Midterm Review

Unit 1: Method, Measurement, & Problem Solving

I. What is Chemistry?

A. Definition of Chemistry
   1. Chemistry is the study of all matter and the changes it can undergo.
   2. Chemistry is referred to as the central science due to its overlapping nature with various other scientific disciplines. B. Definition of Chemical
   1. A chemical is any substance with a definite composition.

II. The Scientific Method

A. Description of the Scientific Method
   1. The Scientific Method is a systematic approach used to gather knowledge.
   2. Steps involved in the Scientific Method:
      1. Observation
      2. Question
      3. Hypothesis
      4. Experiment
      5. Conclusion
   3. Note: All hypotheses must be testable to qualify as valid.
   4. The flow of scientific exploration typically moves from conducting many experiments, leading to the formulation of Natural Laws (descriptions of how nature behaves) and subsequently to Theories (explanations of why nature behaves in that manner). B. Factors in an Experiment
   1. Independent Variable: The variable that is manipulated by the experimenter; plotted on the x-axis.
   2. Dependent Variable: The variable that responds to changes in the independent variable; plotted on the y-axis.
   3. Experimental Control: An aspect of the experiment that remains unchanged or unmanipulated, used for comparison purposes.

III. Scientific Notation

A. Purpose and Use
   1. Scientific notation is a method used to express very large or very small numbers in a concise and manageable form.
B. Conversion Table
   | Power of 10 | Equivalent Number | Reason |
   |--------------|-------------------|---------------------------|
   | 10^0 | 1 | Any number raised to the 0 power equals 1 |
   | 10^1 | 10 | 10 * 1 |
   | 10^2 | 100 | 10 * 10 |
   | 10^3 | 1000 | 10 * 10 * 10 |
   | 10^5 | 100,000 | 10 * 10 * 10 * 10 * 10 |
   | 10^(-1) | 0.1 | 1/10 |
   | 10^(-3) | 0.001 | 1/1000 |
   | 10^(-5) | 0.00001 | 1/100,000 |

IV. Metric System

A. International System of Measurements (SI)
   1. The standard metric system adopted by all scientists, based on multiples of 10.
B. Metric Units in Chemistry
   | Measurement | Unit | Instrument | Equation |
   |--------------|-------|-------------------|------------------------|
   | Mass | gram | scale | —- |
   | Length | meter | meterstick | —- |
   | Time | second| watch | —- |
   | Temperature | kelvin/celsius | thermometer | —- |
   | Quantity | mole | —- | —- |
   | Area | m²/cm² | meterstick | Length * Width |
   | Volume | m³/cm³ | graduated cylinder | Length * Width * Height |
   | Density | g/cm³ | —- | D = M/V |
   | Pressure | atm/kPa | barometer | Force/Area |
   | Energy | Cal or J | calorimeter | —- |
C. Prefixes in the Metric System
   | Prefix | Abbreviation | Meaning | Scientific Notation |
   |--------------|----------------|----------------|---------------------|
   | giga- | G | 1,000,000,000 | 1 * 10^9 |
   | mega- | M | 1,000,000 | 1 * 10^6 |
   | kilo- | k | 1,000 | 1 * 10^3 |
   | hecto- | h | 100 | 10 * 10^2 |
   | deka- | D, da, dk | 10 | 1 * 10 |
   | Base Unit | meter/liter/gram | 1 | 1 |
   | deci- | d | 0.1 | 1 * 10^(-1) |
   | centi- | c | 0.01 | 1 * 10^(-2) |
   | milli- | m | 0.001 | 1 * 10^(-3) |
   | micro- | μ | 0.000001 | 1 * 10^(-6) |
   | nano- | n | 0.000000001 | 1 * 10^(-9) |
   | pico- | p | 0.000000000001 | 1 * 10^(-12) |

V. Uncertainty in Measurement

A. Causes of Uncertainty
   1. All measuring instruments contain some level of error.
   2. Measurement inherently involves estimations.
B. Estimating with a Scale
   - You should estimate one digit more than what the measuring instrument displays.
   - Use ± to signify uncertainty.
C. Definitions
   1. Precision: Refers to the consistency of measurement results under similar conditions.    2. Accuracy: Indicates how close a measured value is to the actual or true value.
   3. The finer the increments of measurement an instrument has, the higher its potential accuracy.
   4. Precision is determined by the instrument, while accuracy is influenced by the operator's skill and methodology in measurement.

VI. Significant Digits

A. Important Aspects of Significant Digits
   1. Significant digits encompass all measured digits and estimated digits.
   2. Apply the Atlantic-Pacific rule to determine the count of significant digits.
B. Rules for Operations
   1. Addition and Subtraction:
      - Sum or subtract numbers normally.
      - The result must reflect the number with the maximum uncertainty (therefore the least number of decimal places).    2. Multiplication and Division:
      - Perform the multiplication or division as per usual.
      - Round the result to match the number of significant digits in the quantity with the fewest significant digits.

VII. Important Formulas

A. Percent Error
   1. Definition: Percent error compares an experimentally obtained measurement with an accepted value. It is always expressed as a positive percentage.
   2. Formula:
    ext{% error} = rac{| ext{measured value} - ext{accepted value}|}{| ext{accepted value}|} imes 100 ext{%}
B. Density Calculation
   1. Formula:
extDensity=extmassextvolumeext{Density} = \frac{ ext{mass}}{ ext{volume}}
   2. Rearrangement:
M=VDM = VD
V=MDV = \frac{M}{D}

VIII. Dimensional Analysis (The Factor-Label Method)

A. Description
   1. Dimensional analysis uses unit equalities to transition between units.
   2. Unit equality is defined as an equation connecting different units (for example: 12 in = 1 ft, 60 sec = 1 min, 1 kg = 1000 g).
B. Conversion Factors
   1. Conversion factors derived from unit equalities are always equivalent to “1”.
   2. Example: 1000 m/1 km or 1 km/1000 m represent conversion factors.
   3. The conversion factor serves as a definition; thus, it holds infinite precision, resulting in the answer retaining the same significant digits as the provided value.
C. Useful Chemistry Conversion Factors
   - 1 inch = 2.54 centimeters
   - 1 foot = 12 inches
   - 1 mile = 5280 feet
   - 1 minute = 60 seconds
   - 1 hour = 60 minutes
   - 1 standard atmosphere = 760 millimeters of mercury
   - 1 standard atmosphere = 101,325 pascal
   - 1 calorie = 4.184 Joules
   - 1 gallon = 3.785 liters

Unit 2: Energy & Matter

I. Energy

A. Definition of Energy
   1. Energy is defined as the capacity to do work or produce heat.
B. Types of Energy
   1. There are 7 primary forms of energy which include: mechanical, thermal, radiant, sound, electrical, chemical, and nuclear energy.
   2. Kinetic Energy: This is the energy associated with motion (examples: thermal energy and mechanical energy).
   3. Potential Energy: This refers to stored energy which is influenced by the position of an object (examples: electrical potential energy and chemical potential energy).
   4. Energy Transfer Examples: Energy can be transferred from a system to its surroundings (example: In photosynthesis, light energy is converted to chemical energy).
   5. Classifications based on energy change:
      - Endothermic Changes: Processes that absorb energy (example: heating food in a hot pocket).
      - Exothermic Changes: Processes that release energy (example: explosions). C. Measuring Energy
   1. The common unit for measuring energy is the calorie, defined as the amount of heat required to raise 1 gram of water by 1 degree Celsius (fundamentally equivalent to one calorie = 1g).
   2. The SI unit for energy is Joule (J). D. Law of Conservation of Energy
   1. This law states that energy can neither be created nor destroyed; it merely transitions from one form to another. E. Temperature
   1. Energy can be transferred in the form of heat.
   2. Temperature serves as a measure of heat or kinetic energy, equating to the average speed of particle movement.
   3. Common Temperature Scale Conversions:
   | Fahrenheit | Celsius | Kelvin |
   |-------------|---------|--------|
   | 212 | 100 | 373 |
   | 98.6 | 37 | 310 |
   | 70 | 20 | 293 |
   | 32 | 0 | 273 |
   | -459.67 | -273 | 0 |
          4. Conversion formulas:
℃=K−273℃ = K - 273
K=℃+273K = ℃ + 273
F. Absolute Zero
   1. The concept of absolute zero corresponds to the lowest possible temperature (−273℃ or 0 K). At absolute zero, all particle motion ceases, leading to zero kinetic energy.

II. Matter

A. Definition of Matter
   1. Matter is any substance that possesses mass and volume.
   2. Volume is defined as the amount of space an object occupies.
      - States defining volume include solid and liquid; additionally, gases/vapors and plasmas are also recognized.    3. Mass is defined as the quantity of matter within a substance and remains constant throughout.       - Three states regarding mass include:
         - Solid: Holds a definite shape and has a definite volume.
         - Liquid: Does not maintain its own shape, yet occupies a defined volume.
         - Gas/Vapor: Lacks a defined shape and volume.    4. Weight represents the force exerted by gravity on a mass. The weight of an object varies depending on its location. B. Properties of Matter
   1. Physical Properties:
      - These can be observed using sensory perception (examples: density, color, melting point).
      - Characteristics that can be identified without changing the identity of the substance are classified as physical properties.
      - Physical changes do not alter the substance's identity (such as cutting or changing state).    2. Chemical Properties:
      - Refers to a substance's capability to react with another (for instance, flammability).
      - Properties that can only be observed through altering a substance's identity.    3. Intensive Properties:
      - These depend on the type of matter (examples: solid, liquid, gas, plasma).    4. Extensive Properties:
      - Vary based on the amount of matter present (examples: mass, volume, length, weight).

III. States of Matter

A. Comparative Overview of States
   | State | Shape | Volume | Movement | Structure |
   |--------|-----------|----------|------------------|---------------------|
   | Solid | Definite | Definite | Vibrational (slow)| Highly organized |
   | Liquid | Indefinite| Definite | Translational (medium)| Fluid |
   | Gas | Indefinite| Indefinite| Translational (fast)| Dispersed randomly |
B. Kinetic Theory of Matter
   1. Gases possess the greatest kinetic energy among the states of matter.
   2. Two essential factors influencing a substance's state are: speed of particles and distance between them.
   3. These factors additionally affect the attractive forces between particles.
   4. Phase changes occur when these attractive forces are overcome.
   5. The overall kinetic energy (temperature) remains constant until a complete state change is achieved. C. Changes in Matter
   1. Physical Changes:
      - Physical changes do not alter a substance's identity; typically involve changes in appearance (for example, cutting or dyeing).    2. Chemical Changes:
      - These changes alter the identity of a substance, leading to new properties and compositions.       - Examples of chemical reactions include burning and oxidation.       - Signs of chemical changes may include gas release (bubbles or smoke), color changes (can be physical or chemical), formation of precipitates (insoluble solids precipitating from solution), and temperature fluctuations. D. Law of Conservation of Matter
   1. The law asserts that matter is neither created nor destroyed; rather, it transitions from one form to another. E. Classification of Matter
   1. Pure Substances:
      - Unique sets of physical and chemical properties.
      - Elements: The fundamental substances composed of atoms, represented by one or two-letter symbols.
        - Elements cannot be separated into simpler substances.
      - Compounds: Substances composed of two or more different atoms that are chemically bonded in a fixed ratio and are represented by formulas.
   2. Mixtures:
      - Heterogeneous Mixtures: Different components are visually identifiable and they separate upon standing (for example: salad dressing, chocolate chip cookies).
      - Homogeneous Mixtures: Components are uniformly distributed and remain mixed (for example: Kool-Aid, gold jewelry). F. Separation Techniques for Mixtures
   1. Heterogeneous Mixtures can be separated using methods such as filtration, where the material left on the filter paper is referred to as the residue while the liquid that passes through is termed the filtrate (for example: separating sand from water).    2. Homogeneous mixtures can be separated through:
      - Distillation: Separating liquids based on boiling points, where the remaining material is called the residue and the distillate is the liquid that passes through.       - Crystallization: Involves evaporation leading to crystallization of the solute from the solution.       - Chromatography: Utilizes solubility differences to separate mixtures, often utilized in the separation of pigments.    3. Compounds:
      - Can only be separated into their elemental components through decomposition techniques like electrolysis, which breaks down compounds (example: decomposing water into oxygen and hydrogen).

Unit 3: Atomic Structure

I. Early Models of the Atom

A. Historical Contributions
   1. Democritus (450 B.C.): Proposed that matter consists of tiny indivisible particles termed atoms.
      - Definition of atoms: The smallest indivisible unit of an element that retains the chemical properties of that element.
   2. Antoine Lavoisier (A.D. 1780): Formulated the Law of Conservation of Matter; recognized as the father of chemistry.
   3. Joseph Proust (A.D. 1799): Established the Law of Definite Proportions, stating that a compound always contains the same elements in the same proportions by mass.
   4. John Dalton (A.D. 1803): Proposed the Atomic Theory of Matter, comprising the following tenets:
      1. All elements are composed of atoms.
      2. All atoms of a given element are identical in mass and properties.
      3. Atoms cannot be subdivided, created, or destroyed in chemical reactions.       4. Compounds are combinations of different types of atoms in fixed proportions.

II. Atomic Structure

A. Electrification Insights
   1. Benjamin Franklin (1790): Suggested the relation of atom structure to electricity, observing that:
      - Like charges repel each other, while opposite charges attract (negative with positive).    2. Cathode Ray Tube: An evacuated glass tube in which a beam of electrons flows from the cathode (negative electrode) to the anode (positive electrode).    3. J.J. Thomson (1897): Demonstrated that cathode rays consist of electrons, which are negatively charged particles with mass.    4. Henri Becquerel (1896): Discovered radioactive elements using uranium ore, leading to the understanding of radioactivity.
      - Definition of radioactivity: The spontaneous emission of matter and energy from a sample.    5. Marie and Pierre Curie (1903): Shared the Nobel Prize with Becquerel for discovering radioactive elements such as radium and polonium.
   6. Ernest Rutherford (1903): Identified types of radioactive decay:
      1. Alpha (α) particles
      2. Beta (β) particles
      3. Gamma (γ) rays    7. Rutherford’s Gold Foil Experiment (1909): Resulted in discerning a small, dense, positive nucleus within the atom, establishing that much of the atom is empty space.

III. Models of the Atom

A. Evolution of Atomic Models
   1. J.J. Thomson’s Plum Pudding Model (1897): Visualized the atom as a sphere with diffuse positive charge containing negatively charged electrons.    2. Ernest Rutherford’s Nuclear Model (1909): Conceptualized an atom featuring a small, dense nucleus (protons) with electrons orbiting outside.    3. Niels Bohr's Solar System Model (1913): Proposed that electrons occupy defined orbits around the nucleus, a model considered inaccurate due to oversimplification.
   4. Wave or Electron Cloud Model (1924-present): Employing quantum mechanics, posits that electrons exist within a probability region rather than defined orbits. B. Subatomic Particles
   1. Atoms are composed of three main subatomic particles:
      | Particle | Mass (amu) | Location | Charge |
      |-----------|------------|--------------|---------|
      | Proton | 1 | Nucleus | Positive|
      | Neutron | 1 | Nucleus | Neutral |
      | Electron | 0 | Outside nucleus| Negative|
   2. John Moseley (1914): Determined that each atom is characterized by a unique proton count (atomic number), maintaining that atoms are electrically neutral by having equal numbers of protons and electrons.    3. Mass Number: Defined as the sum of protons and neutrons within the atom's nucleus.    4. Ions: Formed when atoms gain or lose electrons.
      - The charge is calculated as:
extCharge=extNumberofProtons−extNumberofElectronsext{Charge} = ext{Number of Protons} - ext{Number of Electrons}
   - Positively charged ions are termed cations; negatively charged ions are called anions.    5. Isotopes: Atoms having identical proton counts yet differing in neutron numbers.
      - Isotopic Notation: This notation conveys isotopes of an element.
      - Format:
   | Isotope | Protons | Neutrons | Mass Number | Electrons | Isotopic Notation |
   |------------|---------|----------|--------------|-----------|-------------------|
   | Carbon-12 | 6 | 6 | 12 | 6 | 12<em>6C^{12}<em>{6}C |    | Carbon-13 | 6 | 7 | 13 | 6 | 13</em>6C^{13}</em>{6}C |
   | Carbon-14 | 6 | 8 | 14 | 6 | 614C^{14}_{6}C |
   6. Atomic Mass: Expressed in atomic mass units (amu), one amu corresponds to half the mass of a carbon-12 atom.    7. Average Atomic Mass: The weighted average of all isotopes of an element calculated using:
    ext{Average Atomic Mass} = ext{(mass}_1 imes ext{%}_1) + ext{(mass}_2 imes ext{%}_2)

IV. Reading the Periodic Table

A. Information Content
   1. Each square on the periodic table includes:
      - Atomic number (protons)
      - Symbol of the element
      - Name of the element
      - Average atomic mass
B. Table Organization
   1. Vertical Columns: Represent groups or families (18 total).
   2. Horizontal Rows: Represent periods (7 total).
C. Elemental Families and Categories
   1. Metals:
      - Properties: Efficient conductors of heat/electricity, dense, malleable, ductile, and generally possessing high melting points.
   2. Nonmetals:
      - Properties: Brittle when solid, non-lustrous, poor conductors, and do not react with acids.    3. Metalloids (Semimetals):
      - Display properties intermediary between metals and nonmetals.

Unit 4: The Electron

I. Waves

A. Characteristics of Waves
   1. Amplitude: The height of a wave; increased amplitude correlates with increased intensity.
   2. Wavelength (λ): Measure from crest to crest or trough to trough, expressed in nanometers (1 * 10^-9 m).
   3. Frequency (ν): The count of cycles a wave passes a fixed point per second, denoted in Hertz (Hz); for example, FM radio identified as 93.3 megahertz equals 93.3 * 10^6 Hz.    4. Speed of Light: Constant speed at 3.0 * 10^8 m/s or 186,000 miles/second.    5. Relationship equations:
   - λ=cνλ = \frac{c}{ν}
   - ν=cλν = \frac{c}{λ}
     (illustrating inversely proportional relationship).

II. Quantum Theory

A. Planck’s Hypothesis (Max Planck, 1900)
   1. Energy is absorbed or emitted in discrete packets known as quanta.
   2. Energies are quantized.    3. Energy relates to frequency via:
E=hνE = hν
   (demonstrating direct proportionality between energy and frequency). B. Electromagnetic Radiation
   1. A quantum of light is termed a photon.
   2. Light exhibits wave-like behavior as it travels through space while displaying particle characteristics during interactions.    3. This dual nature of light underscores its complex behavior. C. Atomic Emission Line Spectra
   1. Unique spectra showcasing distinct colors or wavelengths of light exists for every element, functioning like a fingerprint.

III. Bohr Model of Hydrogen (1911)

A. Bohr’s Contributions
   1. Stated that an electron's energy is quantized, positing specific orbits corresponding to distinct energy levels.    2. Quantum numbers (n) denote each energy level, where n=1 represents the ground state (lowest energy level).
   3. Electrons leap to higher energy states (excited states) upon energy absorption.
   4. Light is emitted as electrons revert from higher to lower energy levels.

IV. Heisenberg’s Uncertainty Principle (1927)

A. Principle's Claims
   1. It states that one cannot simultaneously know both the position and momentum (speed, direction, mass) of a moving particle precisely.
   2. The future position of particles cannot be predicted due to inherent uncertainties in quantum mechanics.
B. Quantum Mechanical Model
   1. This model integrates previous theories and frames the electron as a wave possessing quantized energy.    2. Exact positions and momenta are indeterminable, but probabilities of electron locations are determinable, leading to the concept of electron density.    3. Atomic Orbitals
      - Defined as regions around the nucleus where an electron of specific energy is likely found; differing from Bohr's fixed orbits.       - Noted features of orbitals include shapes, sizes, and energy characteristics.
      - A three-dimensional representation of the electron’s probable presence is envisioned within orbitals, where it is likely found 90% of the time.       - Higher principal levels yield larger orbitals that accommodate more electrons.

V. Quantum Numbers

A. Quantum Addressing
   1. Quantum numbers compose a hierarchical structure to identify an electron's location:
      1. Principal Quantum Number (n): Denotes the energy level, ranging from 1-7.
      2. Sublevel Shape: Defined by shapes (s, p, d, f).
      3. Orbital Designation: Specific configurations in space (example: px, py, pz).
      4. Spin: The directional spin of an electron (clockwise or counterclockwise).
   2. As the principal quantum number increases, so does the number of sublevels.
   3. Orbital capacity varies:
      - S-sublevel: 1 orbital, max 2 electrons.
      - P-sublevel: 3 orbitals, max 6 electrons.
      - D-sublevel: 5 orbitals, max 10 electrons.
      - F-sublevel: 7 orbitals, max 14 electrons. B. Pauli Exclusion Principle
   1. Proclaims that each orbital can hold a maximum of 2 electrons, necessitating opposite spins for both electrons. C. Hund’s Rule
   1. States that electrons will occupy separate orbitals first before pairing up in occupied orbitals. D. Electron Configurations
   1. Explains the distribution of electrons among orbitals; demonstrating their locations and energy.
   2. According to the Aufbau principle, electrons occupy the lowest energy orbitals first.

Ch 5 & 6: Formulas and Naming Notes

I. Types of Chemical Bonds

A. Ionic Bonding
   1. Ionic bonds form through the electrostatic attraction between positively charged ions (cations) and negatively charged ions (anions), resulting in neutral compounds.    2. Properties of Ionic Compounds:
      - Typically possess high melting points.       - Soluble in water, forming electrolytic solutions that conduct electricity.       - Characterized by significant electronegativity differences between constituent elements.       - Often formed between metals (which lose electrons) and nonmetals (which gain electrons).    3. The Octet Rule: Atoms gain or lose electrons to achieve full valence electron shells (an octet).
   4. Electrons are transferred during the ionic bond formation (Example: Sodium (Na, atomic number 11) donates one electron, becoming Na+Na^{+}; Chlorine (Cl, atomic number 17) accepts that electron, becoming Cl−Cl^{-}, resulting in a stable octet).    5. Types of Ionic Compounds:
      - Binary Compounds: Composed of one cation and one anion; examples include Mg2+Mg^{2+} and O2−O^{2-} forming MgOMgO, or Ca2+Ca^{2+} and Cl−Cl^{-} forming CaCl2CaCl_{2}.
      - Tertiary Compounds: Composed of polyatomic ions—groups of bonded atoms containing a charge (example: Ammonium NH4+NH_{4}^{+} and Sulfate SO42−SO_{4}^{2-} forming Ammonium Sulfate, (NH4)<em>2SO</em>4(NH_{4})<em>{2}SO</em>{4}).    6. Polyvalent Metals: Transition metals may form multiple types of cations; such ions are designated with Roman numerals for differentiation (for instance: Fe2+Fe^{2+} is iron(II) and Fe3+Fe^{3+} is iron(III))). An example is FeCl2FeCl_{2} (iron(II) chloride) and FeCl3FeCl_{3} (iron(III) chloride).

B. Covalent Bonding
   1. Covalent bonds result from electron pair sharing between two nonmetals, characterized by low electronegativity differences.    2. Molecules: Groups of atoms interconnected by covalent bonds.
   3. Naming Covalent Compounds:
      - Utilizes prefixes indicating atom numbers: 1) Mono, 2) Di, 3) Tri, 4) Tetra, 5) Penta, 6) Hexa, 7) Hepta, 8) Octa, 9) Nona, 10) Deca.
      - The names conclude with “-ide.”       - The more electronegative element appears last in the name.       - A prefix precedes the first element only if multiple atoms are present (the prefix mono is never applied to the first atomic symbol).       - A prefix is always assigned to the second element (example: Water is identified as H2OH_{2}O, named dihydrogen monoxide).    4. Types of Formulas for Covalent Bonding
      - Molecular Formula: Illustrates the number of atoms writing the compound (examples: CH4CH_{4} and H2OH_{2}O).       - Structural Formula: Graphically depicts how atoms bond to each other, employing two dots for unshared electron pairs and dashes for covalent bonds representing shared electrons.       - Empirical Formula: Indicates the lowest whole number ratio of elements present in the compound (example: Benzene C6H6C_{6}H_{6} simplifies to hexacarbon hexahydride).       - Multiple Bonds: Bonds facilitate achieving the octet rule:
         - Single Bonds: Share 1 pair of electrons (example: Methane).
         - Double Bonds: Share 2 pairs of electrons (example: oxygen).
         - Triple Bonds: Share 3 pairs of electrons (the strongest bond, found in nitrogen and related compounds).    5. Properties of Covalent Bonds:
      - Typically exhibit low melting points and brittleness while being poor conductors of electricity.
      - Polar Bonds: Occur between elements with significant electronegativity variations, leading to uneven electron sharing.       - Nonpolar Bonds: Feature equal electron sharing between the bonded atoms.