3.4 The mole

Atomic Mass Unit (AMU)

• Definition: AMU is a unit of measurement used to describe the mass of atoms and molecules.

• Size Comparison: AMU is exceedingly small, making it impractical for everyday measurements.

• Conversion to Grams: 1 AMU = 1.66 x 10^(-24) grams.

  • Conversely, there are approximately 6.02 x 10^(23) AMUs in 1 gram, which provides a useful relationship for conversions between these two units.

Counting Terms in Chemistry

• Counting Terms: Terms like "dozen" and "gross" are understood quantities.

• Mole: The term in chemistry equivalent to a precise counting term, representing a specific quantity of entities.

  • Abbreviation: "mole" is abbreviated as "mol" (dropping the "e").

  • Definition: 1 mole contains 6.022 x 10^(23) particles, known as Avogadro's number.

  • Origin: A mole corresponds to the number of atoms in 12 grams of Carbon-12.

Avogadro's Number

• Significance: Fundamental in relating macroscopic quantities of material to atomic/molecular quantities.

• Application: 1 mole of any substance equals 6.022 x 10^(23) particles of that substance.

• Example Calculation: For 3.2 moles of NaCl, calculating the total formula units:

  • Step 1: Use Avogadro's number as a conversion factor.

  • Step 2: 3.2 moles NaCl x (6.022 x 10^(23) units/1 mole) = 1.93 x 10^(24) NaCl units.

Molar Mass

• Definition: Molar mass is the mass of 1 mole of a substance measured in grams per mole (g/mol).

  • For monatomic elements, molar mass equals atomic mass from the periodic table.

• Calculation: For compounds, sum the total masses of all atoms in the formula:

  • Example for water (H2O): 2 moles of H (2 x 1.01 g) + 1 mole of O (1 x 16.00 g) = 18.02 g/mol.

• Method for Compounds: Identify the formula, multiply the atomic weights of the constituent elements by their respective quantities, and sum:

  • For NaCl: Na = 23.0 g/mol + Cl = 35.5 g/mol = 58.5 g/mol.

Conversion between Moles and Grams

• Using Molar Mass as a Conversion Factor:

  • Example Calculation: To convert 0.25 moles of oxygen gas (O2) to grams:

    1. Molar Mass of O2 = 32 g/mol.

    2. Calculation: 0.25 moles x (32 g/1 mole) = 8 grams.

Mole Ratios from Chemical Formulas

• Example: For ethane (C2H6):

  • 1 mole of ethane = 6.022 x 10^(23) molecules of C2H6.

  • Contains 2 x (6.022 x 10^(23)) = 1.2044 x 10^(24) carbon atoms and 6 x (6.022 x 10^(23)) = 3.6132 x 10^(24) hydrogen atoms.

Mole Ratios from Balanced Equations

• Use coefficients to determine mole relationships:

  • Example Reaction: 2H2 + O2 → 2H2O

    • This indicates a mole ratio of 2 moles of H2 for every 1 mole of O2 to yield 2 moles of H2O.

Concept Application: Ranking Compounds by Carbon Atoms

• Given: 12 g of Carbon-12, 1 mole of acetylene (C2H2), 9 x 10^(23) molecules of CO2.

• Conversion Process:

  • 12 g Carbon-12: Convert grams to moles (12 g/12 g/mol = 1 mole) then to atoms (1 mole x 6.022 x 10^(23) = 6.022 x 10^(23) atoms).

  • 1 mole of acetylene (C2H2): Contains 2 moles of carbon atoms (2 x 6.022 x 10^(23) = 1.2044 x 10^(24) atoms).

  • 9 x 10^(23) molecules of CO2: Each CO2 contains 1 carbon atom (9 x 10^(23) carbon atoms).

• Ranking of Carbon Atoms: 12 g C (6.022 x 10^(23)), CO2 (9 x 10^(23)), Acetylene (C2H2) (1.2044 x 10^(24)) would rank as 1) acetylene, 2) CO2, 3) Carbon-12.