Comprehensive Chemistry Notes: Units, Matter, Atomic Structure, Nomenclature, and Stoichiometry

The Study of Chemistry and the Scientific Method

• Definition of Chemistry: Chemistry is the study of matter and the changes it undergoes.

• Applications of Chemistry in the 21st Century:

  • Health and Medicine: Development of sanitation systems, surgery with anesthesia, vaccines and antibiotics, and gene therapy.
  • Energy and the Environment: Optimization of fossil fuels, solar energy capture, and nuclear energy utilization.
  • Materials and Technology: Development of polymers, ceramics, liquid crystals, potential room-temperature superconductors, and molecular computing.
  • Food and Agriculture: Creation of genetically modified crops, "natural" pesticides, and specialized fertilizers.

• The Scientific Method: A systematic approach to research and problem-solving.

  • Hypothesis: A tentative explanation for a set of observations.
  • Law: A concise statement of a relationship between phenomena that is always the same under the same conditions (e.g., Force = mass $\times$ acceleration, or \mathbf{F} = m\mathbf{a}).
  • Theory: A unifying principle that explains a body of facts and/or those laws that are based on them (e.g., Atomic Theory).
  • Iterative Cycle: Scientific inquiry progresses through a continuous cycle of Observation, Representation, and Interpretation.

Classification, States, and Properties of Matter

• Classification of Matter:
  • Matter: Anything that occupies space and has mass.
  • Substance: A form of matter that has a definite composition and distinct properties.
  • Mixture: A combination of two or more substances in which the substances retain their distinct identities.
    • Homogeneous Mixture: The composition of the mixture is uniform throughout (e.g., dissolved sugar in water).
    • Heterogeneous Mixture: The composition is not uniform throughout (e.g., sand mixed with iron filings).
    • Separation of Mixtures: Physical methods can be used to separate a mixture into its pure components (e.g., using a magnet to separate iron filings from sand, or distillation to separate liquid mixtures).
  • Element: A substance that cannot be separated into simpler substances by chemical means.
    • Total identified elements: $118$
    • Naturally occurring elements on Earth: $82$ (e.g., gold, aluminum, lead, oxygen, carbon)
    • Synthetic elements created by scientists: $36$ (e.g., technetium, americium, seaborgium)
  • Compound: A substance composed of atoms of two or more elements chemically united in fixed proportions. Compounds can only be separated into their pure elemental components by chemical means.

• The Three Common States of Matter:
  • Solid: Possesses a rigid structure with particles held tightly in fixed positions; maintains a definite shape and volume.
  • Liquid: Particles are close together but free to move past one another; maintains a definite volume but takes the shape of its container.
  • Gas: Particles are separated by distances large compared to their sizes; possesses neither a definite shape nor a definite volume, expanding to fill its container.

• Types of Changes and Properties:
  • Physical Change: Does not alter the composition or identity of a substance (e.g., ice melting, sugar dissolving in water).
  • Chemical Change: Alters the composition or identity of the substance(s) involved (e.g., hydrogen burning in air to form water, iron rusting to form iron(III) oxide).
  • Extensive Property: Depends on how much matter is being considered (e.g., mass, length, volume).
  • Intensive Property: Independent of how much matter is being considered (e.g., density, temperature, color).

• Mass vs. Weight:
  • Mass: A measure of the quantity of matter. The SI base unit of mass is the kilogram ($\text{kg}$). 1\n\text{kg} = 1000\text{ g} = 1 \times 10^3\text{ g}.
  • Weight: The force that gravity exerts on an object. $\text{Weight} = c \times \text{mass}$. A $1\text{ kg}$ bar weighs $1.0\text{ kg}$ force equivalent on Earth, but only $0.1\text{ kg}$ force equivalent on the Moon due to the lower gravitational pull.

Measurements, SI Units, and Handling Numbers

• SI Base Units:

  • Length: Meter ($\text{m}$)
  • Mass: Kilogram ($\text{kg}$)
  • Time: Second ($\text{s}$)
  • Electrical current: Ampere ($\text{A}$)
  • Temperature: Kelvin ($\text{K}$)
  • Amount of substance: Mole ($\text{mol}$)
  • Luminous intensity: Candela ($\text{cd}$)

• Prefixes Used with SI Units:

  • Peta- ($\text{P}$): $1,000,000,000,000,000 = 10^{15}$ (Example: $1\text{ Petameter (Pm)} = 1 \times 10^{15}\text{ m}$)
  • Tera- ($\text{T}$): $1,000,000,000,000 = 10^{12}$ (Example: $1\text{ Terameter (Tm)} = 1 \times 10^{12}\text{ m}$)
  • Giga- ($\text{G}$): $1,000,000,000 = 10^9$ (Example: $1\text{ Gigameter (Gm)} = 1 \times 10^9\text{ m}$)
  • Mega- ($\text{M}$): $1,000,000 = 10^6$ (Example: $1\text{ Megameter (Mm)} = 1 \times 10^6\text{ m}$)
  • Kilo- ($\text{K}$): $1,000 = 10^3$ (Example: $1\text{ Kilometer (km)} = 1 \times 10^3\text{ m}$)
  • Deci- ($\text{d}$): $1/10 = 10^{-1}$ (Example: $1\text{ Decimeter (dm)} = 0.1\text{ m}$)
  • Centi- ($\text{c}$): $1/100 = 10^{-2}$ (Example: $1\text{ Centimeter (cm)} = 0.01\text{ m}$)
  • Milli- ($\text{m}$): $1/1,000 = 10^{-3}$ (Example: $1\text{ Millimeter (mm)} = 0.001\text{ m}$)
  • Micro- ($\mu$): $1/1,000,000 = 10^{-6}$ (Example: 1\text{ Micrometer (}̣̣\mu\text{m)} = 1 \times 10^{-6}\text{ m})
  • Nano- ($\text{n}$): $1/1,000,000,000 = 10^{-9}$ (Example: $1\text{ Nanometer (nm)} = 1 \times 10^{-9}\text{ m}$)
  • Pico- ($\text{p}$): $1/1,000,000,000,000 = 10^{-12}$ (Example: $1\text{ Picometer (pm)} = 1 \times 10^{-12}\text{ m}$)
  • Femto- ($\text{f}$): $1/1,000,000,000,000,000 = 10^{-15}$ (Example: $1\text{ Femtometer (fm)} = 1 \times 10^{-15}\text{ m}$)
  • Atto- ($\text{a}$): $1/1,000,000,000,000,000,000 = 10^{-18}$ (Example: $1\text{ Attometer (am)} = 1 \times 10^{-18}\text{ m}$)

• Derived SI Units:

  • Volume: SI derived unit is cubic meter ($\text{m}^3$).
    • $1\text{ cm}^3 = (1 \times 10^{-2}\text{ m})^3 = 1 \times 10^{-6}\text{ m}^3$
    • $1\text{ dm}^3 = (1 \times 10^{-1}\text{ m})^3 = 1 \times 10^{-3}\text{ m}^3$
    • $1\text{ L} = 1000\text{ mL} = 1000\text{ cm}^3 = 1\text{ dm}^3$
    • $1\text{ mL} = 1\text{ cm}^3$

*   **Density:** Mass divided by volume ($d = \frac{m}{v}$). SI derived unit is $\text{kg/m}^3$.
    *   $1\text{ g/cm}^3 = 1\text{ g/mL} = 1000\text{ kg/m}^3$
    *   *Densities of select substances at $25\,^\circ\text{C}$ ($1\text{ atm}$):* Air ($0.001\text{ g/cm}^3$), Ethanol ($0.79\text{ g/cm}^3$), Water ($1.00\text{ g/cm}^3$), Graphite ($2.2\text{ g/cm}^3$), Table salt ($2.2\text{ g/cm}^3$), Aluminum ($2.70\text{ g/cm}^3$), Diamond ($3.5\text{ g/cm}^3$), Iron ($7.9\text{ g/cm}^3$), Lead ($11.3\text{ g/cm}^3$), Mercury ($13.6\text{ g/cm}^3$), Gold ($19.3\text{ g/cm}^3$), Osmium ($22.6\text{ g/cm}^3$; densest element known).

• Temperature Scales and Conversions:
  • Scale relationships:
    • $K = ^\circ\text{C} + 273.15$
    • $^\circ\text{F} = \frac{9}{5} \times ^\circ\text{C} + 32$
    • $^\circ\text{C} = (^\circ\text{F} - 32) \times \frac{5}{9}$
  • Reference points:
    • Freezing point of water: $273.15\text{ K} = 0\,^\circ\text{C} = 32\,^\circ\text{F}$
    • Room temperature: $298.15\text{ K} = 25\,^\circ\text{C} = 77\,^\circ\text{F}$
    • Body temperature: $310.15\text{ K} = 37\,^\circ\text{C} = 98.6\,^\circ\text{F}$
    • Boiling point of water: $373.15\text{ K} = 100\,^\circ\text{C} = 212\,^\circ\text{F}$

• Scientific Notation:

  • Format: $N \times 10^n$, where $1 \le N < 10$ and $n$ is an integer.
  • Addition/Subtraction: Express all quantities with the same exponent $n$, combine $N_1$ and $N_2$, and keep exponent $n$ constant.
  • Multiplication: Multiply $N_1 \times N_2$ and add exponents ($n_1 + n_2$).
  • Division: Divide $N_1 \div N_2$ and subtract exponents ($n_1 - n_2$).

• Significant Figures Rules:

  1. Any digit that is not zero is significant (e.g., $1.234\text{ kg}$ has 4 sig figs).
  2. Zeros between nonzero digits are significant (e.g., $606\text{ m}$ has 3 sig figs).
  3. Zeros to the left of the first nonzero digit are not significant (e.g., $0.08\text{ L}$ has 1 sig fig; $0.043\text{ kg}$ has 2 sig figs).
  4. If a number is greater than 1, all zeros to the right of the decimal point are significant (e.g., $2.0\text{ mg}$ has 2 sig figs; $1.310 \times 10^{22}$ has 4 sig figs).
  5. If a number is less than 1, only zeros at the end and middle are significant (e.g., $0.00420\text{ g}$ has 3 sig figs).
  6. Trailing zeros in whole numbers without decimal points are ambiguous (e.g., $7000\text{ mL}$ can be 1, 2, 3, or 4 sig figs) and must be written in scientific notation ($7.000 \times 10^3\text{ mL}$ for 4 sig figs; $7.00 \times 10^3\text{ mL}$ for 3; $7.0 \times 10^3\text{ mL}$ for 2; $7 \times 10^3\text{ mL}$ for 1).
  • Calculations: Addition/Subtraction output decimal places are limited by the entry with the fewest decimal places. Multiplication/Division output total sig figs are limited by the entry with the fewest total sig figs. Exact numbers (from definitions or object counts) have infinitely many sig figs.

• Accuracy versus Precision:

  • Accuracy: How close a measurement is to the true value.
  • Precision: How close a set of measurements are to each other.

• Worked Examples for Measurements and Calculations:
  • Density Calculation (Gold): Mass = $301\text{ g}$, Volume = $15.6\text{ cm}^3$.         $d = \frac{m}{v} = \frac{301\text{ g}}{15.6\text{ cm}^3} = 19.3\text{ g/cm}^3$
  • Mass Calculation (Mercury): Density = $13.6\text{ g/mL}$, Volume = $5.50\text{ mL}$.         $m = d \times v = 13.6\text{ g/mL} \times 5.50\text{ mL} = 74.8\text{ g}$
  • Temperature Conversion 1 (Solder melting point): $224\,^\circ\text{C}$ to $^\circ\text{F}$.         $\frac{9\,^\circ\text{F}}{5\,^\circ\text{C}} \times (224\,^\circ\text{C}) + 32\,^\circ\text{F} = 435\,^\circ\text{F}$
  • Temperature Conversion 2 (Helium boiling point): $-452\,^\circ\text{F}$ to $^\circ\text{C}$.         $(-452\,^\circ\text{F} - 32\,^\circ\text{F}) \times \frac{5\,^\circ\text{C}}{9\,^\circ\text{F}} = -269\,^\circ\text{C}$
  • Temperature Conversion 3 (Mercury melting point): $-38.9\,^\circ\text{C}$ to $\text{K}$.         $(-38.9\,^\circ\text{C} + 273.15\,^\circ\text{C}) \times \frac{1\text{ K}}{1\,^\circ\text{C}} = 234.3\text{ K}$
  • Dimensional Analysis (Glucose intake): Convert $0.0833\text{ lb}$ to $\text{mg}$ ($1\text{ lb} = 453.6\text{ g}$).         $0.0833\text{ lb} \times \frac{453.6\text{ g}}{1\text{ lb}} \times \frac{1\text{ mg}}{1 \times 10^{-3}\text{ g}} = 3.78 \times 10^4\text{ mg}$
  • Volume Conversion (Blood): $5.2\text{ L}$ to $\text{m}^3$.         $5.2\text{ L} \times \frac{1000\text{ cm}^3}{1\text{ L}} \times \left(\frac{1 \times 10^{-2}\text{ m}}{1\text{ cm}}\right)^3 = 5.2 \times 10^{-3}\text{ m}^3$
  • Density Conversion (Liquid Nitrogen): Convert $0.808\text{ g/cm}^3$ to $\text{kg/m}^3$.         $\frac{0.808\text{ g}}{1\text{ cm}^3} \times \frac{1\text{ kg}}{1000\text{ g}} \times \frac{1\text{ cm}^3}{1 \times 10^{-6}\text{ m}^3} = 808\text{ kg/m}^3$
  • Pencil Lead Mass Estimation: Length = $18\text{ cm}$, Diameter = $2\text{ mm} = 0.2\text{ cm}$ ($r = 0.1\text{ cm}$). Density of graphite = $2.2\text{ g/cm}^3$$V = \pi r^2 l = \pi (0.1\text{ cm})^2 (18\text{ cm}) = 0.57\text{ cm}^3$$m = d \times V = 2.2\text{ g/cm}^3 \times 0.57\text{ cm}^3 = 1.25\text{ g} \approx 1\text{ g}$
  • Real-world unit failure case study: On September 23, 1999, the $\$125,000,000$ Mars Climate Orbiter entered Mars' atmosphere $100\text{ km}$ ($62\text{ miles}$) lower than planned and was destroyed by heat due to confusion between English pounds of force ($\text{lbf}$) and metric Newtons ($\text{N}$), where $1\text{ lb} = 4.45\text{ N}$.

Atomic Theory and Structure of the Atom

• Dalton’s Atomic Theory (1808):
  1. Elements are composed of extremely small particles called atoms.
  2. All atoms of a given element are identical, having the same size, mass, and chemical properties. The atoms of one element are different from the atoms of all other elements.
  3. Compounds are composed of atoms of more than one element. In any compound, the ratio of the numbers of atoms of any two of the elements present is either an integer or a simple fraction.
  4. A chemical reaction involves only the separation, combination, or rearrangement of atoms; it does not result in their creation or destruction (Law of Conservation of Mass).
  • Law of Multiple Proportions: Illustrated by carbon monoxide ($\text{CO}$, ratio $\text{O/C} = 1/1$) and carbon dioxide ($\text{CO}_2$, ratio $\text{O/C} = 2/1$).

• Discovery of Subatomic Particles:
  • Electron ($e^-$): Discovered by J.J. Thomson (1906 Nobel Prize in Physics) using a Cathode Ray Tube. He determined the ratio of electric charge to mass for electrons:         $\text{charge/mass of } e^- = -1.76 \times 10^8\text{ C/g}$

*   **Millikan Oil Drop Experiment:** Robert Millikan (1923 Nobel Prize in Physics) determined the charge of an electron:

        $e^- \text{ charge} = -1.6022 \times 10^{-19}\text{ C}$         Using Thomson's charge-to-mass ratio, the mass of an electron was calculated:         $e^- \text{ mass} = \frac{-1.6022 \times 10^{-19}\text{ C}}{-1.76 \times 10^8\text{ C/g}} = 9.10938 \times 10^{-28}\text{ g}$

*   **Radioactivity:** Spontaneous emission of particles/radiation from radioactive substances (e.g., uranium compound). Deflection between electrically charged plates reveals three types:
    *   $\alpha$ (alpha) rays: Positively charged particles; velocity $\sim 1.4 \times 10^7\text{ m/s}$ ($\sim 5\%$ speed of light).
    *   $\beta$ (beta) rays: Negatively charged particles (electrons).
    *   $\gamma$ (gamma) rays: High-energy, neutral rays unaffected by external fields.

*   **Thomson's Plum Pudding Model:** Proposed that an atom was a uniform sphere of positive charge with electrons embedded throughout like plums in a pudding.

*   **Rutherford’s Experiment (1908 Nobel Prize in Chemistry):** Ernest Rutherford bombarded a thin gold foil with $\alpha$ particles surrounded by a zinc-sulfide screen. Most $\alpha$ particles passed straight through, but a few deflected at large angles or bounced back.
    *   *Conclusion:* An atom's positive charge and mass are concentrated in a tiny, dense nucleus. Protons ($p$) have a positive charge equal in magnitude to the electron's charge.
    *   *Dimensions:* Atomic radius $\sim 100\text{ pm} = 1 \times 10^{-10}\text{ m}$; Nuclear radius $\sim 5 \times 10^{-3}\text{ pm} = 5 \times 10^{-15}\text{ m}$. Analogy: If an atom were expanded to the size of a sports stadium, the nucleus would be the size of a marble.

*   **Chadwick’s Experiment (1932, 1935 Nobel Prize in Physics):** James Chadwick bombarded beryllium with $\alpha$ particles:

        $^9\text{Be} + \alpha \rightarrow ^{12}\text{C} + n$         Discovered the neutron ($n$), a electrically neutral subatomic particle (charge = 0) with a mass slightly larger than that of a proton ($1.67493 \times 10^{-24}\text{ g}$).

• Summary of Subatomic Particles:
  • Electron ($e^-$): Mass = $9.10938 \times 10^{-28}\text{ g}$, Coulomb Charge = $-1.6022 \times 10^{-19}\text{ C}$, Unit Charge = $-1$
  • Proton ($p$): Mass = $1.67262 \times 10^{-24}\text{ g}$, Coulomb Charge = $+1.6022 \times 10^{-19}\text{ C}$, Unit Charge = $+1$
  • Neutron ($n$): Mass = $1.67493 \times 10^{-24}\text{ g}$, Coulomb Charge = $0\text{ C}$, Unit Charge = $0$
  • Mass Ratio: $\text{mass } p \approx \text{mass } n \approx 1840 \times \text{mass } e^-$

Atomic Notation, Isotopes, and the Periodic Table

• Atomic Notation: Expressed as ${}_Z^A\text{X}$

  • $\text{X}$ = Element symbol
  • $Z$ = Atomic number = number of protons in nucleus
  • $A$ = Mass number = number of protons + number of neutrons = $Z + \text{number of neutrons}$
  • $\text{Number of neutrons} = A - Z$
  • In a neutral atom, $\text{number of electrons} = \text{number of protons} = Z$

• Isotopes: Atoms of the same element ($Z$) with different numbers of neutrons in their nuclei (different $A$).

  • Hydrogen Isotopes: Protium (${}_1^1\text{H}$), Deuterium (${}_1^2\text{H}$ or $\text{D}$), Tritium (${}_1^3\text{H}$ or $\text{T}$).
  • Uranium Isotopes: ${}_{92}^{235}\text{U}$ ($143$ neutrons) and ${}_{92}^{238}\text{U}$ ($146$ neutrons).
  • Sodium Isotopes: ${}_{11}^{20}\text{Na}$ ($9$ neutrons) and ${}_{11}^{22}\text{Na}$ ($11$ neutrons).

• Structure of the Modern Periodic Table:
  • Arranged by atomic number ($Z$) in horizontal rows called Periods (1 to 7) and vertical columns called Groups (1 to 18 or 1A to 8A).
  • Metals: Good conductors of heat and electricity (occupy left and center).
  • Nonmetals: Poor conductors of heat and electricity (occupy top right).
  • Metalloids: Properties intermediate between metals and nonmetals (B, Si, Ge, As, Sb, Te).

• Natural Abundance of Elements:
  • Earth's Crust: Oxygen ($45.5\%$), Silicon ($27.2\%$), Aluminum ($8.3\%$), Iron ($6.2\%$), Calcium ($4.7\%$), Magnesium ($2.8\%$), All others ($5.3\%$).
  • Human Body: Oxygen ($65\%$), Carbon ($18\%$), Hydrogen ($10\%$), Nitrogen ($3\%$), Calcium ($1.6\%$), Phosphorus ($1.2\%$), All others ($1.2\%$).

• Subatomic Particle Determination Examples:
  • ${}_{11}^{20}\text{Na}$: $11$ protons, $11$ electrons, $20 - 11 = 9$ neutrons.
  • ${}_{11}^{22}\text{Na}$: $11$ protons, $11$ electrons, $22 - 11 = 11$ neutrons.
  • ${}^{17}\text{O}$: Atomic number $Z = 8$, $8$ protons, $8$ electrons, $17 - 8 = 9$ neutrons.
  • Carbon-14 (${}_6^{14}\text{C}$): Atomic number $Z = 6$, $6$ protons, $6$ electrons, $14 - 6 = 8$ neutrons.

Molecules, Ions, and Chemical Formulas

• Molecules: An aggregate of two or more atoms in a definite arrangement held together by chemical forces.
  • Diatomic Molecules: Contains only two atoms.
    • Diatomic elements: $\text{H}_2, \text{N}_2, \text{O}_2, \text{F}_2, \text{Cl}_2, \text{Br}_2, \text{I}_2$
    • Diatomic compounds: $\text{HCl}, \text{CO}$
  • Polyatomic Molecules: Contains more than two atoms (e.g., $\text{O}_3, \text{H}_2\text{O}, \text{NH}_3, \text{CH}_4$).

• Ions: An atom or group of atoms that has a net positive or negative charge.
  • Cation: Ion with a positive charge. Formed when a neutral atom loses electrons.
    • Example: $\text{Na} \rightarrow \text{Na}^+ + e^-$ ($11$ protons, $10$ electrons).
  • Anion: Ion with a negative charge. Formed when a neutral atom gains electrons.
    • Example: $\text{Cl} + e^- \rightarrow \text{Cl}^-$ ($17$ protons, $18$ electrons).
  • Monatomic Ion: Contains only one atom (e.g., $\text{Na}^+, \text{Cl}^-, \text{Ca}^{2+}, \text{O}^{2-}, \text{Al}^{3+}, \text{N}^{3-}$).
  • Polyatomic Ion: Contains more than one atom (e.g., $\text{OH}^-, \text{CN}^-, \text{NH}_4^+, \text{NO}_3^-$).

• Types of Formulas:
  • Molecular Formula: Shows the exact number of atoms of each element in the smallest unit of a substance.
  • Empirical Formula: Shows the simplest whole-number ratio of the atoms in a substance.
  • Comparisons:
    • Water: Molecular = $\text{H}_2\text{O}$, Empirical = $\text{H}_2\text{O}$
    • Glucose: Molecular = $\text{C}_6\text{H}_{12}\text{O}_6$, Empirical = $\text{CH}_2\text{O}$
    • Ozone: Molecular = $\text{O}_3$, Empirical = $\text{O}$
    • Hydrazine: Molecular = $\text{N}_2\text{H}_4$, Empirical = $\text{NH}_2$
    • Acetylene: Molecular = $\text{C}_2\text{H}_2$, Empirical = $\text{CH}$
    • Nitrous oxide: Molecular = $\text{N}_2\text{O}$, Empirical = $\text{N}_2\text{O}$
  • Methylamine Example: Molecular formula = $\text{CH}_5\text{N}$, written structurally as $\text{CH}_3\text{NH}_2$.

Chemical Nomenclature and Compounds

• Ionic Compounds: Consist of cations (metals or $\text{NH}_4^+$) and anions (nonmetals or polyatomic ions).
  • Formulas match the empirical formula. Sum of charges on cation(s) and anion(s) must equal zero.
  • Crossover Rule: The charge magnitude of cation becomes subscript of anion and vice versa. For $\text{Mg}^{2+}$ and $\text{N}^{3-}$, (+2)X + (-3)Y = 0 \implies X/Y = 3/2 \implies \text{Mg}_3\text{N}_2$.\n\n\n\n* **Naming Ionic Compounds:**\n * Name metal cation first, then monatomic nonmetal anion ending in "-ide".\n * \text{BaCl}2 = barium chloride\n * \text{K}_2\text{O} = potassium oxide\n * \text{Mg(OH)}_2 = magnesium hydroxide\n * \text{KNO}_3 = potassium nitrate\n * **Monatomic Anions ("-ide"):**\n * Group 14: Carbide (\text{C}^{4-}$), Silicide ($\text{Si}^{4-})\n * Group 15: Nitride (\text{N}^{3-}$), Phosphide ($\text{P}^{3-})\n * Group 16: Oxide (\text{O}^{2-}$), Sulfide ($\text{S}^{2-}$), Selenide ($\text{Se}^{2-}$), Telluride ($\text{Te}^{2-})\n * Group 17: Fluoride (\text{F}^-$), Chloride ($\text{Cl}^-$), Bromide ($\text{Br}^-$), Iodide ($\text{I}^-)\n * **Transition Metal Compounds (Stock System):** Charges specified with Roman numerals in parentheses.\n * \text{FeCl}_2$= iron(II) chloride ($\text{Fe}^{2+})\n * \text{FeCl}_3$= iron(III) chloride ($\text{Fe}^{3+})\n * \text{Cr}_2\text{S}_3$= chromium(III) sulfide ($\text{Cr}^{3+})\n * \text{Cu(NO}_3)_2 = copper(II) nitrate\n * \text{Hg}_2(\text{NO}_2)_2$= mercury(I) nitrite (note: mercury(I) exists as diatomic pair$\text{Hg}_2^{2+})\n * \text{Cs}_2\text{S} = cesium sulfide\n * \text{Ca}_3(\text{PO}_4)_2 = calcium phosphate\n\n\n\n* **Naming Molecular Compounds (Nonmetal + Nonmetal):**\n * First element is furthest left in period and lower in group. Second element ends in "-ide".\n * Greek Prefixes: mono- (1), di- (2), tri- (3), tetra- (4), penta- (5), hexa- (6), hepta- (7), octa- (8), nona- (9), deca- (10). Prefix "mono-" omitted for first element.\n * \text{HI} = hydrogen iodide\n * \text{NF}_3 = nitrogen trifluoride\n * \text{SO}_2 = sulfur dioxide\n * \text{N}_2\text{Cl}_4 = dinitrogen tetrachloride\n * \text{NO}_2 = nitrogen dioxide\n * \text{N}_2\text{O} = dinitrogen monoxide\n * \text{SiCl}_4 = silicon tetrachloride\n * \text{P}_4\text{O}{10} = tetraphosphorus decoxide (drop "a" in deca)\n * \text{CS}2 = carbon disulfide\n * \text{Si}_2\text{Br}_6 = disilicon hexabromide\n\n* **Acids and Bases:**\n * **Acid:** Yields hydrogen ions (\text{H}^+) when dissolved in water.\n * Binary Acids: hydro- + stem + -ic acid.\n * \text{HF} = hydrofluoric acid\n * \text{HCl} = hydrochloric acid\n * \text{HBr} = hydrobromic acid\n * \text{HI} = hydroiodic acid\n * \text{HCN} = hydrocyanic acid\n * \text{H}_2\text{S} = hydrosulfuric acid\n * **Oxoacids:** Acid containing hydrogen, oxygen, and a central element.\n * Reference acid = "-ic" acid (\text{HNO}_3$nitric acid,$\text{H}_2\text{CO}_3$carbonic acid,$\text{H}_3\text{PO}_4$phosphoric acid,$\text{HClO}_3 chloric acid).\n * +1\text{ O atom}$: per- -ic acid ($\text{HClO}_4 perchloric acid)\n * -1\text{ O atom}$: -ous acid ($\text{HClO}_2$chlorous acid,$\text{H}_3\text{PO}_3 phosphorous acid)\n * -2\text{ O atoms}$: hypo- -ous acid ($\text{HClO} hypochlorous acid)\n * **Oxoanions:** Removal of all \text{H}^+ ions from oxoacids.\n * "-ic" acid \rightarrow$"-ate" anion ($\text{ClO}_4^-$perchlorate,$\text{ClO}_3^-$chlorate,$\text{IO}_4^- periodate)\n * "-ous" acid \rightarrow$"-ite" anion ($\text{ClO}_2^-$chlorite,$\text{ClO}^- hypochlorite)\n * Partial removal of \text{H}^+$:$\text{H}_2\text{PO}_4^-$(dihydrogen phosphate),$\text{HPO}_4^{2-}$(hydrogen phosphate),$\text{PO}_4^{3-} (phosphate).\n\n\n\n * **Bases:** Yields hydroxide ions (\text{OH}^-$) when dissolved in water (e.g.,$\text{NaOH}$sodium hydroxide,$\text{KOH}$potassium hydroxide,$\text{Ba(OH)}_2 barium hydroxide).\n\n* **Hydrates:** Compounds with a specific number of water molecules attached.\n * \text{BaCl}_2 \cdot 2\text{H}_2\text{O} = barium chloride dihydrate\n * \text{LiCl} \cdot \text{H}_2\text{O} = lithium chloride monohydrate\n * \text{MgSO}_4 \cdot 7\text{H}_2\text{O} = magnesium sulfate heptahydrate\n * \text{Sr(NO}_3)_2 \cdot 4\text{H}_2\text{O} = strontium nitrate tetrahydrate\n * \text{CuSO}_4 \cdot 5\text{H}_2\text{O}$= copper(II) sulfate pentahydrate (blue) vs. anhydrous$\text{CuSO}_4 (white)\n\n\n\n* **Common and Systematic Names Table:**\n * \text{H}_2\text{O}: Water / Dihydrogen monoxide\n * \text{NH}_3: Ammonia / Trihydrogen nitride\n * \text{CO}_2: Dry ice / Solid carbon dioxide\n * \text{NaCl}: Table salt / Sodium chloride\n * \text{N}_2\text{O}: Laughing gas / Dinitrogen monoxide\n * \text{CaCO}_3: Marble, chalk, limestone / Calcium carbonate\n * \text{CaO}: Quicklime / Calcium oxide\n * \text{Ca(OH)}_2: Slaked lime / Calcium hydroxide\n * \text{NaHCO}_3: Baking soda / Sodium hydrogen carbonate\n * \text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O}: Washing soda / Sodium carbonate decahydrate\n * \text{MgSO}_4 \cdot 7\text{H}_2\text{O}: Epsom salt / Magnesium sulfate heptahydrate\n * \text{Mg(OH)}_2: Milk of magnesia / Magnesium hydroxide\n * \text{CaSO}_4 \cdot 2\text{H}_2\text{O}: Gypsum / Calcium sulfate dihydrate\n\n* **Organic Chemistry & Straight-Chain Alkanes:**\n * Organic chemistry deals with carbon compounds containing functional groups (e.g., methanol \text{CH}_3\text{OH}$, methylamine$\text{CH}_3\text{NH}_2$, acetic acid$\text{CH}_3\text{COOH}).\n * **First 10 Straight-Chain Alkanes (\text{C}_n\text{H}{2n+2}):**\n 1. Methane (\text{CH}4)\n 2. Ethane (\text{C}_2\text{H}_6)\n 3. Propane (\text{C}_3\text{H}_8)\n 4. Butane (\text{C}_4\text{H}{10})\n 5. Pentane (\text{C}5\text{H}{12})\n 6. Hexane (\text{C}6\text{H}{14})\n 7. Heptane (\text{C}7\text{H}{16})\n 8. Octane (\text{C}8\text{H}{18})\n 9. Nonane (\text{C}9\text{H}{20})\n 10. Decane (\text{C}{10}\text{H}{22})\n\n# Mass Relationships in Chemical Reactions\n\n* **Atomic Mass Unit (\text{amu}$):** By definition, 1 atom of carbon-12 (${}^{12}\text{C}$) has a mass of exactly$12\text{ amu}.\n * 1\text{ amu} = 1.66 \times 10^{-24}\text{ g}\n * 1\text{ g} = 6.022 \times 10^{23}\text{ amu}\n\n* **Average Atomic Mass:** Weighted average of all naturally occurring isotopes of an element.\n * *Calculation Formula:* \text{Average Mass} = \sum (\text{fractional abundance} \times \text{isotopic mass})\n * *Copper Example:* {}^{63}\text{Cu}$($69.09\%$, mass$62.93\text{ amu}$) and${}^{65}\text{Cu}$($30.91\%$, mass$64.9278\text{ amu}).\n        \text{Average mass} = (0.6909)(62.93\text{ amu}) + (0.3091)(64.9278\text{ amu}) = 63.55\text{ amu}\n\n* **The Mole (\text{mol}$) and Molar Mass ($\mathcal{M}):**\n * **Mole:** The amount of a substance that contains exactly 6.0221415 \times 10^{23}$elementary entities (Avogadro’s number,$N_A).\n * **Molar Mass:** The mass of 1 mole of units in grams (\text{g/mol}$). For any element, atomic mass ($\text{amu}$) = molar mass ($\text{g/mol}).\n * 1\text{ mole }{}^{12}\text{C} = 6.022 \times 10^{23}\text{ atoms} = 12.00\text{ g}\n * 1\text{ mole Li} = 6.941\text{ g}\n\n\n\n* **Mole and Mass Worked Calculations:**\n * *Moles of Helium in 6.46\text{ g}$:* Molar mass =$4.003\text{ g/mol}.\n        6.46\text{ g He} \times \frac{1\text{ mol He}}{4.003\text{ g He}} = 1.61\text{ mol He}\n * *Mass of Zinc in 0.356\text{ mol}$:* Molar mass =$65.39\text{ g/mol}.\n        0.356\text{ mol Zn} \times \frac{65.39\text{ g Zn}}{1\text{ mol Zn}} = 23.3\text{ g Zn}\n * *Mass of 1 Molecule of Buckminsterfullerene (\text{C}{60}):*\n        1\text{ molecule C}{60} \times \frac{60\text{ C atoms}}{1\text{ C}{60}\text{ molecule}} \times \frac{1\text{ mol C}}{6.022 \times 10^{23}\text{ C atoms}} \times \frac{12.011\text{ g C}}{1\text{ mol C}} = 1.197 \times 10^{-21}\text{ g}\n * *Molecular Mass:* Sum of atomic masses in a molecule.\n * \text{SO}_2$:$32.07 + 2(16.00) = 64.07\text{ amu}$(molar mass =$64.07\text{ g/mol})\n * Caffeine (\text{C}_8\text{H}{10}\text{N}4\text{O}_2$):$8(12.01) + 10(1.008) + 4(14.01) + 2(16.00) = 194.20\text{ amu}\n * *Moles in 6.07\text{ g}$of Methane ($\text{CH}_4$):* Molar mass =$16.04\text{ g/mol}.\n        6.07\text{ g CH}_4 \times \frac{1\text{ mol CH}_4}{16.04\text{ g CH}_4} = 0.378\text{ mol CH}_4\n * *Hydrogen Atoms in 25.6\text{ g}$of Urea [$(\text{NH}_2)_2\text{CO}$]:* Molar mass =$60.06\text{ g/mol}.\n        25.6\text{ g urea} \times \frac{1\text{ mol urea}}{60.06\text{ g urea}} \times \frac{4\text{ mol H}}{1\text{ mol urea}} \times \frac{6.022 \times 10^{23}\text{ H atoms}}{1\text{ mol H}} = 1.03 \times 10^{24}\text{ H atoms}\n\n* **Mass Spectrometry:** An experimental method for determining atomic and molecular masses using mass-to-charge ratios of gas-phase ions.\n * Gaseous sample ionized by electron beam, accelerated through charged plates, deflected by a magnetic field onto a detecting screen.\n * *Neon Spectrum:* {}^{20}\text{Ne}$($90.92\%$),${}^{21}\text{Ne}$($0.26\%$),${}^{22}\text{Ne}$($8.82\%).\n\n\n\n\n\n* **Percent Composition and Formula Determination:**\n * \text{Percent composition} = \frac{n \times \text{molar mass of element}}{\text{molar mass of compound}} \times 100\%\n * *Phosphoric Acid (\text{H}_3\text{PO}_4$, Molar Mass =$97.99\text{ g/mol}):*\n * \%\text{H} = \frac{3(1.008\text{ g})}{97.99\text{ g}} \times 100\% = 3.086\%\n * \%\text{P} = \frac{30.97\text{ g}}{97.99\text{ g}} \times 100\% = 31.61\%\n * \%\text{O} = \frac{4(16.00\text{ g})}{97.99\text{ g}} \times 100\% = 65.31\%\n * *Empirical Formula Determination (Ascorbic Acid):* Mass percents: 40.92\%\text{ C}$,$4.58\%\text{ H}$,$54.50\%\text{ O}.\n * Assume 100\text{ g}$sample:$40.92\text{ g C}$,$4.58\text{ g H}$,$54.50\text{ g O}.\n * Convert to moles: n_C = \frac{40.92}{12.01} = 3.407\text{ mol}$,$n_H = \frac{4.58}{1.008} = 4.54\text{ mol}$,$n_O = \frac{54.50}{16.00} = 3.406\text{ mol}.\n * Divide by smallest subscript (3.406$):$\text{C}_1\text{H}{1.33}\text{O}1\n * Multiply by 3 to reach integer subscripts: \text{C}_3\text{H}_4\text{O}_3\n * *Mass of Element in Sample (Chalcopyrite \text{CuFeS}_2$):* Molar mass =$183.5\text{ g/mol}$, Molar mass of Cu =$63.55\text{ g/mol}.\n * \%\text{Cu} = \frac{63.55}{183.5} \times 100\% = 34.63\%\n * Mass of Cu in 3.71 \times 10^3\text{ kg}$sample =$0.3463 \times 3.71 \times 10^3\text{ kg} = 1.28 \times 10^3\text{ kg}\n * **Combustion Analysis:** Used to measure composition of organic compounds.\n * \text{g CO}_2 \rightarrow \text{mol CO}_2 \rightarrow \text{mol C} \rightarrow \text{g C}\n * \text{g H}_2\text{O} \rightarrow \text{mol H}_2\text{O} \rightarrow \text{mol H} \rightarrow \text{g H}\n * \text{g O} = \text{g sample} - (\text{g C} + \text{g H})\n\n\n\n * *Molecular Formula from Empirical Formula:* \text{Molecular Formula} = (\text{Empirical Formula})_n\n * n = \frac{\text{Molar Mass}}{\text{Empirical Molar Mass}}\n * *Example:* Compound containing 30.46\%\text{ N}$and$69.54\%\text{ O}$with experimental molar mass between$90\text{ g}$and$95\text{ g}.\n * n_N = 2.174\text{ mol}$,$n_O = 4.346\text{ mol} \implies \text{Empirical formula } \text{NO}_2\n * Empirical molar mass = 14.01 + 2(16.00) = 46.01\text{ g/mol}\n * n = \frac{90\text{ to }95\text{ g}}{46.01\text{ g}} \approx 2\n * Molecular formula = (\text{NO}_2)_2 = \text{N}_2\text{O}_4$(exact molar mass =$92.02\text{ g/mol}).\n\n* **Chemical Reactions, Equations, and Stoichiometry:**\n * **Chemical Reaction:** A process in which one or more substances are changed into one or more new substances.\n * **Chemical Equation:** Uses chemical symbols to show reactants on left and products on right.\n * *Balancing Rules:* Balance elements that appear in only one reactant and product first; balance free elements last; adjust coefficients (never subscripts); clear fractions by multiplying whole equation.\n * *Example:* 4\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3\n\n\n\n * *Stoichiometry Calculations:* \n * *Glucose degradation:* \text{C}_6\text{H}{12}\text{O}6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O}\n            856\text{ g C}_6\text{H}{12}\text{O}6 \times \frac{1\text{ mol C}_6\text{H}{12}\text{O}6}{180.2\text{ g}} \times \frac{6\text{ mol CO}_2}{1\text{ mol C}_6\text{H}{12}\text{O}_6} \times \frac{44.01\text{ g CO}_2}{1\text{ mol CO}_2} = 1.25 \times 10^3\text{ g CO}_2\n * *Lithium and Water:* 2\text{Li}(s) + 2\text{H}_2\text{O}(l) \rightarrow 2\text{LiOH}(aq) + \text{H}_2(g)\n            9.89\text{ g H}_2 \times \frac{1\text{ mol H}_2}{2.016\text{ g H}_2} \times \frac{2\text{ mol Li}}{1\text{ mol H}_2} \times \frac{6.941\text{ g Li}}{1\text{ mol Li}} = 68.1\text{ g Li}\n\n* **Limiting Reagents and Yields:**\n * **Limiting Reagent:** The reactant that is completely consumed first in a reaction, limiting the amount of product formed.\n * **Excess Reagent:** The reactant present in quantities greater than necessary to react with the limiting reagent.\n * *Urea Synthesis Example:* 2\text{NH}_3(g) + \text{CO}_2(g) \rightarrow (\text{NH}_2)_2\text{CO}(aq) + \text{H}_2\text{O}(l)$. Reacting$637.2\text{ g NH}_3$with$1142\text{ g CO}_2\n * Moles of urea from \text{NH}_3$=$637.2\text{ g} \times \frac{1\text{ mol NH}_3}{17.03\text{ g}} \times \frac{1\text{ mol urea}}{2\text{ mol NH}_3} = 18.71\text{ mol}\n * Moles of urea from \text{CO}_2$=$1142\text{ g} \times \frac{1\text{ mol CO}_2}{44.01\text{ g}} \times \frac{1\text{ mol urea}}{1\text{ mol CO}_2} = 25.95\text{ mol}\n * Limiting reagent = \text{NH}_3\n * Theoretical mass of urea = 18.71\text{ mol} \times 60.06\text{ g/mol} = 1124\text{ g}\n * Mass of \text{CO}_2$consumed =$18.71\text{ mol urea} \times \frac{1\text{ mol CO}_2}{1\text{ mol urea}} \times \frac{44.01\text{ g}}{1\text{ mol CO}_2} = 823.4\text{ g}\n * Excess \text{CO}_2$remaining =$1142\text{ g} - 823.4\text{ g} = 319\text{ g}\n\n * **Theoretical Yield:** The amount of product that would result if all the limiting reagent reacted.\n * **Actual Yield:** The amount of product actually obtained from a reaction.\n * **Percent Yield:** \n        \text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%\n * *Titanium Production Example:* \text{TiCl}_4(g) + 2\text{Mg}(l) \rightarrow \text{Ti}(s) + 2\text{MgCl}_2(l)$. Reacting$3.54 \times 10^7\text{ g TiCl}_4$with$1.13 \times 10^7\text{ g Mg}.\n * Moles of Ti from \text{TiCl}_4$=$1.87 \times 10^5\text{ mol} (Limiting Reagent)\n * Moles of Ti from \text{Mg}$=$2.32 \times 10^5\text{ mol}\n * Theoretical yield of Ti = 1.87 \times 10^5\text{ mol} \times 47.88\text{ g/mol} = 8.95 \times 10^6\text{ g}\n * Actual yield = 7.91 \times 10^6\text{ g}\n * \text{Percent Yield} = \frac{7.91 \times 10^6\text{ g}}{8.95 \times 10^6\text{ g}} \times 100\% = 88.4\%\n\n* **Green Chemistry Metrics and Industrial Processes:**\n * **Atom Economy:** A measure of the efficiency of a reaction in incorporating atoms from reactants into the desired product.\n        \text{Atom Economy} = \frac{\text{Total mass of atoms in desired product}}{\text{Total mass of atoms in all reactants}} \times 100\%\n * *Propylene Glycol Example:* \text{C}_3\text{H}_8\text{O}_3 + \text{H}_2 \rightarrow \text{C}_3\text{H}_8\text{O}_2 + \text{H}_2\text{O}\n * Mass of desired product (\text{C}_3\text{H}_8\text{O}_2$) =$76.1\text{ amu}\n * Mass of reactants (\text{C}_3\text{H}_8\text{O}_3 + \text{H}_2$) =$92.1 + 2.02 = 94.12\text{ amu}\n * \text{Atom Economy} = \frac{76.1\text{ amu}}{94.12\text{ amu}} \times 100\% = 80.9\%\n * **Chemical Fertilizers:** Plants require N, P, K, Ca, S, and Mg.\n * Ammonia synthesis: 3\text{H}_2(g) + \text{N}_2(g) \rightarrow 2\text{NH}_3(g)\n * Ammonium nitrate synthesis: \text{NH}_3(aq) + \text{HNO}_3(aq) \rightarrow \text{NH}_4\text{NO}_3(aq)\n * Superphosphate from fluorapatite: 2\text{Ca}_5(\text{PO}_4)_3\text{F}(s) + 7\text{H}_2\text{SO}_4(aq) \rightarrow 3\text{Ca}(\text{H}_2\text{PO}_4)_2(aq) + 7\text{CaSO}_4(aq) + 2\text{HF}(g)$$