Lecture Notes: Finding Empirical and Molecular Formulas

Introduction

• Objective: Learn how to find the empirical formula from percent composition and molecular formula given the molar mass.

Problem 1: Finding Empirical Formula from Percent Composition

• Given:
  • Carbon: 52.14%
  • Hydrogen: 13.13%
  • Oxygen: 34.73%
• Approach:
  1. Assume a 100g sample of the compound.
  2. Convert percentages to grams:
     • Carbon: 52.14 grams
     • Hydrogen: 13.13 grams
     • Oxygen: 34.73 grams
  3. Convert grams to moles:
     • Carbon: 52.14 / 12.01 = 4.34 moles
     • Hydrogen: 13.13 / 1.008 = 13.026 moles
     • Oxygen: 34.73 / 16 = 2.171 moles
  4. Divide by smallest number of moles:
     • Carbon: 4.34 / 2.171 ≈ 2
     • Hydrogen: 13.026 / 2.171 ≈ 6
     • Oxygen: 2.171 / 2.171 = 1
  5. Empirical Formula: C₂H₆O

Problem 1: Finding Molecular Formula

• Given: Molar mass = 138.204 g/mol
• Steps:
  1. Calculate molar mass of empirical formula (C₂H₆O) = 46.068 g/mol
  2. Divide the molecular molar mass by empirical molar mass:
     • 138.204 / 46.068 = 3
  3. Multiply empirical subscripts by 3:
     • C: 2 x 3 = 6
     • H: 6 x 3 = 18
     • O: 1 x 3 = 3
  4. Molecular Formula: C₆H₁₈O₃

Problem 2: Finding Empirical Formula from Grams

• Given:
  • Carbon: 20.32g
  • Hydrogen: 5.12g
  • Nitrogen: 7.9g
• Approach:
  1. Convert grams to moles:
     • Carbon: 20.32 / 12.01 = 1.692 moles
     • Hydrogen: 5.12 / 1.008 = 5.079 moles
     • Nitrogen: 7.9 / 14.01 = 0.5639 moles
  2. Divide by smallest number of moles:
     • Carbon: 1.692 / 0.5639 ≈ 3
     • Hydrogen: 5.079 / 0.5639 ≈ 9
     • Nitrogen: 0.5639 / 0.5639 = 1
  3. Empirical Formula: C₃H₉N

Problem 2: Finding Molecular Formula

• Given: Molar mass = 236.448 g/mol
• Steps:
  1. Calculate molar mass of empirical formula (C₃H₉N) = 59.112 g/mol
  2. Divide the molecular molar mass by empirical molar mass:
     • 236.448 / 59.112 = 4
  3. Multiply empirical subscripts by 4:
     • C: 3 x 4 = 12
     • H: 9 x 4 = 36
     • N: 1 x 4 = 4
  4. Molecular Formula: C₁₂H₃₆N₄

Conclusion

• Summary: The empirical formula is determined by converting mass (or percent) to moles, then normalizing by the smallest amount of moles. To find the molecular formula, multiply the empirical formula by the ratio of the molecular to empirical molar mass.
• Key Formula:
  • Empirical Formula Calculation: Normalize atom ratios by smallest mole amount.
  • Molecular Formula Calculation: (Molar mass of molecular formula) / (Molar mass of empirical formula) to find the integer to multiply subscripts by.