Final answer:
To estimate the surface-to-volume ratio of a C60 fullerene, treat the molecule as a hollow sphere and calculate its surface area and volume. The surface area is found using the formula A = 4πr² and the volume is found using the formula V = (4/3)πr³, where r is the radius of the sphere. Dividing the surface area by the volume gives the surface-to-volume ratio.
Step-by-step explanation:
To estimate the surface-to-volume ratio of a C60 fullerene, we can treat the molecule as a hollow sphere and calculate its surface area and volume.
The surface area of a sphere is given by the formula A = 4πr^2, where r is the radius of the sphere.
The volume of a sphere is given by the formula V = (4/3)πr^3.
Since the C60 fullerene is composed of 60 carbon atoms, we can divide the atomic radius of carbon by 2 to get the radius of the molecule. Using the given atomic radius of 77pm, the radius of the C60 fullerene is 38.5pm (or 0.385nm).
Using these values, we can calculate the surface area and volume of the C60 fullerene:
- Surface Area (A) = 4π(0.385nm)^2
- Volume (V) = (4/3)π(0.385nm)^3
Now we can calculate the surface-to-volume ratio by dividing the surface area by the volume:
Surface-to-Volume Ratio = A / V
Substituting the calculated values into the formula, we get:
Surface-to-Volume Ratio = (4π(0.385nm)^2) / ((4/3)π(0.385nm)^3)
Simplifying the equation, we find that the surface-to-volume ratio of the C60 fullerene is approximately 0.649 nm-1.