Final answer:
The molecular formula of a compound with the empirical formula C13H19O2 and molar mass of 414.64 g/mol is C26H38O4.
Step-by-step explanation:
To find the molecular formula of a compound with the empirical formula C13H19O2 and a molar mass of 414.64 g/mol, we first need to calculate the empirical formula mass. The empirical formula mass of C13H19O2 is (13 × 12.01 g/mol for carbon) + (19 × 1.01 g/mol for hydrogen) + (2 × 16.00 g/mol for oxygen), which equals 205.32 g/mol. Then, we divide the given molar mass by the empirical formula mass to determine how many times the empirical formula fits into the molar mass.
414.64 g/mol ÷ 205.32 g/mol ≈ 2
Since the result is approximately 2, we multiply the subscripts in the empirical formula by 2 to obtain the molecular formula, resulting in C26H38O4 as the molecular formula of the compound.