Determine molecular formulas from empirical formulas and molecular weights using precise stoichiometric calculations
You can use subscripts (₂) or regular numbers (2)
Empirical Formula: Simplest whole-number ratio of atoms
Molecular Formula: Actual number of atoms in a molecule
Relationship: Molecular Formula = (Empirical Formula) × n
Calculate n: n = Molecular Weight / Empirical Formula Mass
Example: CH₂O (empirical) → C₆H₁₂O₆ (molecular), n = 6
Find simplest ratio
Calculate molar mass
Mass percent analysis
Reaction calculations
n = MW / EFM
Multiplier from molecular weight
Molecular = Empirical × n
Apply multiplier to formula
The molecular formula represents the actual number of atoms of each element present in one molecule of a compound. Unlike the empirical formula, which shows only the simplest whole-number ratio of atoms, the molecular formula provides the exact composition of a molecule. This distinction is crucial in chemistry because compounds with different molecular formulas (but the same empirical formula) have entirely different properties.
The empirical formula shows the simplest ratio of elements in a compound. For example, glucose has the empirical formula CH₂O, indicating that for every carbon atom, there are two hydrogen atoms and one oxygen atom. However, the molecular formula of glucose is C₆H₁₂O₆, showing that a single glucose molecule contains six carbon atoms, twelve hydrogen atoms, and six oxygen atoms.
The relationship between empirical and molecular formulas is expressed mathematically as: Molecular Formula = (Empirical Formula) × n, where n is a whole number multiplier. This multiplier can be calculated by dividing the molecular weight by the empirical formula mass: n = Molecular Weight / Empirical Formula Mass.
Empirical Formula: CH₂O
Empirical Mass: 30.03 g/mol
Molecular Weight: 180.16 g/mol
Multiplier: n = 180.16 / 30.03 = 6
Molecular Formula: C₆H₁₂O₆
Empirical Formula: CH
Empirical Mass: 13.02 g/mol
Molecular Weight: 78.11 g/mol
Multiplier: n = 78.11 / 13.02 = 6
Molecular Formula: C₆H₆
Empirical Formula: CH₂O
Empirical Mass: 30.03 g/mol
Molecular Weight: 60.05 g/mol
Multiplier: n = 60.05 / 30.03 = 2
Molecular Formula: C₂H₄O₂
Empirical Formula: CH₂
Empirical Mass: 14.03 g/mol
Molecular Weight: 28.05 g/mol
Multiplier: n = 28.05 / 14.03 = 2
Molecular Formula: C₂H₄
Some compounds have molecular formulas identical to their empirical formulas. For example, water (H₂O), formaldehyde (CH₂O), and carbon dioxide (CO₂) all have n = 1. In these cases, the empirical and molecular formulas are the same because the simplest ratio already represents the actual molecular composition.
Different compounds can have the same molecular formula but different structures. These are called isomers. For instance, both glucose and fructose have the molecular formula C₆H₁₂O₆, but they have different structural arrangements and therefore different properties. The molecular formula alone doesn't tell us about the structure or connectivity of atoms.
Analytical Chemistry: When analyzing unknown compounds using techniques like mass spectrometry, chemists first determine the molecular weight. Combined with elemental analysis that provides the empirical formula, they can calculate the molecular formula, which is a crucial step in identifying the compound.
Organic Synthesis: In organic chemistry, knowing the molecular formula helps predict possible structures and plan synthesis routes. The molecular formula provides essential information about the degree of unsaturation and possible functional groups present in organic molecules.
Biochemistry: Molecular formulas are essential for understanding biological molecules. Carbohydrates often have molecular formulas that are multiples of CH₂O, proteins have complex formulas based on their amino acid composition, and nucleic acids have specific formulas that reflect their nucleotide building blocks.
To experimentally determine a molecular formula, chemists typically follow these steps:
Polymers: For polymers, the concept of molecular formula becomes more complex. Polymers are large molecules made of repeating units, and their molecular weights can vary. Instead of a single molecular formula, polymers are often described by their repeating unit and average molecular weight or degree of polymerization.
Non-stoichiometric Compounds: Some compounds, particularly certain metal oxides and semiconductors, don't have exact whole-number ratios of atoms. These non-stoichiometric compounds require special consideration and may be represented with variable compositions (e.g., Fe₀.₉₅O).
Hydrates: When dealing with hydrated compounds, the molecular formula includes water molecules. For example, copper(II) sulfate pentahydrate has the molecular formula CuSO₄·5H₂O. The water molecules are part of the crystal structure and must be considered in molecular weight calculations.
Multiplier: n = Molecular Weight ÷ Empirical Formula Mass
Molecular Formula: (Empirical Formula) × n
Verification: Calculate molecular weight from molecular formula and compare to experimental value