Lecture Notes: Empirical and Molecular Formulas from Percent Composition

Introduction

• Discussion on finding the empirical and molecular formulas of a compound
• Two key scenarios covered:
  1. Finding empirical formula from percent composition
  2. Determining molecular formula given molar mass

Problem 1: Empirical Formula from Percent Composition

• Given:
  • Compound consists of 52.14% carbon, 13.13% hydrogen, and 34.73% oxygen by mass
• Approach:
  1. Assume 100 grams of the compound:
     • 52.14 grams carbon
     • 13.13 grams hydrogen
     • 34.73 grams oxygen
  2. Convert grams to moles:
     • Carbon: 52.14 g / 12.01 g/mol = 4.34 moles
     • Hydrogen: 13.13 g / 1.008 g/mol = 13.026 moles
     • Oxygen: 34.73 g / 16 g/mol = 2.171 moles
  3. Divide by smallest number of moles (oxygen):
     • C: 4.34 / 2.171 ≈ 2
     • H: 13.026 / 2.171 ≈ 6
     • O: 2.171 / 2.171 = 1
  4. Empirical Formula: C₂H₆O

Problem 1: Molecular Formula

• Given:
  • Molar mass is 138.204 g/mol
• Approach:
  1. Calculate molar mass of empirical formula (C₂H₆O):
     • 2(12.01) + 6(1.008) + 16 = 46.068 g/mol
  2. Divide molar mass of compound by molar mass of empirical formula:
     • 138.204 / 46.068 ≈ 3
  3. Multiply subscripts of empirical formula by 3:
     • Molecular Formula: C₆H₁₈O₃

Problem 2: Empirical Formula from Given Grams

• Given:
  • 20.32 g carbon, 5.12 g hydrogen, 7.9 g nitrogen
• Approach:
  1. Convert grams to moles:
     • Carbon: 20.32 g / 12.01 g/mol = 1.692 moles
     • Hydrogen: 5.12 g / 1.008 g/mol = 5.079 moles
     • Nitrogen: 7.9 g / 14.01 g/mol = 0.5639 moles
  2. Divide by smallest number of moles (nitrogen):
     • C: 1.692 / 0.5639 ≈ 3
     • H: 5.079 / 0.5639 ≈ 9
     • N: 0.5639 / 0.5639 = 1
  3. Empirical Formula: C₃H₉N

Problem 2: Molecular Formula

• Given:
  • Molar mass is 236.448 g/mol
• Approach:
  1. Calculate molar mass of empirical formula (C₃H₉N):
     • 3(12.01) + 9(1.008) + 14.01 = 59.112 g/mol
  2. Divide molar mass of compound by molar mass of empirical formula:
     • 236.448 / 59.112 ≈ 4
  3. Multiply subscripts of empirical formula by 4:
     • Molecular Formula: C₁₂H₃₆N₄

Conclusion

• Learned how to determine empirical and molecular formulas from percent composition and given masses.
• Key steps involve conversion of mass to moles, normalization by smallest moles, and scaling to obtain molecular formula.