3.091SC | Fall 2010 | Undergraduate

Introduction to Solid State Chemistry

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Session Overview

Modules Organic Materials
Concepts organic chemistry nomenclature, chains, alkanes, alkenes, alkynes, aromatics, functional groups, isomers
Keywords hydrocarbon, radical, sp3 orbital, sp2 orbital, sp orbital, straight chain, branched chain, saturated hydrocarbon, unsaturated hydrocarbon, methylated, conformational isomer, constitutional isomer, stereoisomer, aromatic compound, resonant hybrid structure, combustion, conductivity, IUPAC
Chemical Substances carbon (C), hydrogen (H), isomers of C4H10 (butane, isobutene, 2-methyl propane), methylene radical, ethyl radical, ethyl alcohol, ethylene (aka ethane); butane (C4H8), cis-2-butene, trans-2-butene, propene, propylene, allyl, acetylene, benzene; 1,3 butadiene; gasoline
Applications gasoline automobile engine knocking, octane rating

Prerequisites

This session assumes you’ve completed the Bonding and Molecules module (Session 7 through Session 12), in particular understanding the concepts of

  • hybridization (spx orbitals)
  • different types of bonds (pi bond, double bond, triple bond, resonance)
  • dipole moments

Looking Ahead

This session is the first of six sessions on organic compounds. The next two sessions cover polymers, followed by three sessions applying these concepts to biochemistry.

Learning Objectives

After completing this session, you should be able to:

  • Define what constitutes an organic compound.
  • Apply the naming and drawing conventions to describe different organic compounds.
  • Compare and contrast the three types of hydrocarbons - alkanes, alkenes, and alkynes.
  • Describe the range of molecular structures (e.g. straight vs. branched chains) found among organic compounds.
  • Describe the physical structure of chemical isomers.

Reading

Book Chapters Topics
[Saylor] 24.1, “Functional Groups and Classes of Organic Compounds.” Overview of five organic compound families: hydrocarbons, halogen-containing, oxygen-containing, carboxylic acid derivatives, and nitrogen-containing; common nomenclature
[Saylor] 24.2, “Isomers of Organic Compounds.” Conformational isomers, structural isomers, stereoisomers

Lecture Video

Resources

Lecture Slides (PDF - 1.6MB)

Lecture Summary

This lecture is a single-session introduction to organic chemistry: the chemistry of hydrocarbon compounds containing both carbon (C) and hydrogen (H), plus other elements. The class begins with a review of what makes carbon special: uniquely capable of forming multiple bonds, capable of self-linking, etc. Most of the session is a survey of three types of hydrocarbons: alkanes, alkenes, and alkynes. A hydrocarbon’s properties are determined by characteristics like the type of chain (straight chains vs. branched chains), bond types (pi, double, and triple bonds), and resonance.

Naming and nomenclature conventions receive much attention. Woven throughout the lecture are discussions about:

  • name prefixes (e.g. meth-, eth-) and suffixes (e.g. -ane, -ene)
  • drawing conventions for different bond types
  • IUPAC (International Union of Pure and Applied Chemistry) nomenclature
  • ways to represent different isomers

Among the applications used for illustration, the lecture describes why acetylene is so energetic as a fuel, why graphite is a good electrical conductor, and the chemical basis of gasoline octane ratings.

Homework

No homework is assigned for this session.

For Further Study

As a single-session overview of organic chemistry, this class has limited scope. For instance, it does not introduce every class of organic compounds, leaving aldehydes, ketones, and esters for further study.

People

August Kekulé

Other OCW and OER Content

Content Provider Level Notes
5.12 Organic Chemistry I MIT OpenCourseWare Undergraduate (second-year) The first of a two-semester sequence on organic chemistry, taken after 3.091 or equivalent

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Session Overview

Modules Organic Materials
Concepts polymer architecture, polymer composition, backbone structure, polymer material properties, natural and synthetic polymers
Keywords macromolecule, -mer, monomer, polymerization index, ordered solid, disordered solid, Dalton (atomic mass unit), cooling curve, partial crystallization, homopolymer, copolymer, tacticity, stereoisomerism, isotactic, syndiotactic, atactic, conformality, covalent bridge, crosslinking, elastomer, disulfide bond
Chemical Substances polyethylene (PE), low density polyethelene (LDPE), high density polyethelene (LDPE), polyvinyl chloride (PVC), acrylonitrile butadiene styrene (ABS), natural rubber
Applications Manufactured products of the past 80-100 years, vulcanized rubber

Prerequisites

Before starting this session, you should be familiar with:

Looking Ahead

This session is the first of two devoted to polymers. The polymers sessions are prerequisites for Sessions 30-32 on biochemistry.

Learning Objectives

After completing this session, you should be able to:

  • Define key terms used in polymer chemistry.
  • Describe a polymer’s structure in terms of –mer type ordering, tacticity, and backbone chain configuration.
  • Explain how polymer structure determines material properties, such as flexibility or transparency.
  • Explain how crosslinking produces the characteristic properties of an elastomer.
  • Appreciate the role of polymers in both natural and synthetic materials.

Reading

Book Chapters Topics
[Saylor] 12.8, “Polymeric Solids.” Overview of biological and synthetic polymers

Lecture Video

Resources

Lecture Slides (PDF)

Lecture Summary

Polymer chemistry is an example of applied organic chemistry. Polymers are long chain macromolecules built from repeated smaller chemical structures or ‘-mers.’ They are found widely in the natural world (e.g. proteins, rubber, cellulose) and, increasingly the past century, in synthetic form (e.g. “plastics”). Polymers have been central to many technological innovations that shape the modern world, such as film that enabled the cinema, or the progression of vinyl LPs to polycarbonate CDs and DVDs that enabled recorded music and video distribution.

This lecture begins by describing some basic characteristics of polymers. A polymer’s physical properties are influenced by the degree of ordering in the molecular chains. A comparison of low-density and high-density polyethylene (LDPE and HDPE) reveals that HDPE is molecularly more ordered, with more zones of partial crystallization, and thus more dense and rigid than LDPE. As a result, LDPE is quite flexible and transparent, suited for food wrap; whereas HDPE is optically translucent and more rigid, suited for a milk jug.

The lecture describes polymer molecular architecture in terms of:

  • Comparing pure (homopolymer) vs. mixed or “alloy” compositions (copolymer)
  • Ordering of -mer types (random, alternating, block, graft)
  • Forms of tacticity (isotactic, syndiotactic, atactic, eutactic)
  • Backbone chain configurations (conformality, linear vs. branched chains)
  • Crosslinking with disulfide covalent bridges, to create an elastomer with “rubbery” qualities

The class ends with a quick recounting of the discovery and impact of rubber vulcanization, in which difficult-to-manage raw rubber gum becomes a more useful material by heating and adding sulfide to create crosslinking.

Homework

Problems (PDF)

Solutions (PDF)

Textbook Problems

[saylor] Sections Conceptual Numerical
[Saylor] 24.2, “Isomers of Organic Compounds.” 1, 3, 4, 5 none
[Saylor] 24.5, “Common Classes of Organic Compounds.” 1, 4 none

For Further Study

Culture

The Beatles. “Polythene Pam.” Abbey Road. Apple Records, 1969.

Other OCW and OER Content

Content Provider Level
Polymer Basics DoITPoMS Undergraduate

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Session Overview

Modules Organic Materials
Concepts polymer synthesis by addition and condensation, polymer structure-property relationships, social and culture implications of polymers
Keywords plastics, addition polymerization, radical, condensation polymerization, amide bond, carbonyl group, electrical insulator, thermoplastic, thermoset, crystallization zone, Wallace Carothers, glass transition temperature, recycling, design for environment (DFE)
Chemical Substances polyester, poly(ethylene terephthalate) (PET), silicone, nylon, polyurethane, norbornene, isoprene, Bakelite
Applications polypropylene in lithium ion batteries, soda bottles and fabrics, electrical insulators, recycling and packaging

Prerequisites

Before starting this session, you should be familiar with:

Looking Ahead

The next segment on biochemistry (Sessions 30 through 32) builds upon these introductory polymers sessions.

Learning Objectives

After completing this session, you should be able to:

  • Define, compare and contrast the two forms of polymer synthesis.
  • Summarize the key properties of polymers that determine their suitability for various applications.
  • Explain the relationship between polymer structure and material properties, for instance the effect of crystallization zones on strength and transparency.
  • Describe some factors that affect the recyclability of polymers.

Reading

Book Chapters Topics
[PB-OC] 28, “Synthetic Polymers.” Addition and condensation synthesis; addition (chain growth) and condensation (step growth) polymers; stereochemistry; dienes and rubber; copolymers; structure-property relationships
[JS] 13.1, “Polymerization.” Polymer form as it relates to synthesis; example of collagen
[JS] 13.2, “Structural Features of Polymers.” Polymer structure as it relates to synthesis; example of rubber vulcanization

Lecture Video

Lecture 29: Polymers: Synthesis, Properties & Applications

Resources

Lecture Slides (PDF - 3.0MB)

Lecture Summary

This session focuses on polymer synthesis, the relationships between polymer structure and properties, and the culture implications of polymers.

The two forms of polymer synthesis (addition and condensation) are described in terms of processes, resulting chemical structures and properties, and example materials. Factors affecting recyclability are described, along with defining thermoplastic and thermoset characteristics. Crystallization zones are presented as a means for controlling a polymer’s mechanical performance.

Prof. Sadoway summarizes the properties of polymers as follows:

  • Electrically insulating
  • Transparent to visible light (amorphous material) vs. opaque
  • Chemically inert
  • Strong covalent bonds (thus good for packaging)
  • Low density
  • Solid at room temperature

Polymers have had significant impact on society. The economic and performance improvements introduced by polymer-based substitute materials have transformed many aspects of modern daily life, and led to entirely new products. The class discussion ranges from early 20th century inventions (e.g. nylon, Bakelite), to the late 1960s fascination with plastics, to present-day concerns about recycling and human health impacts.

Homework

Problems (PDF)

Solutions (PDF)

Textbook Problems

[JS] Chapter 13, Sample Problems 13.1 and 13.4

For Further Study

Supplemental Readings

Perree, R. Bakelite: The Material of a Thousand Uses. Amsterdam, NL: Cadre, 1996. ISBN: 9789053492338.

Meikle, J. American Plastic: A Culture History. New Brunswick, NJ: Rutgers University Press, 1995. ISBN: 9780813522357.

Buy at MIT Press Brown, D. E. Inventing Modern America: From the Microwave to the Mouse. Cambridge, MA: MIT Press, 2001. ISBN: 9780262523493. 

Carothers, W.H. Collected Papers of Wallace Hume Carothers on High Polymeric Substances. New York, NY: Interscience Publishers, 1940. ISBN: 9781406759259. [Download or view complete work from Internet Archive]

Furukawa, Y. Inventing Polymer Science: Staudinger, Carothers, and the Emergence of Macromolecular Science. Philadelphia, PA: University of Pennsylvania Press, 1998. ISBN: 9780812233360.

People

Wallace Carothers

Culture

“Mr. Cellophane.” Chicago. DVD. Miramax, 2003.

The Graduate. Directed by M. Nichols. DVD. MGM, 1967.

Other OCW and OER Content

Content Provider Level
Polymer Basics, The Glass Transition in Polymers, Crystallinity in Polymers DoITPoMS Undergraduate
3.063 Polymer Physics MIT OpenCourseWare Undergraduate (elective)
3.064 Polymer Engineering MIT OpenCourseWare Undergraduate (elective)
10.467 Polymer Science Laboratory MIT OpenCourseWare Undergraduate (elective) / Graduate
10.569 Synthesis of Polymers MIT OpenCourseWare Graduate
Introduction to Polymers OpenUniversity UK Masters

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Session Overview

Modules Organic Materials
Concepts amino acids, peptides, proteins
Keywords molecular biology, biomolecule, amino acid, polymer, protein, pH, Brønsted base, amine group, carboxylic acid, alpha carbon, substituent, hydrophilic, chirality, enantiomer, optical activity, polarized light, dextrorotatory, levorotatory, sugars, invert sugar, racemic, teratogenic, zwitterions, Henderson-Hasselbalch equation, protonation, Le Châtelier principle
Chemical Substances thalidomide, Ritalin, trinitrotoluene (TNT)
Applications biology, pharmaceuticals, explosives

Prerequisites

Before starting this session, you should be familiar with:

Looking Ahead

This is the first of three sessions on biochemistry.

Learning Objectives

After completing this session, you should be able to:

  • Understand the common characteristics of amino acids.
  • Highlight the variations among individual amino acids.
  • Describe the role of chirality in amino acid chemistry.
  • Predict the influence of pH on amino acid chemical structure and properties.

Reading

Book Chapters Topics
[Saylor] 12.8, “Polymeric Solids.” Introduction to biological polymers (peptides and proteins)
[Saylor] 24.6, “The Molecules of Life.” Survey of proteins, carbohydrates, lipids, and nucleic acids
[PB-EOC] 17-1 through 17-4 in Chapter 17, “Amino Acids, Peptides, and Proteins.” Overview and configurations of the 20 common amino acids; acid-base properties; isoelectric point pI
[RH] 3, “Amino Acids and the Primary Structures of Proteins.” General structure of amino acids; details on each of the 20 common amino acids; other amino acids and derivatives; ionization of amino acids; creating proteins with peptide bond links

Lecture Video

Resources

Lecture Slides (PDF - 1.2MB)

Lecture Summary

Biochemistry is an integrative topic that connects many prior topics, and governed by the same laws that apply to inanimate matter. Biology – especially at the molecular level - is solid state chemistry. “Mother Nature is a polymer engineer gone wild!”

This lecture starts with amino acids as the building blocks of proteins, and in particular looks at their structure.

  • All amino acids have an sp3 hybridized carbon at their center (aka “alpha carbon”).
  • Three of the four bonds are identical in all amino acids (amine group, lone hydrogen, carboxyl group). The fourth bond is the side chain — “R” or the substituent, i.e. “nature’s choice.”
  • Twenty amino acids comprise all proteins.
  • Nineteen of these twenty amino acids in proteins are chiral.

Prof. Sadoway surveys some amino acid properties, focusing on behavior in water. In an aqueous solution, the amino acid transfers a proton, becoming a zwitterion. Applying the Le Châtelier principle to scenarios of increased and decreased pH, Prof. Sadoway walks through the amino acid chemical responses, concluding: “This is what animates the stuff of life!”

Chirality can have profound implications for the biological response to particular chemicals. The drug thalidomide contained an enantiomer that had unforseen interactions with a human enzyme, leading to a wave of birth defects.

The lecture ends with discussion of the kinetics of organic compounds, specifically the extreme case of explosives. Prof. Sadoway describes the tremendous damage caused by the 1917 Halifax explosion, in which a ship loaded with TNT and other explosive chemicals caught fire in the harbor, causing the largest explosion of the pre-nuclear age.

Homework

Problems (PDF)

Solutions (PDF)

Textbook Problems

[saylor] Sections Conceptual Numerical
[Saylor] 12.8, “Polymeric Solids.” 1 none

For Further Study

Supplemental Readings

Halifax Explosion

Thalidomide

Culture

Michael Jackson. “Man in the Mirror.” Bad. Epic Records, 1987.

Other OCW and OER Content

Content Provider Level Notes
7.01SC Fundamentals of Biology MIT OpenCourseWare Undergraduate (first-year) See Unit 1: Biochemistry

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Session Overview

Modules Organic Materials
Concepts primary, secondary, and tertiary protein structures; protein synthesis
Keywords zwitterion, protonation, deprotonation, titratable, electrophoresis, isoelectric point (pI), isoelectric focusing (IEF), protein synthesis, macromolecule, condensation reaction, peptide bond, disulfide bond, kilopeptide, primary structure, protein sequence, secondary structure, tertiary structure, alpha helix, beta pleated sheet, residue, substituent, conformation, hydrophobic, hydrophilic
Chemical Substances nylon, polyamides, insulin
Applications DNA analysis with electrophoresis gel, laundry detergent

Prerequisites

Before starting this session, you should be familiar with:

Looking Ahead

This session is the second of three sessions on biochemistry, and completes the foundation for the next session’s culminating exploration of the structure of DNA.

Learning Objectives

After completing this session, you should be able to:

  • Sketch the structures of various amino acids as a function of pH.
  • Explain the behavior of the zwitterion.
  • Define and show the significance of the isoelectric point (pI).
  • Understand the basis of primary, secondary, and tertiary structures of proteins.
  • Explain the role of hydrophobic and hydrophilic effects in protein structures.

Reading

Book Chapters Topics
[PB-EOC] 17-6 through 17-12 in Chapter 17, “Amino Acids, Peptides, and Proteins.” Peptide and disulfide bonds; overview of protein structure; primary, secondary, tertiary, and quaternary structures; protein denaturation

Lecture Video

Resources

Lecture Slides (PDF - 1.8MB)

Lecture Summary

The lecture begins with further discussion about zwitterion behavior (introduced in Session 30), with the titration curve used to depict the relationship between degree of protonation and pH. An interesting application of zwitterion behavior is gel electrophoresis, in which an electrified gel column of varying pH allows a mix of different amino acids to be separated and analyzed.

Most of the lecture is devoted to protein structure. The peptide bond is the means of creating long macromolecule chains out of individual amino acids. These chains become a basis of life, as they encode information in different sequences of amino acids. (As an aside, amino acids can be remembered by their 3-letter “airport code” analogs.)

  • Primary structure is the backbone amino acid sequence order.
  • Secondary structure relates to packing, and comes in three forms: 1) the alpha helix, as the chain coils back on itself to maximize hydrogen bonding between “galleries” around the spiral; and 2) the beta pleated sheet, in which hydrogen bonds are maximized between macromolecules; and 3) random structure.
  • Tertiary structure affects the macromolecule’s conformation: a range of interactions between nearby R-groups cause the backbone chain to fold. Mechanisms include covalent (disulfide) and hydrogen bonds, electrostatic attraction, and hydrophobic and hydrophilic interactions.

Homework

Problems (PDF)

Solutions (PDF)

For Further Study

Other OCW and OER Content

Content Provider Level Notes
7.01SC Fundamentals of Biology MIT OpenCourseWare Undergraduate (first-year) See Unit 1: Biochemistry
7.343 Protein Folding, Misfolding and Human Disease MIT OpenCourseWare Undergraduate (elective) Seminar on some biological implications of protein tertiary structure

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Session Overview

Modules Organic Materials
Concepts denaturing proteins, lipids and their self assembly into bilayers, nucleic acids, DNA, and encoding information for protein synthesis, history of the discovery of DNA double helix structure
Keywords denaturing, disulfide bond, triglyceride, zwitterion, aliphatic compound, cell wall, nucleotide, amphipathic, amine, base pairs, codon, Laue pattern, alpha helix, Oswald Avery, Erwin Chargaff, Rosalind Franklin, Francis Crick, James Watson, Maurice Wilkins, x-ray crystallography, biological replication
Chemical Substances fats, oils, cholesterols, hormones, phospholipid, phosphatide, phosphatidylethanolamine, ribose, 2-deoxyribose, DNA, RNA, guanine, cytosine, adenine, thymine
Applications cooking food, pickling food, hair styling, laundry detergent

Prerequisites

Before starting this session, you should be familiar with:

  • Prior sessions in this Organic Materials module (starting with Session 27), and particularly the fundamentals of protein structure as described in Session 31
    • Composition (primary structure of amino acid chains)
    • Packing (secondary structures of alpha helix, beta pleated sheet, and random coil),
    • Conformation (tertiary structure or folding caused by R-group interactions)
  • X-ray crystallography, as introduced in Session 18: X-Ray Diffraction Techniques

Learning Objectives

After completing this session, you should be able to:

  • Describe several methods of denaturing proteins and provide practical examples of each method.
  • List the characteristics and properties of lipids.
  • List the characteristics and properties of nucleic acids.
  • Draw the chemical structure of DNA, and indicate the role of hydrogen bonding in forming the structure.
  • Describe how the chemical structure of DNA carries information and supports replication.

Reading

Book Chapters Topics
[Saylor] 24.6, “The Molecules of Life.” Overview of lipids and nucleic acids
[PB-EOC] 20-1 through 20-5 in Chapter 20, “Lipids.” Fatty acids; waxes; fats and oils; soaps, detergents, and micelles; phospholipids
[PB-EOC] 21-2, 21-5, and 21-8 in Chapter 21, “Nucleosides, Nucleotides, and Nucleic Acids.” Overview of nucleic acids; DNA and heredity; biosynthesis of proteins via translation

Lecture Video

Resources

Lecture Slides (PDF - 4.1MB)

Lecture Summary

After a quick review of the previous session, Prof. Sadoway begins with a discussion of denaturing proteins – disrupting protein secondary and tertiary structures. Examples of the denaturing process include:

  • Changing temperature (frying an egg)
  • Changing pH (pickling food)
  • Introducing oxidizing/reducing agents to rearrange disulfide bonds (hair styling)
  • Introducing detergents, which destabilize hydrophobic pockets

Next, the lecture introduces lipids.

  • Lipids are defined by their properties, not by their chemical composition; they are soluble in solvents of low polarity.
  • Examples include fats, oils, cholesterols, and hormones. Some lipids have a hydrophilic head and hydrophobic tail; arranged in two layers, tail to tail, they produce a lipid bilayer capable of self-assembly.
  • The lipid bilayer is the basis of cell walls. It includes integral proteins that change conformation in response to certain conditions, creating dynamic physical responses in the cell wall – once again, chemistry as the animating force of life.

After lipids, the lecture proceeds with the structure of nucleic acids.

  • Nucleic acids carry information that directs metabolic activity, including replication.
  • They are macromolecules whose structural unit is the nucleotide, consisting of three building blocks: a sugar (ribose or 2-deoxyribose), a phosphate acting as a bridge and a ‘spacer,’ and an amine group (one from the set AGCU for RNA, and AGCT for DNA).
  • The amine groups combine in pairs (A-T or C-G), and intermolecular spacing and hydrogen bonds lead to the double helix structure.
  • The order of A-T and C-G pairs (“letters”) in chains creates “word” sequences of the genetic code.

This lecture ends with a history of the discovery of DNA’s double helix structure: early insights by Oswald, Chargaff’s rule, Franklin’s x-ray crystallography experiment and its subsequent controversial use by Watson and Crick.

Homework

Problems (PDF)

Solutions (PDF)

For Further Study

Supplemental Readings

Watson, J. D., and F. H. C. Crick. “Molecular Structure of Nucleic Acids.Nature 171 (1953): 737-738. (PDF)

Franklin, R., and R. G. Gosling. “Molecular Configuration in Sodium Thymonucleate.Nature 171 (1953): 740-741. (PDF)

Judson, Horace Freeland. The Eighth Day of Creation: Makers of the Revolution in Biology. 25th anniversary edition. Woodbury, NY: Cold Spring Harbor Laboratory Press, 1996. ISBN: 9780879694784.

Maddox, Brenda. Rosalind Franklin: The Dark Lady of DNA. New York, NY: HarperCollins, 2002. ISBN: 9780060184070.

Watson, James D. The Double Helix: A Personal Account of the Discovery of the Structure of DNA. New York, NY: Touchstone/Simon & Schuster, 2001 (original publication 1968). ISBN: 9780743216302.

People

Oswald Avery

Erwin Chargaff

Francis Crick, James Watson, Maurice Wilkins1962 Nobel Prize in Physiology or Medicine

Rosalind Franklin

Culture

“It’s a Chemical Reaction, That’s All.” Music and lyrics by Cole Porter. From Silk Stockings. Fred Astaire, Cyd Charisse; directed by Rouben Mamoulian and Roy Mack. Original film release MGM, 1957. DVD, Warner Home Video, 2003.

Hank Ballard and the Midnighters. “The Twist.” (B-side with “Teardrops on Your Letter.”) Original release: King Records, 1959. Available on many reissue compilations, such as Their Very Best: Hank Ballard & The Midnighters. K-Tel, 2007.

Other OCW and OER Content

Content Provider Level Notes
7.01SC Fundamentals of Biology MIT OpenCourseWare Undergraduate (first-year) See Unit 1: Biochemistry

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This self-assessment page completes the Organic Materials module, and covers material from the following sessions.

On this page are two weekly quizzes and solutions; relevant exam problems and solutions from the 2009 class; help session videos that review selected solutions to the exam problems; and supplemental exam problems and solutions for further study.

Weekly Quiz and Solutions

These short quizzes are given approximately once for every three lecture sessions. You should work through the quiz problems in preparation for the exam problems.

Polymers Quiz

Biomaterials Quiz

Exam Problems and Solutions

These exam problems are intended for you to demonstrate your personal mastery of the material, and should be done alone, closed-book, with just a calculator, the two permitted reference tables (periodic table, physical constants), and one 8 1/2" x 11" aid sheet of your own creation.

After you’ve taken the exam, watch the help session videos below for insights into how to approach some of the exam problems.

Exam Help Session Videos

In these videos, 3.091 teaching assistants review some of the exam problems, demonstrating their approach to solutions, and noting some common mistakes made by students.

Clip 1: Final Exam, Problem 5

Clip 2: Final Exam, Problem 13

Supplemental Exam Problems and Solutions

These additional exam problems from prior years’ classes are offered for further study.

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Course Info

As Taught In
Fall 2010
Learning Resource Types
Course Introduction
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Recitation Videos
Exams
Problem Sets
Exam Materials