Final answer:
To find the area of the oil slick one molecule thick, we first determine the volume of one molecule and then calculate the number of these molecules needed to cover 2.5 cubic meters. The area is found to be 5.0 x 106 m2 when expressed in two significant figures.
Step-by-step explanation:
To calculate the area of the oil slick that is one molecule thick, we need to find the volume each molecule occupies and then determine how many of these molecules cover 2.5 cubic meters. The side of each molecule's cube is 0.50 µm, so the volume is (0.50 µm) x (0.50 µm) x (0.50 µm) = 0.125 µm3 per molecule. However, we need to convert this to cubic meters for consistency with the oil volume given. 1 µm3 is 10-18 m3, so each molecule occupies 0.125 x 10-18 m3. To find the number of molecules, we divide the total volume by the volume of one molecule: 2.5 m3 / 0.125 x 10-18 m3 = 2.0 x 1019 molecules. Assuming a square layout, the length of one side covered by the molecules can be found by taking the square root of the number of molecules: √(2.0 x 1019) = 4.47 x 109. Since each molecule covers a side of 0.50 µm, the total length in meters is 0.50 µm (or 0.50 x 10-6 m) x 4.47 x 109 = 2235 meters. The area is thus the side length squared: (2235 m)2 = 4.99 x 106 m2, or to two significant figures, 5.0 x 106 m^2.