Introduction to Chemistry: Atomic Mass, Formulas, and Nomenclature

Concepts of Average Atomic Mass and Isotopic Abundance

• Definition of Atomic Mass: The numbers found on the periodic table, such as Hydrogen weighing $1.008\,g/mol$, represent the average atomic mass. These are not whole numbers because they are averages of all naturally occurring isotopes.
• Isotopes: Variants of an element with the same number of protons but different numbers of neutrons. Isotopes exist in different quantities in nature, defined as their abundance.
• Measuring Abundance: Usually expressed as a percentage. For example, atoms of Oxygen exhibit these abundances:     * $^{16}O$: $99.76\%$ (most common).     * $^{17}O$: $0.038\%$.     * $^{18}O$: $0.205\%$.

Mathematical Calculation of Average Atomic Mass

To find the average atomic mass for any element, follow these three steps:

1. Step 1: Convert Percentages to Decimals: Divide the abundance percentage by $100$.     * Example: $99.76\% / 100 = 0.9976$.
2. Step 2: Multiply Decimal Abundance by Isotopic Mass: Multiply each decimal value by the atomic mass unit ($amu$) for that specific isotope.
3. Step 3: Sum the Products: Add the results together to find the final average mass.

Case Study: Oxygen (O)

• Isotope 1 ($^{16}O$): $0.9976 \times 15.99\,amu = 15.952$
• Isotope 2 ($^{17}O$): $0.00038 \times 16.99\,amu = 0.00646$
• Isotope 3 ($^{18}O$): $0.00205 \times 17.99\,amu = 0.0369$
• Total Sum: $15.952 + 0.00646 + 0.0369 = 15.99\,amu$ (matching the value on the periodic table).

Case Study: Lead (Pb)

Lead has four major isotopes:

• $^{204}Pb$: $1.4\%$ abundance ($203.97\,amu$) \rightarrow $0.014 \times 203.97 = 2.855$
• $^{206}Pb$: $24.1\%$ abundance ($205.97\,amu$) \rightarrow $0.241 \times 205.97 = 49.639$
• $^{207}Pb$: $22.1\%$ abundance ($206.97\,amu$) \rightarrow $0.221 \times 206.97 = 45.740$
• $^{208}Pb$: $52.4\%$ abundance ($207.97\,amu$) \rightarrow $0.524 \times 207.97 = 108.976$
• Calculation: Summing these values gives an average atomic mass of approximately $207.22\,amu$.

Types of Chemical Formulas

• Molecular Formula: Shows the actual, exact number of each type of atom in one molecule (e.g., Glucose is $C_6H_{12}O_6$, Methane is $CH_4$, Water is $H_2O$).
• Empirical Formula: The simplest whole-number ratio of atoms in a compound.     * Example: The empirical formula for Glucose ($C_6H_{12}O_6$) is found by dividing all subscripts by the greatest common factor ($6$), resulting in $CH_2O$.     * Example: For Water ($H_2O$) and Methane ($CH_4$), the molecular and empirical formulas are identical because they cannot be simplified further.
• Structural Formula: Shows how the atoms are connected (the bonding arrangement).     * Methanol ($CH_3OH$): A methyl group ($CH_3$) connected to a hydroxy group ($OH$).     * Hydrogen Cyanide ($HCN$): Contains a triple bond between Carbon and Nitrogen.     * Water ($H_2O$): Actually a "bent" molecule with lone electron pairs on the Oxygen.

Diatomic Elements and Visualizations

• Diatomic Molecules: Certain elements always exist as pairs in nature. They are never found as single atoms.
• Memory Mnemonic: "Have No Fear Of Ice Cold Beer"     * Hydrogen ($H_2$)     * Nitrogen ($N_2$)     * Fluorine ($F_2$)     * Oxygen ($O_2$)     * Iodine ($I_2$)     * Chlorine ($Cl_2$)     * Bromine ($Br_2$)
• Subscripts vs. Coefficients:     * Subscript: The small number below/after the symbol (e.g., the "2" in $H_2$) indicates atoms bonded within a molecule.     * Coefficient: The large number before the symbol (e.g., $2H_2$) indicates the number of separate molecules or atoms.

Isomers: Structural and Spatial

• Definition: Compounds with the same molecular formula but different structures.
• Structural Isomers: Same formula, but atoms are connected in a different order.     * Example: Acetic Acid ($C_2H_4O_2$) is vinegar, used in cooking. Methyl Formate ($C_2H_4O_2$) is an industrial solvent and insecticide. Consuming methyl formate instead of vinegar can be fatal.
• Spatial Isomers (Stereoisomers): Same formula and connectivity, but different orientation in 3D space.     * Enantiomers: Mirror-image isomers (e.g., R-Carvone smells like Spearmint; S-Carvone smells like Caraway seeds).

Development of the Periodic Table

• Aristotle: Early theorizing on atoms.
• 1829: Identification of similar properties in certain elements.
• 1865 (Newlands): Law of Octaves; observed that every eighth element had similar properties.
• 1869 (Mendeleev): The "father" of the periodic table. Arranged elements by atomic mass and famously left gaps for elements not yet discovered.
• 1870 (Meyer): Published a table but focused less on prediction.
• 1875: Discovery of Gallium, which validated Mendeleev’s gaps.
• 1913 (Mosley): Developed the concept of the atomic number (number of protons). This is how the modern table is organized.

Organization of the Modern Periodic Table

• Periods: The 7 horizontal rows. Elements in the same period have the same number of electron shells.
• Groups/Families: The 18 vertical columns. Elements in a group share similar chemical properties.
• Main Classifications:     * Metals: Located on the left and center. Properties: Shiny, malleable, ductile, good conductors. They tend to form cations (lose electrons).     * Nonmetals: Located on the far right (plus Hydrogen). Properties: Dull, poor conductors, brittle. They tend to form anions (gain electrons).     * Metalloids: Located along the "staircase" line. They have intermediate properties (semiconductors).
• Specific Group Names:     * Group 1: Alkali Metals (excluding Hydrogen).     * Group 2: Alkaline Earth Metals.     * Groups 3-12: Transition Metals.     * Group 17: Halogens (highly reactive).     * Group 18: Noble Gases (stable; full octet).     * Lanthanides and Actinides: Inserted in Period 6 and 7; usually pulled out to the bottom to save space.
• Periodic Table Facts: There are 118 official elements. No "J" or "Q" exists on the table. Elements named after the sun (Helium), the moon (Selenium), and Iris (the Greek goddess of rainbows).

Chemical Bonding and Properties

• Ionic Bonds: Electrons are transferred from a metal to a nonmetal.     * Forms a crystal lattice.     * High melting points.     * Conducts electricity when molten or dissolved in water.     * Examples: $NaCl$ (Sodium Chloride), $CaO$ (Calcium Oxide), $MgCl_2$ (Magnesium Chloride).
• Covalent Bonds: Electrons are shared between nonmetals.     * Forms discrete molecules.     * Lower melting points.     * Poor conductors.     * Examples: $H_2O$ (Water), $CO_2$ (Carbon Dioxide), $CH_4$ (Methane).

Chemical Nomenclature (Naming Compounds)

1. Binary Molecular Compounds (Two Nonmetals)

• Use Greek prefixes to indicate numbers: mono ($1$), di ($2$), tri ($3$), tetra ($4$), penta ($5$), hexa ($6$), hepta ($7$), octa ($8$), nona ($9$), deca ($10$).
• Rules:     * The first element keeps its name. Use a prefix only if there is more than one (never use "mono-" on the first element).     * The second element always uses a prefix and ends in "-ide."     * Grammar Rule: Drop the "a" or "o" at the end of a prefix if the element starts with a vowel (e.g., "Tetroxide" instead of "Tetraoxide").     * Example: $N_2O_4$ is Dinitrogen Tetroxide; $SF_6$ is Sulfur Hexafluoride.

2. Ionic Compounds (Metal + Nonmetal)

• Fixed Charge Metals: Name the metal, then the root of the nonmetal + "-ide."     * Example: $NaCl$ is Sodium Chloride; $CaI_2$ is Calcium Iodide.
• Variable Charge (Transition) Metals: Use Roman numerals in parentheses to indicate the charge.     * Example: $FeCl_2$ is Iron (II) Chloride; $FeCl_3$ is Iron (III) Chloride.     * To find the charge, look at the anion. In $SnF_2$, Fluorine is $-1$. Two Fluorines = $-2$. Therefore, Tin must be $+2$ \rightarrow Tin (II) Fluoride.
• Polyatomic Ions: Groups of atoms that stay together and have an overall charge.     * Must Memorize:         * Nitrate: $NO_3^{-1}$         * Nitrite: $NO_2^{-1}$         * Phosphate: $PO_4^{-3}$         * Sulfite: $SO_3^{-2}$         * Carbonate: $CO_3^{-2}$     * If you need multiple polyatomic ions to balance a charge, use parentheses: $Mg_3(PO_4)_2$.

3. Acids (Optional for Exam but Taught)

• Binary Acids (H + Element): Hydro- + root + -ic acid. (e.g., $HCl$ is Hydrochloric acid).
• Oxyacids (H + Polyatomic):     * If polyatomic ends in "-ate," change to "-ic acid" (Carbonate \rightarrow Carbonic acid).     * If polyatomic ends in "-ite," change to "-ous acid" (Nitrite \rightarrow Nitrous acid).

Exam Prep and Complex Calculations

• Precision vs. Accuracy: Accuracy is closeness to the true value. Precision is the consistency of repeated measurements.
• Significant Figures (Sig Figs): Apply specific rules for addition/subtraction (decimal places) and multiplication/division (total sig figs).
• Unit Conversions (Dimensional Analysis):     * Carats to Pounds: 3,106 carats \rightarrow milligrams \rightarrow grams \rightarrow kilograms \rightarrow pounds.     * Velocity Conversion: $1250\,km/hr$ to $ft/s$.         * $1250\,km/hr \times (1000\,m / 1\,km) \times (1\,ft / 0.3048\,m) \times (1\,hr / 60\,min) \times (1\,min / 60\,s)$.
• Density Problems: Volume = Mass / Density. Remember to convert standard volume units (mL) to specific asked units (teaspoons).     * $1\,tsp = 4.93\,mL$.

Questions & Discussion

• Question: Why are some atomic masses in parentheses on certain periodic tables?
• Response: This indicates we do not have a stable, confirmed average mass for all isotopes. It usually applies to radioactive elements where we only know the most "stable" versions discovered in labs rather than naturally recurring balances.
• Question: Does our naming convention for ionic compounds use prefixes like "di-" or "tri-"?
• Response: No. Ionic naming is based strictly on charge balance. If you see prefixes, you should immediately recognize the compound is covalent/molecular.