Question

In 1774 Benjamin Franklin described
some experiments he had performed on a pond at Clapham Common in
London. He observed that a teaspoon (volume 4.5 cm^{3}) of
olive oil [Oleic Acid
CH_{3}(CH_{2})_{7}CH=CH(CH_{2})_{7}COOH
; density 0.92 g cm^{-3}] when spread of a water surface of
half an acre (2 x 10^{3} m^{2}) would calm that
entire surface.

Calculate the thickness (in nm) of the surface film and the surface
area (in nm^{2}) occupied by an oleic acid molecule on
water. Account briefly for your answers.

Answer #1

Part a

Volume of oleic acid V = 4.5 cm3 x 10^-6 m3/cm3

V = 4.5 x 10^-6 m3

Area of surface A = 2 x 10^3 m2

Thickness of surface film = V/A

= 4.5 x 10^-6 m3 / 2 x 10^3 m2

= 2.25 x 10^-9 m x 10^9 nm/m

= 2.25 nm

Part b

Avogadro number = 6.022 x 10^23 molecules / mol

6.022*10^23 molecules cover = 2000 m2

1 molecule will cover = 2000 m2 / 6.022*10^23

= 3.321 x 10^-21 m2

surface area (in nm2) occupied by an oleic acid molecule

= 3.321 x 10^-21 m2 x (10^9 nm/m)^2

= 0.003321 nm2

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