3.5 | Formula weights and elemental composition of substances

Empirical and Molecular Formulas

• Empirical Formula: Represents the relative number of atoms of each element in a substance.

  • Example: Water (H₂O) has 2 H atoms for every 1 O atom.

  • Applies to moles: 1 mole of H₂O = 2 moles of H and 1 mole of O.

  • Links to mole concept for computing empirical formulas from experimental data.

Calculating Empirical Formulas from Mass Percentages

• Objective: Determine empirical formulas from mass percentages of elements present in a compound.

  • Example Compound: 74% Mercury (Hg) and 26% Chlorine (Cl) by mass.

  • Sample Size: Generally use a hypothetical 100 g sample for simplicity.

  • Calculation:

    • Hg mass in sample = 74 g, Cl mass = 26 g.

    • Convert mass to moles using atomic weights:

      • Moles of Hg: ( \frac{74 \text{ g Hg}}{200.6 \text{ g/mol}} = 0.369 \text{ mol Hg} )

      • Moles of Cl: ( \frac{26 \text{ g Cl}}{35.5 \text{ g/mol}} = 0.732 \text{ mol Cl} )

Mole Ratio and Empirical Formula

• Divide the larger mole quantity by the smaller:

  • ( \frac{0.732 \text{ mol Cl}}{0.369 \text{ mol Hg}} \approx 1.98 \text{ mol Cl: 1 mol Hg} )

• Interpretation: Round 1.98 to 2.

• Resulting Empirical Formula: HgCl₂, as the subscripts reflect the smallest integer ratio of atoms.

Relationship Between Empirical and Molecular Formulas

• Molecular Formula: Can differ from empirical formula (C₆H₆ for benzene has empirical formula CH).

• Determining Molecular Formula:

  • Requires empirical formula and molecular weight (could be measured using techniques like mass spectrometry).

  • Whole number multiple = ( \frac{Molecular Weight}{Empirical Formula Weight} )

Example: Ascorbic Acid (Vitamin C)

• Empirical Formula: C₃H₄O₃

• Empirical Formula Weight: ( 3(12 , ext{amu}) + 4(1.0 , ext{amu}) + 3(16 , ext{amu}) = 88 , ext{amu} )

• Molecular Weight: 176 amu.

• Whole Number Multiple Calculation:

  • ( \frac{176 , ext{amu}}{88 , ext{amu}} = 2 )

• Molecular Formula: Multiply subscripts by 2, resulting in C₆H₈O₆.

Techniques for Determining Empirical Formulas

• Combustion Analysis: Common for carbon and hydrogen compounds.

  • Carbon is converted to CO₂; hydrogen to H₂O during combustion.

  • Measured masses of CO₂ and H₂O allow calculation of moles of C and H in the original sample.

  • If a third element is present, its mass can be derived by subtracting the masses of C and H from the original sample mass.