA). - Disponibile IV edizione

  - William H. Brown, M.K. Campbell - S.O. Farrell “Elementi di Chimica Organica” – II Edizione EdiSES (II PARTE PROGRAMMA).

  - William H. Brown, Thomas Poon “Introduzione alla Chimica Organica” – V Edizione EdiSES (disponibilità e-book personalizzato) (II PARTE PROGRAMMA). (Versione approfondita del testo "Elementi di Chimica Organica")

• Mathematics

  (1) M. Gionfriddo: Istituzioni di Matematiche. Tringale Editore

  (2) M.Gionfriddo, B. Mtarazzo, S. Milici: Esercitazioni di matematiche. Spazio Libri.

  (3) P. Marcellini, C. Sbordone: Elementi di Matematica. Liguori Editore.

  (4) C. Sbordone e F. Sbordone: Matematica per le scienze della vita. EdiSES

  (5) V. Villani, Matematica per discipline biomediche. Mc Graw-Hill

  In linea di massima si farà riferimento al testo 1. Approfondimenti e chiarimenti si possono trovare nei testi consigliati.