Atoms, Elements, Molecules & Compounds

Dalton's Atomic Theory and the Foundational Laws

John Dalton proposed in the early 1800s that all matter is composed of indivisible atoms, that atoms of a given element are identical in mass and properties, and that compounds form from atoms combining in fixed whole-number ratios. Dalton's theory explained three empirical laws that had already been observed experimentally. Although later discoveries revealed atoms are divisible into subatomic particles, Dalton's core ideas about fixed atomic ratios remain central to chemistry today.

• •Law of conservation of mass: mass is neither created nor destroyed in a chemical reaction.
• •Law of definite proportions: a given compound always contains the same elements in the same fixed mass ratio.
• •Law of multiple proportions: when two elements form more than one compound, the mass ratios of the second element per fixed mass of the first are small whole-number ratios (e.g., CO vs. CO₂).

Key Experiments in the Discovery of Subatomic Particles

Several landmark experiments dismantled Dalton's 'indivisible atom' and revealed internal atomic structure. J.J. Thomson's cathode ray tube experiments showed that atoms contain negatively charged particles (electrons) far lighter than the whole atom, leading to his 'plum pudding' model. Robert Millikan's oil drop experiment precisely measured the charge of the electron. Henri Becquerel and Marie and Pierre Curie discovered radioactivity, showing atoms could spontaneously emit particles/energy, hinting at internal atomic substructure. Ernest Rutherford's gold foil experiment, in which most alpha particles passed through foil but some deflected sharply, proved that atoms have a tiny, dense, positively charged nucleus surrounded mostly by empty space.

• •Thomson (cathode ray tube): discovered the electron; determined mass-to-charge ratio.
• •Millikan (oil drop): measured the precise charge of a single electron.
• •Becquerel/Curie (radioactivity): discovered spontaneous nuclear emissions, revealing atoms are not indivisible.
• •Rutherford (gold foil): discovered the small, dense, positive nucleus; most of the atom is empty space.

Subatomic Particles and Atomic Notation

Atoms are composed of three subatomic particles distinguished by charge, mass, and location. Protons and neutrons reside in the tiny, dense nucleus and account for essentially all the atom's mass, while electrons occupy the much larger surrounding volume of space. Atomic number (Z) equals the number of protons and defines the element's identity, while mass number (A) is the sum of protons and neutrons; isotopes are atoms of the same element with different numbers of neutrons (and thus different mass numbers).

• •Proton: charge +1, mass ≈ 1 amu, located in the nucleus.
• •Neutron: charge 0, mass ≈ 1 amu, located in the nucleus.
• •Electron: charge −1, mass ≈ 1/1836 amu (negligible), located outside the nucleus in the electron cloud.
• •Isotope notation: ᴬZX, where A = mass number, Z = atomic number, X = element symbol.
• •Ions form when atoms gain electrons (anions, negative charge) or lose electrons (cations, positive charge); the number of protons never changes when an ion forms.

Mass Spectrometry and Weighted-Average Atomic Mass

Mass spectrometry separates and detects ions based on their mass-to-charge ratio, allowing scientists to determine both the exact masses of individual isotopes and their relative natural abundances. Because most elements exist as a mixture of isotopes, the atomic mass listed on the periodic table is a weighted average that accounts for both the mass and the fractional abundance of each naturally occurring isotope. This weighted average will always be closer to the mass of the more abundant isotope.

• •Weighted average atomic mass = Σ(isotope mass × fractional abundance) for all naturally occurring isotopes.
• •The atomic mass on the periodic table rarely matches any single isotope's mass exactly.
• •Mass spectrometry data (mass and % abundance) are typically given in these calculations.

The Modern Periodic Table

Dmitri Mendeleev arranged the known elements by increasing atomic mass (later corrected to atomic number) and noticed that chemical properties repeated periodically, allowing him to leave gaps that correctly predicted undiscovered elements. The modern periodic table arranges elements by increasing atomic number into seven horizontal periods and eighteen vertical groups (families), with elements in the same group sharing similar valence electron configurations and chemical behavior. Metals occupy the left and center, nonmetals the upper right, and metalloids form a diagonal staircase border between them.

• •Group 1: alkali metals (highly reactive, +1 ions); Group 2: alkaline earth metals (+2 ions).
• •Group 17: halogens (highly reactive nonmetals, −1 ions); Group 16: chalcogens.
• •Group 18: noble gases (largely unreactive, stable octets).
• •Groups 3–12: transition metals, often forming multiple possible cation charges.
• •Lanthanides and actinides: the two rows placed below the main table (inner transition metals).
• •Metalloids (e.g., B, Si, Ge, As, Sb, Te) have properties intermediate between metals and nonmetals.

Diatomic Elements and Ion Charges

Seven elements exist naturally as diatomic molecules rather than lone atoms, and students must memorize this list because it affects formula writing and equation balancing throughout the course. Main-group elements tend to gain or lose electrons to achieve a noble-gas electron configuration, and their most common ionic charge can be predicted directly from their group number on the periodic table.

• •Seven diatomic elements: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂ ('Have No Fear Of Ice Cold Beer' mnemonic).
• •Group 1 (alkali metals) → +1 cations; Group 2 (alkaline earth) → +2 cations.
• •Group 13 → +3 cations (typically); Group 15 → −3 anions; Group 16 → −2 anions; Group 17 (halogens) → −1 anions.
• •Transition metals often have variable charge and require a Roman numeral to specify the charge in the compound name.

Ionic vs. Covalent Bonding

An ionic bond forms through the transfer of one or more electrons from a metal to a nonmetal, creating oppositely charged ions held together by electrostatic attraction; ionic compounds typically involve a metal and a nonmetal (or a metal and a polyatomic ion). A covalent bond forms through the sharing of electron pairs between two nonmetal atoms. Electronegativity difference (ΔEN) between bonded atoms predicts the bond's character along a continuum from pure covalent to polar covalent to ionic.

• •ΔEN ≈ 0 (same or very similar elements): pure (nonpolar) covalent bond, electrons shared equally.
• •ΔEN roughly 0.4–1.7: polar covalent bond, electrons shared unequally, creating partial charges (δ+/δ−).
• •ΔEN greater than about 1.7: ionic bond, electrons essentially transferred rather than shared.
• •Metal + nonmetal → typically ionic; nonmetal + nonmetal → typically covalent.

Properties of Ionic vs. Molecular Compounds

Ionic and molecular (covalent) compounds display strikingly different macroscopic properties that reflect their different bonding and structure. Ionic compounds form rigid, ordered crystal lattices held together by strong electrostatic forces extending in all directions, whereas molecular compounds exist as discrete individual molecules held together internally by covalent bonds but attracted to neighboring molecules only by weaker intermolecular forces.

• •Ionic compounds: high melting/boiling points, hard and brittle solids at room temperature, conduct electricity when molten or dissolved (but not as solids).
• •Molecular compounds: relatively low melting/boiling points, may be gases/liquids/soft solids at room temperature, generally do not conduct electricity.
• •Ionic compounds are often soluble in water and dissociate into ions; many molecular compounds are less water-soluble unless polar.

Writing Ionic Formulas: The Crossover Method

Because compounds must be electrically neutral overall, the formula of an ionic compound is determined by balancing the total positive charge from cations against the total negative charge from anions. The 'crossover method' provides a fast shortcut: the numerical charge (ignoring sign) of each ion becomes the subscript of the other ion, then subscripts are reduced to the lowest whole-number ratio if possible.

• •Write the cation first, then the anion, each with its charge.
• •Cross the magnitude of each ion's charge down as the other ion's subscript.
• •Reduce subscripts to the smallest whole-number ratio (e.g., Mg²⁺ and O²⁻ → Mg₂O₂ reduces to MgO).
• •Polyatomic ions needing a subscript greater than 1 are enclosed in parentheses (e.g., Ca(NO₃)₂).

Empirical, Molecular, and Structural Formulas

Chemists represent compounds with several types of formulas that carry different amounts of structural information. The empirical formula shows the simplest whole-number ratio of atoms in a compound, the molecular formula shows the actual number of each type of atom in one molecule, and the structural formula shows how atoms are actually bonded and arranged in space, often visualized with ball-and-stick models (showing bond geometry) or space-filling models (showing relative atomic sizes and overall molecular shape).

• •Empirical formula example: CH₂O (simplest ratio for both formaldehyde and glucose).
• •Molecular formula example: glucose is C₆H₁₂O₆, six times the empirical formula.
• •Structural formulas show actual bonding connectivity, useful for distinguishing isomers with identical molecular formulas.
• •Ball-and-stick models emphasize bond angles/geometry; space-filling models emphasize relative atomic volume and overall molecular shape.

Reference Table: Common Polyatomic Ions

Polyatomic ions are groups of covalently bonded atoms that carry an overall charge and act as a single unit in ionic compounds. Memorizing their formulas and charges is essential for writing correct ionic formulas and equations throughout the course, since these ions cannot be broken apart by the crossover method.

• •Nitrate NO₃⁻; Nitrite NO₂⁻
• •Sulfate SO₄²⁻; Sulfite SO₃²⁻
• •Carbonate CO₃²⁻; Bicarbonate (hydrogen carbonate) HCO₃⁻
• •Phosphate PO₄³⁻; Hydrogen phosphate HPO₄²⁻
• •Hydroxide OH⁻; Cyanide CN⁻
• •Ammonium NH₄⁺ (the common polyatomic cation)
• •Acetate C₂H₃O₂⁻ (CH₃COO⁻); Permanganate MnO₄⁻
• •Chromate CrO₄²⁻; Dichromate Cr₂O₇²⁻

Reference Table: Common Strong/Weak Acids and Bases

Recognizing the small set of common strong acids and strong bases by memory is critical, since every acid or base not on this list is assumed weak. Strong acids and bases ionize essentially completely in water, while weak acids and bases ionize only partially, establishing an equilibrium between ionized and un-ionized forms.

• •Strong acids: HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄, HClO₃.
• •Strong bases: LiOH, NaOH, KOH, RbOH, CsOH, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂ (Group 1 hydroxides and heavier Group 2 hydroxides).
• •Common weak acids: CH₃COOH (acetic acid), HF, H₂CO₃, H₃PO₄, HCN.
• •Common weak bases: NH₃ (ammonia) and amines.

An atom has 17 protons, 18 neutrons, and 17 electrons. Write its isotope symbol and determine if it is neutral or an ion.

1. 1Atomic number Z = number of protons = 17 (this is chlorine).
2. 2Mass number A = protons + neutrons = 17 + 18 = 35.
3. 3Compare protons (17) to electrons (17): they are equal, so the atom is neutral.
4. 4Write the isotope symbol using A and Z: ³⁵₁₇Cl.

³⁵₁₇Cl, a neutral atom (chlorine-35)

Chlorine has two isotopes: ³⁵Cl (mass 34.969 amu, abundance 75.77%) and ³⁷Cl (mass 36.966 amu, abundance 24.23%). Calculate the weighted-average atomic mass.

1. 1Convert percentages to decimal fractions: 0.7577 and 0.2423.
2. 2Multiply each isotope's mass by its fractional abundance: 34.969 × 0.7577 = 26.499 amu.
3. 3Second term: 36.966 × 0.2423 = 8.960 amu.
4. 4Add the two contributions: 26.499 + 8.960 = 35.459 amu.
5. 5Round appropriately to match periodic table precision: 35.45 amu.

35.45 amu

Determine the ionic formula formed between aluminum (Al³⁺) and oxygen (O²⁻) using the crossover method.

1. 1Write the ions with charges: Al³⁺ and O²⁻.
2. 2Cross the numerical charges: the 3 from Al³⁺ becomes the subscript on O; the 2 from O²⁻ becomes the subscript on Al.
3. 3This gives Al₂O₃.
4. 4Check that subscripts are in lowest whole-number ratio: 2:3 cannot be reduced further.
5. 5Verify charge balance: 2(+3) + 3(−2) = +6 − 6 = 0, confirming neutrality.

Al₂O₃

Classify the bond in HF and in NaCl using electronegativity differences (H = 2.20, F = 3.98, Na = 0.93, Cl = 3.16).

1. 1Calculate ΔEN for HF: 3.98 − 2.20 = 1.78.
2. 2Calculate ΔEN for NaCl: 3.16 − 0.93 = 2.23.
3. 3Apply the electronegativity scale: ΔEN > ~1.7 generally indicates ionic character, but HF (1.78) is a well-known exception classified as strongly polar covalent because both are nonmetals sharing electrons.
4. 4NaCl (2.23) involves a metal and nonmetal with a large ΔEN, consistent with an ionic bond.
5. 5Conclude: HF is polar covalent (nonmetal-nonmetal); NaCl is ionic (metal-nonmetal).

HF: polar covalent; NaCl: ionic

A compound has the empirical formula CH₂ and a molar mass of 84.16 g/mol. Determine its molecular formula.

1. 1Calculate the empirical formula mass: C (12.01) + 2H (2×1.008) = 12.01 + 2.016 = 14.03 g/mol.
2. 2Divide the molecular molar mass by the empirical formula mass: 84.16 ÷ 14.03 = 6.00.
3. 3This whole number (6) is the multiplier for every subscript in the empirical formula.
4. 4Multiply subscripts: C(1×6)H(2×6) = C₆H₁₂.

C₆H₁₂

Q1. Which law states that a compound always contains the same elements in the same fixed mass ratio?

Q2. Rutherford's gold foil experiment provided evidence for:

Q3. Which subatomic particle has essentially no contribution to atomic mass?

Q4. An atom with 20 protons and 22 neutrons has a mass number of:

Q5. Isotopes of the same element differ in their number of:

Q6. Which technique is used to determine isotopic masses and relative abundances?

Q7. Which family is found in Group 17 of the periodic table?

Q8. Which of the following is NOT one of the seven diatomic elements?

Q9. What charge would an ion of sulfur (Group 16) most likely have?

Q10. Which pair of elements would most likely form an ionic bond?

Q11. Which property is characteristic of ionic compounds rather than molecular compounds?

Q12. Using the crossover method, what is the correct formula for the compound formed between Ca²⁺ and PO₄³⁻?

Q13. The empirical formula of a compound represents:

Q14. A bond between two atoms with nearly identical electronegativities is best classified as:

Q15. Which model emphasizes the relative sizes of atoms and the overall three-dimensional shape of a molecule?