Chem 1045: Unit 5 Moles
Chem 1045: Unit 5 Moles
Formula Mass and the Mole Concept
Formula Mass
Definition: The formula mass of a substance is the sum of the average atomic masses of all the atoms in the substance’s formula.
Covalent substances: Exist as discrete molecules.
Molecular mass: For covalent substances, the formula mass may be correctly referred to as molecular mass.
Molecular Mass Examples
Chloroform (CHCl₃)
Average mass: 119.37 amu
Calculation: Sum of average atomic masses of constituent atoms.
Aspirin (C₉H₈O₄)
Average mass: 180.15 amu
Molecular structure depicted in accompanying model.
Example 3.1: Aspirin Molecular Mass Calculation
Components:
C: 13 atoms, average atomic mass = 12.01 amu
Subtotal = 13 × 12.01 = 156.13 amu
H: 18 atoms, average atomic mass = 1.008 amu
Subtotal = 18 × 1.008 = 18.144 amu
O: 2 atoms, average atomic mass = 16.00 amu
Subtotal = 2 × 16.00 = 32.00 amu
Total Molecular Mass: 206.27 amu
Formula Mass for Ionic Compounds
Ionic Substances:
Composed of discrete cations and anions combined in ratios to yield electrically neutral bulk matter.
Ionic compounds do not exist as molecules.
Formula mass for ionic compounds cannot be referred to as molecular mass.
Average atomic masses of the ions approximate the average atomic masses of the neutral atoms.
Example 3.2: Sodium Chloride (NaCl) Formula Mass Calculation
Formula Mass Computation:
Components:
Al: 2 atoms, average atomic mass = 26.98 amu
Subtotal = 2 × 26.98 = 53.96 amu
S: 3 atoms, average atomic mass = 32.06 amu
Subtotal = 3 × 32.06 = 96.18 amu
O: 12 atoms, average atomic mass = 16.00 amu
Subtotal = 12 × 16.00 = 192.00 amu
Total Formula Mass: 342.14 amu
The Mole
Definition: The mole is a unit of amount similar to a pair, dozen, gross, etc.
Defined as the amount of substance containing the same number of discrete entities as the number of atoms in a sample of pure carbon-12 weighing 12 g.
Importance: The mole provides a connection between the mass of a sample and the number of atoms, molecules, or ions present.
Avogadro’s Number
Constant: The number of entities in a mole is approximately 6.02214179 × 10²³ (Avogadro's Number, denoted as $N_A$).
Diverse Masses: Different elements have different molar masses despite each mole containing the same number of entities.
Example: 65.4 g zinc, 12.0 g carbon, 24.3 g magnesium, 63.5 g copper, and their corresponding quantities of other elements, all containing 1.00 mol of atoms.
Molar Mass
Definition: The molar mass of a substance is the mass in grams of 1 mole of that substance (units: g/mol).
Equivalence: Molar mass numerical values are equivalent to atomic or formula mass in amu.
Example:
A single carbon-12 atom has a mass of 12 amu, hence a mole of carbon-12 atoms weighs 12 g.
Example 3.7: Vitamin C Mass Calculation
Molecular Formula: C₆H₈O₆
Recommended Daily Allowance: 1.42 × 10⁻⁴ mol
Calculated Molar Mass: 176.124 g/mol.
Desired mass in grams: Formula via multiple.
Determining Empirical and Molecular Formulas
Percent Composition: By mass percentage of each element in a compound.
Example Calculation: A compound weighing 10.0 g containing 2.5 g hydrogen and 7.5 g carbon.
Determination of Empirical Formulas
Process:
Convert masses to moles using molar masses.
Divide each number of moles by the smallest number of moles.
If needed, multiply by an integer for whole-number ratios.
Example: For a compound containing 1.71 g C and 0.287 g H.
Summary: Mass ratios can inform about empirical formula formulation.
Derivation of Molecular Formulas
Method: Determined by the empirical formula and its molar mass.
Formula: Molecular formula = empirical formula × n, where 'n' is a whole number that scales it to molecular mass.
Example: From an empirical formula CH₂O with a mass of 30 amu to a molecular mass of 180 amu giving C₆H₁₂O₆.
Miscellaneous Examples
Example 3.8: Saccharin quantity analysis from a 40.0 mg sample.
Apply quantities to figure molecular count.
Example 3.12: Determining the empirical formula from a gas composed of 27.29% C and 72.71% O.
Method involves assumption and calculation of moles from percent composition.
Conclusion
The study of moles, molar mass, and the relationship to empirical and molecular formulas is crucial in understanding chemical composition and stoichiometry in chemistry.