Knowing that the diameter of an oxygen molecule is 0.31 nm, calculate the length of the chain that can be built from

Knowing that the diameter of an oxygen molecule is 0.31 nm, calculate the length of the chain that can be built from 1 mg of oxygen molecules if these molecules are densely arranged in one row. molar mass of oxygen 0.032 kg / mol

The mass of oxygen molecules in 1 mg corresponds to the amount of substance ν:

ν = m / M = (0.000001 kg) / (0.032 kg / mol) = 1 mol / 32000,

(m is the mass of the substance, M is the molar mass).

Number of molecules N:

N = νNA = (1 mol / 32000) * 6.02 ^ 3 * 10 ^ 23 mol-1 =
= (6.02 * 10 ^ 23) / 3.2 * 10 ^ 4 =
= (6.02 * 10 ^ 19) / 3.2 (NA is Avogadro’s number).

The chain length L is equal to the product of the number of molecules N by the diameter of the molecule d:

L = Nd = (6.02 * 10 ^ 19 * 0.31 * 10 ^ -9 m) / 3.2 ≈ 5.8 * 10 ^ 9 m.

Answer: L ≈ 5.8 * 10 ^ 9 m.

For clarity, compare with the length of the Earth’s equator:
40,000 km = 4 * 10 ^ 7 m.

(5.8 * 10 ^ 9 m) / (4 * 10 ^ 7 m) = 145, that is, the length of the chain is equal to 145 equators.