What is the molecular formula of caffeine given its empirical formula and molar mass?

The empirical formula of caffeine is C₄H₅N₂O, and its molar mass is 194 g/mol. To find the molecular formula, we need to determine how many empirical formula units make up the molecular formula.

First, calculate the molar mass of the empirical formula:

• C: 4 atoms × 12.01 g/mol = 48.04 g/mol
• H: 5 atoms × 1.01 g/mol = 5.05 g/mol
• N: 2 atoms × 14.01 g/mol = 28.02 g/mol
• O: 1 atom × 16.00 g/mol = 16.00 g/mol

Total molar mass of empirical formula = 48.04 + 5.05 + 28.02 + 16.00 = 97.11 g/mol

Next, divide the molar mass of the molecular formula by the molar mass of the empirical formula:

194 g/mol ÷ 97.11 g/mol ≈ 2

This means the molecular formula is twice the empirical formula. Therefore, the molecular formula of caffeine is:

C₈H₁₀N₄O₂