Chemical Mass and Empirical Formulas

Molecular Mass (MM)

  • Definition: The molecular mass (MM) is the sum of all atomic masses of all atoms in the molecule.

  • For ionic compounds, the term formula mass (FM) is used instead of molecular mass.

    • Reason: Ionic compounds consist of ions, not molecules.

    • Thus, the formula mass is calculated as:
      FM = ext{Sum of all atomic masses of all atoms in a formula unit}

  • In calculations, molecular mass (MM) and formula mass (FM) will be used interchangeably.

  • Unit: The unit of measure for MM and FM is atomic mass units (amu) or Dalton (Da).

  • Precision in Measurements:

    • Generally, 3 significant figures (SF) are considered sufficient for most purposes.

    • In contexts requiring higher precision, 2 decimal points may be used for larger measurements of MM.

Mole and Molar Mass

  • Definition of Mole:

    • A mole is defined as the quantity of substance that contains as many molecules or formula units as there are atoms in 12 grams of carbon-12 (C-12).

    • This quantity is known as Avogadro’s number (NA):
      N_A = 6.0221367 \times 10^{23}

  • Therefore, one mole (mol) is equivalent to having $N_A$ of molecules (or formula units).

  • Definition of Molar Mass:

    • Molar mass is the mass of one mole of a substance.

    • The numerical value of molar mass is equal to the molecular mass (MM).

    • Unit of molar mass: grams per mole (g/mol).

Determining Chemical Formulas

  • Calculation of Percentage Composition:

    • The % composition is the mass percentage of each element in a compound.

    • Methods to determine % composition include:

    • Combustion analysis (e.g., CHN or CHNS analysis)

    • Gravimetric analysis

    • Optical atomic spectroscopy (both emission and absorption)

    • Neutron activation analysis

  • Formula for Mass Percentage:

    • The mass percentage of element A in a compound can be calculated using:
      ext{Mass \% of element A} = \frac{\text{mass of element A in compound}}{\text{mass of compound}} \times 100\%

Combustion Analysis for Empirical Formula Determination

  • Procedure for Combustion Analysis:

    • An unknown compound is burned in oxygen to isolate and weigh the products (water and carbon dioxide).

    • C (carbon) and H (hydrogen) are the easiest elements to determine, as they produce CO₂ and H₂O, respectively.

  • Diagram Overview:

    • The unknown compound is combusted in a furnace, generating CO₂ and H₂O.

    • CO₂ is absorbed by a CO₂ absorber, and H₂O is captured by an H₂O absorber.

  • Key Steps in Determining Empirical Formula:

    1. From the given % composition of all elements:

    • Assume a 100 g sample and convert percentages into corresponding masses.

    1. Convert these masses into moles of each element.

    2. Formulate a “pseudoformula” based on mole ratios.

    3. If the subscripts are fractions after calculations:

    • Divide all subscripts by the smallest subscript.

    • If resulting subscripts remain fractional, multiply all by a small whole number to convert into whole numbers.

      • For specific fractional scenarios:

        • If the subscripts are 0.2, 0.4, or 0.8, multiply by 5.

        • If the subscripts are 0.25 or 0.75, multiply by 4.

        • If the subscripts are 0.33 or 0.67, multiply by 3.

        • If the subscripts are 0.50, multiply by 2.

  • Example Problem 1:

    • Given combustion data: 60.00% C, 4.48% H, 35.52% O, identify the empirical formula.

Further Examples of Determining Empirical Formula from Combustion Data

  • From Masses of Combustion Products:

    • Convert the masses of CO₂ and H₂O produced into moles.

    • Calculate moles of C and H based on stoichiometric relationships to CO₂ and H₂O:

    • For CO₂: 1 mole of CO₂ contains 1 mole of C.

    • For H₂O: 1 mole of H₂O contains 2 moles of H.

    • Compile a “pseudoformula” based on calculated moles.

    • Follow the previous steps for reducing fractions to smallest whole numbers.

  • Example Problem 2:

    • Find the empirical formula for a compound containing only C and H, if a sample produces 1.83 g CO₂ and 0.901 g H₂O upon combustion.

  • Example Problem 3:

    • Find the empirical formula for a compound containing C, H, and O if a sample weighing 0.8233 g produces 2.445 g CO₂ and 0.6003 g H₂O upon combustion.