Answer:
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
