Final answer:
The molecular formula for buckminsterfullerene is C₆₀, determined by dividing its molar mass (720.6 g/mol) by the atomic mass of carbon (12.01 g/mol), which results in 60 carbon atoms in the molecule.
Step-by-step explanation:
To find the molecular formula for buckminsterfullerene, given that its empirical formula is C₁ and its molar mass is 720.6 g/mol, we must compare the molar mass of the empirical formula to the molar mass of the molecular formula. The molar mass of a single carbon atom (the empirical formula) is approximately 12.01 g/mol, since that is the atomic mass of carbon. Dividing the given molar mass of buckminsterfullerene by the atomic mass of carbon, we get 720.6 g/mol ÷ 12.01 g/mol = 60, which suggests that the molecular formula of buckminsterfullerene is C₆₀, as it contains 60 carbon atoms.
This is consistent with the known structure of buckminsterfullerene, which is a spherical molecule composed of 60 carbon atoms arranged in a pattern of hexagons and pentagons, resembling a soccer ball or a geodesic dome designed by R. Buckminster Fuller. Hence, the molecular formula is C₆₀.