Question

Three liters (3000 cm3) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes a circular oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules are round with a diameter of 2 x 10-10 m.

Answer 1

4.38 km

Step-by-step explanation:

Volume of oil slick, V = Area of oil slick, A × thickness of 1 molecule, d'

Since the oil slick spreads out in a circular area, it has the area of a circle.

So, V = πd²/4 × d'

d² = 4V/πd'

d = 2√(V/πd') where d = diameter of oil slick.

Since V = 3000 cm³ = 3000 × 10⁻⁶ m³ = 3 × 10⁻³ m³ and d' = 2 × 10⁻¹⁰ m

So, d = 2√(3 × 10⁻³ m³/(π × 2 × 10⁻¹⁰ m))

= 2√(3 × 10⁻³ m³/(6.283 × 10⁻¹⁰ m))

= 2√(0.477 × 10⁷ m²) = 2√(4.775 × 10⁶ m²)

= 2 × 2.19 × 10³ m

= 4.38 × 10³ m

= 4.38 km