Estimate the frac

Given:

Diameter of an oxygen molecule (D) = 3 Å

∴ the radius of an oxygen molecule (r) = 1.5 Å (∵ r = D/2)

Fraction = ?

Explanation: We know that the volume occupied by 1 mole of oxygen gas at STP = 22.4 litres. The molecular volume occupied 1 mole of oxygen molecules can be found by multiplying the volume of a single oxygen molecule (considering it to be a sphere) with the

Avogadro's constant. Then dividing the latter by the former the required result is obtained.

Volume of 1 mole of oxygen gas at S.T.P(V_molecular)

V_molecular = πr³ × N_A ---(1)

The actual volume occupied by oxygen gas at STP (V_actual)

V_actual = 22.4 litres = 0.0224 m³

V_actual = 0.0224 m³ ---(2)

(Where N_A = 6.02214086 × 10²³ mol^-1 is Avogadro's constant.)

Substituting for ‘r’ and ‘N_A’ in equation (1) we get

V_molecular = πr³ × N_A = π(1.5 × 10^-10)³ × ( 6.02214086 × 10²³)

= 0.000008513≈ 8.51 × 10^-6 m³

(∵ 1 Å = 1 × 10^-10 m)

∴ V_molecular = 8.52 × 10^-6 m³ ---(3)

Fraction = = = 0.00038007 ≈ 3.8 × 10^-4

Fraction = 3.8 × 10^-4

The required ratio/fraction is 3.8 × 10^-4.