Question

Suppose 3.0 cubic meter of oil is spilled into the ocean. Find the area of the resulting slick, assuming that it is one molecule thick, and that each molecule occupies a cube 0.50 μm on a side.

Answer 1

Let the spill has thickness $t$, and the area of the resulting slick is $A$. The resulting slick can have any shape, but irrespective of the shape, we can write the volume $V$ in terms of the area and the thickness.

$V = A \times t$

One molecule has side of length $0.5 \mu m$, and the layer is one molecule thick. Therefore, the thickness of the layer is also $0.5 \mu m$.

The volume is $3m^{3}$

$3m^{3} = A \times 0.5 \mu m = A \times 0.5 \times 10^{-6}$

$A = \frac{3m^{3}}{0.5\times 10^{-6}m} = 6\times 10^{6} m^{2}$

The slick is spread across 6 square Kilometres area.