Chapter 3: Composition of Substances and Solutions

3.1 Formula Mass and the Mole Concept

• Formula Mass: Sum of atomic masses of all atoms in a chemical formula.

  • For covalent substances, also called molecular mass.

• Mole: Unit for calculations with large numbers; SI abbreviation is mol.

  • 1 mole = 6.022 \times 10^{23} (Avogadro’s number).

• Molar Mass: Mass (g) of 1 mole of atoms or molecules, expressed in \frac{g}{mol}.

  • The molar mass of any substance is numerically equivalent to its atomic or formula mass in amu.

• Mole Conversions:

  • Convert mass (g) to moles using the molar mass.
  • Convert moles to atoms/molecules/ions using Avogadro’s number.

• Examples:

  • Grams to Moles: 4.7 g K \times \frac{1 mol K}{39.10 g} = 0.12 mol K
  • Moles to Mass: 9.2 \times 10^{-4} mol Ar \times \frac{39.95 g Ar}{1 mol} = 0.037 g Ar
  • Moles to Atoms: 4.0 moles \times \frac{6.022 \times 10^{23} atoms C}{1 mole} = 2.4 \times 10^{24} C atoms
  • Grams to Atoms: 5.00 g \times \frac{1 mole Cu}{63.55 g Cu} \times \frac{6.022 \times 10^{23} atoms Cu}{1 mol Cu} = 4.74 \times 10^{22} Cu atoms

3.2 Determining Empirical and Molecular Formulas

• Percent Composition: Percentage by mass of each element in a compound.

  • \% \text{ element A} = \frac{\text{mass element A}}{\text{mass compound}} \times 100

• Determining Empirical Formulas:

  1. Convert elemental masses to moles.
  2. Divide each mole value by the smallest mole value.
  3. Multiply to get the smallest whole-number ratio of subscripts.

• Determining Empirical Formulas from Percent Composition:

  • Assume a 100 g sample.
  • Follow the same steps as above.

• Molecular Formulas:

  • n = \frac{\text{molecular mass}}{\text{empirical formula mass}}
  • Multiply each subscript in the empirical formula by n.

3.3 Molarity

• Solution: Homogeneous mixture with uniform composition and properties.

• Components of a Solution:

  • Solvent: Present in the largest amount.
  • Solute: Present in smaller amounts.
  • Aqueous solution: Water is the solvent.

• Molarity (M): Moles of solute per liter of solution.

  • Molarity = \frac{\text{moles solute}}{\text{L solution}}

• Dilution: Decreasing a solution's concentration by adding solvent.

• Dilution Formula:

  • M1V1 = M2V2

3.4 Other Concentration Units

• Mass Percent:

  • \text{Mass percentage} = \frac{\text{solute mass}}{\text{solution mass}} \times 100

• Volume Percent:

  • \text{Volume percentage} = \frac{\text{solute volume}}{\text{solution volume}} \times 100

• Mass-Volume Percent:

  • \text{Mass-Volume percentage} = \frac{\text{solute mass}}{\text{solution volume}} \times 100

• Parts per Million (ppm) and Parts per Billion (ppb):

  • ppm = \frac{\text{mass solute}}{\text{mass of solution}} \times 10^6