Final answer:
To find the molecular formula of caffeine, percent composition is used to derive the empirical formula, which is then modified according to the molar mass of 195 g/mol to obtain the molecular formula.
Step-by-step explanation:
Calculating the Molecular Formula of Caffeine
To determine the molecular formula of caffeine, we first use percent composition data to find the empirical formula. With a hypothetical 100 grams of the compound, we would have 49.5 grams of C, 5.15 grams of H, 28.9 grams of N, and the remaining mass would be O. By dividing these masses by the respective molar masses of these elements (C: 12.01 g/mol, H: 1.008 g/mol, N: 14.01 g/mol, O: 16.00 g/mol), we can calculate the number of moles of each element.
For example, 49.5 grams of C translates to 49.5 g ÷ 12.01 g/mol ≈ 4.12 moles of C. Implementing this process for each element, we get a preliminary empirical formula. However, because the molar mass of caffeine is provided as 195 g/mol, we must find the ratio between the empirical formula mass and this molar mass, adjusting the empirical formula accordingly to get the true molecular formula for caffeine. The final step is to multiply the empirical formula by the ratio to acquire the molecular formula that matches the provided molar mass.