Empirical and molecular calculations and formular

Percent Composition

• Percent composition of a compound is the percentage by mass of each element in the compound.
• It is calculated by dividing the mass of each element by the mass of the compound and multiplying by 100%.
• The formula to calculate percent composition is:
  • %H = (mass H / mass compound) × 100%
  • %C = (mass C / mass compound) × 100%
  • ...

Determining Percent Composition from Molecular or Empirical Formulas

• Percent composition can be derived from the molecular or empirical formula of a compound.
• The mass of each element in a known mass of compound is needed.
• The formula to calculate percent composition from a molecular formula is:
  • %C = (number of moles of C × molar mass of C) / molar mass of compound × 100%
  • %H = (number of moles of H × molar mass of H) / molar mass of compound × 100%
  • ...

Determination of Empirical Formulas

• Empirical formulas are derived from experimentally measured element masses.
• The steps to derive an empirical formula are:
  1. Derive the number of moles of each element from its mass.
  2. Divide each element's molar amount by the smallest molar amount to yield subscripts for a tentative empirical formula.
  3. Multiply all coefficients by an integer, if necessary, to ensure that the smallest whole-number ratio of subscripts is obtained.
• The empirical formula is a symbol representing the relative numbers of a compound's elements.

Deriving Empirical Formulas from Percent Composition

• Empirical formulas can be derived from percent composition data.
• The steps to derive an empirical formula from percent composition are:
  1. Calculate the mass of each element in a convenient mass of compound (e.g., 100 g).
  2. Derive the number of moles of each element from its mass.
  3. Divide each element's molar amount by the smallest molar amount to yield subscripts for a tentative empirical formula.
  4. Multiply all coefficients by an integer, if necessary, to ensure that the smallest whole-number ratio of subscripts is obtained.

Derivation of Molecular Formulas

• Molecular formulas are derived from the empirical formula and molecular mass (or molar mass).
• The steps to derive a molecular formula are:
  1. Calculate the empirical formula mass.
  2. Divide the molecular mass (or molar mass) by the empirical formula mass to yield the number of empirical formula units per molecule (n).
  3. Multiply each subscript in the empirical formula by n to obtain the molecular formula.
• Molecular formulas are symbols representing the absolute numbers of atoms in a compound's molecules.### Determining the Chemical Formula of a Compound
• Percent Composition: the percentage by mass of each element in a compound
  • Example: a gaseous compound composed of carbon and hydrogen
    • %H = mass H / mass compound × 100%
    • %C = mass C / mass compound × 100%
  • If analysis of a 10.0-g sample showed it to contain 2.5 g H and 7.5 g C, the percent composition would be 25% H and 75% C

Calculating Percent Composition

• Example 3.9: analysis of a 12.04-g sample of a liquid compound composed of carbon, hydrogen, and nitrogen
  • %C = 7.34 g C / 12.04 g compound × 100% = 61.0%
  • %H = 1.85 g H / 12.04 g compound × 100% = 15.4%
  • %N = 2.85 g N / 12.04 g compound × 100% = 23.7%

Determining Percent Composition from Molecular or Empirical Formulas

• Example 3.10: aspirin with the molecular formula C9H8O4
  • To calculate the percent composition, consider 1 mol of C9H8O4 and use its molar mass (180.159 g/mol)
  • %C = 9 mol C × molar mass C / molar mass C9H8O4 × 100% = 60.00%
  • %H = 8 mol H × molar mass H / molar mass C9H8O4 × 100% = 4.476%
  • %O = 4 mol O × molar mass O / molar mass C9H8O4 × 100% = 35.52%

Derivation of Empirical Formulas

• Empirical Formula: symbols representing the relative numbers of a compound's elements
  • Derived from the masses of its constituent elements
  • The most common approach to determining a compound's chemical formula
• Example 3.11: a sample of the black mineral hematite (Fe2O3) contains 34.97 g of iron and 15.03 g of oxygen
  • Moles of iron and oxygen: 0.6261 mol Fe and 0.9394 mol O
  • Iron-to-oxygen molar ratio: 1.000 mol Fe to 1.500 mol O
  • Empirical formula: Fe2O3

Derivation of Molecular Formulas

• Molecular Formula: derived by comparing the compound's molecular or molar mass to its empirical formula mass
  • If the molecular (or molar) mass of the substance is known, it may be divided by the empirical formula mass to yield the number of empirical formula units per molecule (n)
  • Molecular formula: (AxBy)n = AnxBny
• Example 3.13: nicotine with a molecular mass of 180 amu
  • Empirical formula mass: 30 amu (sum of atomic masses of C, H, and O)
  • Number of empirical formula units per molecule: 180 amu / 30 amu = 6
  • Molecular formula: (CH2O)6 = C6H12O6### Empirical Formulas
• Derived from experimentally measured element masses
• Steps to derive empirical formula:
  • Derive number of moles of each element from its mass
  • Divide each element's molar amount by the smallest molar amount to yield subscripts for a tentative empirical formula
  • Multiply all coefficients by an integer, if necessary, to ensure that the smallest whole-number ratio of subscripts is obtained

Calculating Moles of Elements

• Formula: mass of element (g) × (1 mol / molar mass of element (g/mol))
• Example: 1.71 g C × (1 mol C / 12.01 g C) = 0.142 mol C

Converting to Whole-Number Ratios

• Divide each subscript by the smallest subscript to get a whole-number ratio
• If decimal subscripts remain, multiply all subscripts by an integer to get whole numbers

Flow Chart for Deriving Empirical Formula

• Measure mass of elements
• Calculate moles of elements
• Divide by smallest number of moles
• Convert ratio to whole numbers
• Write empirical formula

Examples of Deriving Empirical Formulas

• Hematite (iron oxide): Fe2O3
• Gas from bacterial fermentation of grain: CO2
• Compound with percent composition: CH2O

Molecular Formulas

• Derived from empirical formula and molecular or molar mass
• Molecular mass or molar mass is often determined experimentally
• Empirical formula mass is the sum of average atomic masses of all atoms represented
• Molecular formula is derived by comparing molecular or molar mass to empirical formula mass

Deriving Molecular Formulas

• Formula: molecular or molar mass (amu or g/mol) / empirical formula mass (amu or g/mol) = n formula units/molecule
• Multiply each subscript in the empirical formula by n to get the molecular formula
• Example: (CH2O)6 = C6H12O6

Example of Deriving Molecular Formula

• Nicotine: C10H14N2