8 - Molecular and Empirical Formula

Molecular Composition and Empirical Formula

Definitions

  • Mass Percent:

    • Calculated as the mass of an element in 1 mole of the compound divided by the molar mass of the compound, multiplied by 100%.

    • Example: For C₆H₁₂O₆, calculate mass percent for Carbon, Hydrogen, and Oxygen.

Calculating Mass Percent

  • Carbon:

    • Mass of Carbon = 6 x 12.01 g/mol = 72.06 g

    • Molar mass of C₆H₁₂O₆ = 180.18 g/mol

    • Percent Mass = (72.06 g / 180.18 g) x 100% = 40.00%

  • Hydrogen:

    • Mass of Hydrogen = 12 x 1.008 g/mol = 12.096 g

    • Percent Mass = (12.096 g / 180.18 g) x 100% = 6.71%

  • Oxygen:

    • Percent Mass = 100% - (40.00% + 6.71%) = 53.29%

Empirical vs. Molecular Formulas

  • Empirical Formula:

    • The simplest whole-number ratio of elements in a compound.

  • Molecular Formula:

    • The actual number of atoms of each element in a molecule. It may be the same as the empirical formula or a multiple of it.

Examples of Formulas

  • Example Compound: C₆H₁₂O₆

    • Empirical Formula = CH₂O (divided by 6)

  • Another Compound: C₆H₅O₂

    • Empirical Formula: C₃H₅O (divided by 2)

Solving for Empirical Formula

Scenario Calculation Example

Given:

  • Carbon = 37.51%,

  • Hydrogen = 4.20%,

  • Oxygen = 58.29% (assumed as 100g basis)

  • Convert to grams:

    • C = 37.51 g, H = 4.20 g, O = 58.29 g

  • Convert grams to moles:

    • C: 37.51 g / 12.01 g/mol = 3.12 mol

    • H: 4.20 g / 1.008 g/mol = 4.17 mol

    • O: 58.29 g / 16.00 g/mol = 3.64 mol

  • Calculate ratios (divide by smallest number, 3.12):

    • C = 1

    • H = 1.33

    • O = 1.17

  • Making whole numbers:

    • Multiply by 6: C₆H₈O₇ (empirical formula)

Finding Molecular Formula

  • Given Molecular Mass: 384.25 g/mol

  • Empirical Formula Mass: 192.12 g/mol

  • Ratio: 384.25 / 192.12 = 2

    • Molecular Formula = 2(C₆H₈O₇) = C₁₂H₁₆O₁₄

Tips for Multiplying Ratios to Whole Numbers

  • If decimal ends in 0.5, multiply by 2.

  • If decimal ends in .33, multiply by 3.

  • If decimal ends in .66, multiply by 3.

  • If decimal ends in 0.25, multiply by 4.

Example Problem with Isogenol

  • Given: 0.500g of Isogenol combusted to yield CO₂ and H₂O

  • Calculation involves determining grams of Carbon and Hydrogen from CO₂ and H₂O produced, then finding mass of Oxygen through subtraction from original mass.