Ions, Bonding, and Polyatomic Ions (Vocabulary)

Unit conversions with exponents

• Two-step data-entry approach: convert the unit in the numerator to the base unit, then convert the denominator; cancel units as you go. For example, to convert $cm^2$ to $m^2$, remember that area units mean the base unit is multiplied by itself ($cm imes cm$). Therefore, the conversion factor must also be squared.

• When converting with exponents, square the conversion factor: $100\,\text{cm} = 1\,\text{m}$, so for $cm^2$ to $m^2$ you effectively square each term: $(100\,\text{cm})^2 = (1\,\text{m})^2$ which means $10000\,\text{cm}^2 = 1\,\text{m}^2$. From this, $1\,\text{cm}^2 = 10^{-4}\,\text{m}^2$.

Densities and mass-volume conversions

• Strategy: convert mass of Hg to volume using its density, then use that volume to get the mass of glycerol using glycerol's density. Density ($\rho$) is an intensive property, typically expressed in units like g/mL or g/cm³.

• Key formulas:

  • Volume from mass: V = m / $\rho$ where V is the volume, m is the mass, and $\rho$ is the density of the substance.

  • Mass from volume: m = D*V

    where m is the mass, V is the volume, and \rho is the density of the substance.

Ion formation and electron configurations

• Metals form cations by losing electrons, becoming positively charged ions; nonmetals form anions by gaining electrons, becoming negatively charged ions.

• Atoms tend to achieve the electron configuration of the nearest noble gas because this configuration, usually with a full valence shell (octet rule for many elements), provides maximum stability.

• Common ion charges (Group A): (+1) for Group 1A, (+2) for Group 2A, (+3) for Group 3A; (-3) for Group 5A, (-2) for Group 6A, (-1) for Group 7A. Note that Group 4A elements generally form covalent bonds.

• Hydrogen can form $\text{H}^+$ (a proton) or, less commonly, $\text{H}^-$ (hydride).

• Examples: Na (Group 1A) loses one electron to become Na{+}, Mg (Group 2A) loses two electrons to become Mg{2+}, Cl (Group 7A) gains one electron to become Cl{-}. Transition metals often form multiple stable ions.

Ionic vs covalent bonds

• Ionic bonds: Formed by the electrostatic attraction between oppositely charged ions, which result from the complete transfer of one or more electrons from a metal to a nonmetal. This typically occurs between elements with a large difference in electronegativity.

• Covalent bonds: Formed by the sharing of electron pairs between nonmetals (and metalloids) to achieve a stable electron configuration, typically between atoms with similar electronegativities.

• Metalloids are treated as nonmetals for bonding in this context, generally forming covalent bonds.

Writing formulas for ionic compounds

• Formulas use the smallest whole-number ratio of ions that yields a neutral unit, meaning the total positive charge must exactly balance the total negative charge.

• The cation (positive ion) is written first, followed by the anion (negative ion); individual ion charges are not shown in the final formula unit.

• Examples: NaCl (1:1 ratio of Na+ and Cl-), MgCl2 (one Mg$^{2+}$ ion with two Cl$^{-}$ ions to achieve charge neutrality), Ca3$(PO$4$)$2 (three Ca$^{2+}$ ions with two PO 4{3-} ions).

Polyatomic ions and units

• Polyatomic ions: A group of two or more covalently bonded atoms that carries an overall positive or negative charge (e.g., NO$<em>3^-$ (nitrate), SO$</em>4^{2-}$ (sulfate), PO$<em>4^{3-}$ (phosphate), SO$</em>3^{2-}$ (sulfite), CO$<em>3^{2-}$ (carbonate), NH$</em>4^+$ (ammonium), OH$^-$ (hydroxide)).

• Write neutral formulas by combining ions; use parentheses for multiple units of a polyatomic ion to show that the charge and constituent atoms apply to the entire group: Ca$<em>3$(PO$</em>4$)$<em>2$. If only one polyatomic unit is present, no parentheses are needed (e.g., NaNO$</em>3$).

• Balancing rule (quick trick): Use the magnitude of the ion charges as subscripts for the opposite ion to balance the total charges, then reduce the subscripts to the smallest whole-number ratio if possible. For example, for Ca$^{2+}$ and PO$<em>4$^{3-}$, swap the numerical values of the charges to get Ca$</em>3$(PO$<em>4$)$</em>2$. The sum of charges is $3 \times (+2) + 2 \times (-3) = +6 - 6 = 0$.

Examples and identification

• Molecular compounds (also called covalent compounds) form when nonmetals/metalloids bond to nonmetals (e.g., C$<em>6$H$</em>{14}$ (molecular formula), H$<em>2$O, CO$</em>2$). The formula represents the actual number of atoms in a molecule, or sometimes the simplest empirical ratio.

• Ionic compounds form when metals bond to nonmetals or polyatomic ions (e.g., NaCl, Ca$<em>3$(PO$</em>4$)$_2$). Their formulas always represent the simplest empirical ratio of ions.

• Polyatomic ions can appear in ionic formulas and may be shown with parentheses when multiples are present to clarify stoichiometry.

Quick reference tips

• Always verify units and cancel properly in conversions, especially for complex unit problems; use a calculator you trust and pay attention to significant figures.

• For density problems, combine steps when possible to minimize rounding errors: $m<em>{\text{Gly}} = m</em>{\text{Hg}} \cdot \frac{\rho<em>{\text{Gly}}}{\rho</em>{\text{Hg}}}$.

• In ionic compounds, always write the empirical formula (simplest whole-number ratio); for molecular compounds, use the actual molecular formula unless directed otherwise.

• When in doubt about a compound, determine if it’s ionic (metal + nonmetal, or polyatomic nonmetal+nonmetal)