In 1773 Benjamin Franklin, investigating the calming effect of oil on the water of a pond near London, observed that a teaspoonful of oil would cover about half an acre of the surface. From this information, estimate the height or thickness of an oil molecule in the floating film of oil. Then estimate the cross sectional area of an oil molecule in the floating film You may assume that Franklin used a lamp oil, like camphene, C10H16. Required:
Calculate the thickness (in nm) of the surface film and the surface area (in nm2) occupied by an oleic acid molecule on water.

a. 2.44 nm

b. 15.33 nm²

Explanation:

a. Calculate the thickness (in nm) of the surface film

Since the volume of a teaspoon equals V = 4.93 cm³ and the area of the oil film is half an acre = 1/2 × 4046.86 m² = 2023.43 m²

The volume of the oil film, V' equals the volume of the oil in the teaspoon, V

V' = Ah where A = cross-sectional area of oil film = 2023.43 m² = 2023.43 × 10⁴ cm² and h = height of oil film

So, V' = V

Ah = V

h = V/A

= 4.93 cm³/2023.43 × 10⁴ cm²

= 0.00244 × 10⁻⁴ cm

= 2.44 × 10⁻⁷ cm

=  2.44 × 10⁻⁷ cm × 1m/100 cm

= 2.44 × 10⁻⁹ m

= 2.44 nm

b. The surface area (in nm2) occupied by an oleic acid molecule on water.

Since the height of the oil film equals the diameter of the oil molecule, and the molecule is assumed to be a sphere of radius, r. Its surface area is thus A = 4πr²

r = h/2 = 2.44 nm/2 = 1.22 nm

A = 4πr²

A = 4π(1.22 nm)²

A = 4.88π nm²

A = 15.33 nm²

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