DH

Chemistry Review: Key Terms from Lecture (Chapter 1–3)

Molar Mass, Empirical vs Molecular Formulas, and Percent Composition

  • Key definitions

    • Molar mass (formula mass, formula weight): the mass of one mole of a substance, calculated by summing the atomic masses of all atoms in the formula. For a compound with subscripts, M = ∑(ni × Mi).

    • Molar ratio: the fixed ratio of atoms of each element within one mole of a compound, derived directly from the formula.

    • Empirical formula: the simplest whole-number ratio of the elements in a compound.

    • Molecular formula: the actual number of each type of atom in a molecule.

    • Empirical vs Molecular relationship: empirical formula may or may not equal the molecular formula. If you know the empirical formula and the molar mass, you can determine the molecular formula by finding an integer n such that Molecular formula = (Empirical formula) × n.

    • Elemental analysis (percent by mass): experimental determination of the mass percentages of elements in a compound, used to derive empirical formulas.

  • Example: Glucose (C6H12O6) and ribose

    • Molecular formula glucose: C6H12O6. Molar mass ≈ M{C6H{12}O6} = 6MC + 12MH + 6MO \ (MC \,≈\, 12.01\, g/mol, MH \≈\, 1.008\, g/mol, MO \≈\, 16.00\, g/mol)

    • M \approx 6(12.01) + 12(1.008) + 6(16.00) \approx 180.16\, g/mol.

    • Empirical formula for glucose: CH2O (same as for ribose, which has the same empirical formula but a different molecular formula).

    • Empirical formula is the lowest whole-number ratio. Molecular formula is the actual composition; sometimes identical, sometimes not.

    • To determine empirical formula experimentally, you determine percent by mass for each element and convert to moles, then reduce to the smallest whole-number ratio.

  • Percent by mass (ppm, mass percent)

    • Formula: ext{Percent by mass of element } X = rac{mX}{M{ ext{compound}}} imes 100 ext{%}

    • Example calculation for glucose (C6H12O6):

    • Carbon:

      • Carbon mass = 6 imes M_C = 6 imes 12.01 = 72.06\, \text{g}

      • Percent C ≈ \frac{72.06}{180.16} \times 100\% \approx 40.0\%.

    • Hydrogen:

      • Hydrogen mass = 12 \times M_H = 12 \times 1.008 = 12.096\, \text{g}

      • Percent H ≈ \frac{12.096}{180.16} \times 100\% \approx 6.71\%.

    • Oxygen:

      • Oxygen mass = 6 \times M_O = 6 \times 16.00 = 96.00\, \text{g}

      • Percent O ≈ \frac{96.00}{180.16} \times 100\% \approx 53.29\%.

    • Use the percentages to derive the empirical formula by converting each percent to moles (divide by the element’s atomic mass) and reducing to the smallest whole-number ratio.

    • Important note: Always verify calculated percentages with accurate atomic masses and molar mass; class notes may show approximations, but use standard atomic masses for exams.

  • Experimental determination and relationships

    • Empirical formula is obtained from elemental analysis (percent composition).

    • Molecular formula is determined from empirical formula and molar mass data: find n such that (Empirical formula) × n gives the molecular formula.

    • Sometimes, several formulas share the same empirical formula (e.g., an empirical formula of CH2O could correspond to multiple molecular formulas, depending on molar mass).

  • Isotopes and atomic structure (key concepts)

    • Subatomic particles and notation

    • Proton (p): positive charge, located in the nucleus; mass ≈ 1 amu.

    • Neutron (n): neutral, located in the nucleus; mass ≈ 1 amu.

    • Electron (e−): negative charge, located in the electron cloud; mass ≈ 0 amu.

    • Atomic number Z: number of protons; defines the element.

    • Mass number A: total number of protons and neutrons; A = Z + N.

    • Isotopes: atoms with the same Z and different N (different A).

    • Ions: atoms with a net charge due to loss or gain of electrons.

      • Cation: positively charged (loss of electrons).

      • Anion: negatively charged (gain of electrons).

    • Atomic symbol interpretation (example): for a symbol with A, Z, and N information, you can determine protons, neutrons, and electrons in neutral or charged states.

    • If Z = 11 and A = 22 (symbol often written as $^{22}_{11}$X):

      • Protons = Z = 11

      • Electrons in a neutral atom = Z = 11; if the species has a positive charge (+1), electrons = Z − 1 = 10

      • Neutrons = A − Z = 22 − 11 = 11

    • Weighted atomic mass: the atomic mass on the periodic table is the weighted average of naturally occurring isotopes, not a single isotope mass.

  • Avogadro’s number and mole concept

    • Avogadro’s number: N_A = 6.022 imes 10^{23} particles per mole.

    • Purpose: convert between moles and particles (atoms, molecules, or ions).

    • Common conversions:

    • Moles ⇄ Grams: use molar mass M: n = rac{m}{M}, m = nM.

    • Moles ⇄ Particles: N = n imes N_A.

    • Molar mass, formula weight, and molecular weight are numerically the same value; the difference lies in the units (g/mol vs amu per atom or per molecule).

  • Measurements, accuracy, precision, and significant figures

    • Qualitative vs quantitative data

    • Qualitative: descriptive, non-naceted (e.g., color, state).

    • Quantitative: numerical measurements (e.g., 4.56 g).

    • Measured values come with uncertainty (instrumental error).

    • Accuracy: closeness of measurements to the true value.

    • Precision: closeness of a set of measurements to each other.

    • Significant figures (sig figs): denote measurement precision. Rules to follow during calculations:

    • For multiplication/division: the result should have the same number of sig figs as the measurement with the fewest sig figs.

    • For addition/subtraction: the result should have the same number of decimal places as the measurement with the fewest decimal places.

    • Scientific notation is essential for handling very large or small numbers; do not overestimate precision from calculator display when it isn’t present in the measurement.

  • Density and unit conversions

    • Density as a conversion factor:
      ho = rac{m}{V}

    • Useful conversions involving density include turning volume into mass and vice versa (e.g., using density to convert mL to g).

    • Volume units: 1 mL = 1 cm^3; 1 L = 1000 mL.

    • The relationship between mass, volume, and density is often used to convert between grams, milliliters, and cubic centimeters.

    • Non-metric and metric conversions

    • Base metric steps: kg → g, g → mg, L → mL, etc. Use known equalities: 1 kg = 1000 g; 1 g = 1000 mg; 1 L = 1000 mL; 1 mL = 1 cm^3.

    • Temperature scales: Celsius to Kelvin: K = C + 273.15 (and conversely C = K - 273.15).

  • Chemical nomenclature and bonding basics (Chapter 3 overview)

    • Ionic vs covalent compounds

    • Ionic: typically metal + nonmetal; electrons transferred; formula units and names reflect ions (e.g., NaCl, MgO).

    • Covalent (molecular): typically nonmetals; sharing electrons; names use prefixes for the number of each atom (e.g., CO = carbon monoxide, SO3 = sulfur trioxide).

    • Diatomic molecules (to know by heart): H2, N2, O2, F2, Cl2, Br2, I2.

    • Polyatomic ions: common ions that contain more than one atom (e.g., sulfate SO4^{2-}, nitrate NO3^{-}, ammonium NH4^{+}); names and formulas must be memorized or derived from standard tables.

    • Ionic naming rules (basic): name of cation (metal or polyatomic ion) + name of anion (nonmetal with -ide suffix or polyatomic ion name).

    • Ionic compounds with variable oxidation states (transition metals): use charge to balance; e.g., iron oxides can be FeO (iron(II) oxide) or Fe2O3 (iron(III) oxide).

    • Molecular naming: prefixes indicate numbers (mono-, di-, tri-, etc.) except for the common first element which often does not use the prefix if it has a single atom (e.g., CO is carbon monoxide, not monocarbon monoxide).

    • Oxyacids and binary acids: naming rules differ between acids that contain hydrogen with a halogen (binary acids) and those with polyatomic oxyanions (oxyacids). Typical forms include hydro- + -ic acid for binary acids (e.g., HCl → hydrochloric acid) and the -ic/-ous naming for oxyacids depending on the polyatomic anion.

    • Examples from class: diphosphorus pentoxide (P2O5), sulfur trioxide (SO3), carbon monoxide (CO).

  • Practical exam-ready tips

    • Be fluent with converting between grams, moles, and number of particles (atoms/molecules) using M and N_A.

    • Be competent with empirical formula derivation from percent composition, and with determining molecular formulas from empirical formulas and molar mass.

    • Practice reading measuring devices and applying significant figures correctly in all steps.

    • Review metric prefixes, common density conversions, and the Celsius↔Kelvin temperature conversions.

    • Familiarize yourself with basic ionic vs covalent distinctions, common polyatomic ions, and basic molecular naming conventions.

    • Remember: the exact numbers for atomic masses in class notes may be rounded; use standard atomic masses from the periodic table when performing calculations.

  • Quick reference formulas to memorize

    • Molar mass: M =
      \sumi ni M_i

    • Percent by mass: ext{Percent}{X} = \frac{mX}{M} \times 100\%

    • Avogadro’s number: N_A = 6.022 \times 10^{23}

    • Moles to grams: n = \frac{m}{M} \quad ext{and} \ m = nM

    • Moles to particles: N = n N_A

    • Density: \rho = \frac{m}{V}

    • Volume conversions: 1 L = 1000 mL; 1 mL = 1 cm^3; 1 cm^3 = 1 mL

    • Temperature: K = C + 273.15

    • State of matter and energy notes: kinetic energy is associated with motion; potential energy is stored energy (e.g., in chemical bonds).

  • Summary equation reminders

    • Empirical formula derivation concept: identify smallest whole-number ratios from experimental data.

    • Molecular formula determination: if you know the empirical formula and the molar mass, compute n such that Molecular = (Empirical) × n.

    • Atomic composition from a symbol: given Z (protons) and A (mass number), infer neutrons N = A − Z and electrons (for neutral atoms, E = Z).

    • Isotopes and stability: heavier elements require more neutrons to remain stable; isotopes differ in neutron count while keeping Z constant.

  • Note on exam expectations (from course context)

    • Expect questions on: percent composition, empirical vs molecular formulas, molar mass calculations, conversion factors (metric and density-based), significant figures, measurement uncertainty, and basic ionic/molecular naming and formulas.

    • You may be given a dataset (percent composition) and asked to derive an empirical formula, or to compute a molecular formula from a given molar mass.