Question

Estimate the fraction of molecular volume to the actual volume occupied by Oxygen gas at STP. Take the diameter of an oxygen molecule to be $3 \AA$.

Answer 1

Diameter of an oxygen molecule, d = 3Å
Radius, r = d/2 = 3/2 = 1.5 Å = 1.5 × 10–8 cm
Actual volume occupied by 1 mole of oxygen gas at STP = 22400 cm3
Molecular volume of oxygen gas, V = (4/3)πr3N
Where, N is Avogadro’s number = 6.023 × 1023molecules/mole
∴ V = (4/3) × 3.14 × (1.5 × 10-8)3 × 6.023 × 1023 = 8.51 cm3
Ratio of the molecular volume to the actual volume of oxygen = 8.51 / 22400
= 3.8 × 10-4.

Answer 2

$\large{\underline{\rm{\purple{\bf{Question:-}}}}}$

Estimate the fraction of molecular volume to the actual volume occupied by oxygen at STP. Take the diameter of an oxygen molecule to be 3 Å

$\large{\underline{\rm{\purple{\bf{Given:-}}}}}$

Diameter of an oxygen molecule, d = 3Å

$\large{\underline{\rm{\purple{\bf{To \: Find:-}}}}}$

Estimate the fraction of molecular volume to the actual volume occupied by Oxygen gas at STP.

$\large{\underline{\rm{\purple{\bf{Solution:-}}}}}$

We know that,

• d = Diameter
• r = Radius
• N = Avogardo's number
• V = Volume

Given that,

Diameter of an oxygen molecule, d = 3Å

Then,

$\boxed{ \sf Radius = \dfrac{d}{2} }$

$\sf = 1.5$ Å

$\sf = 1.5 \times 10^{-8} \: cm$

We know,

Actual volume occupied by 1 mole of oxygen at STP = $\sf 22400 \: cm^{2}$

Molecular volume of oxygen, V = $\sf N_A \bigg(\dfrac{4 \pi r^{2}}{2} \bigg)$

Where, N is Avogadro’s number = $\sf 6.023 \times 10^{23} \: molecules/mole$

Therefore, molecular volume of oxygen, V = $\sf 6.023 \times 10^{23} \times 3.14 \: (1.5 \times 10^{-8})^{2} \times \dfrac{4}{3} =8.51 \: cm^{3}$

Thus, the ratio of the molecular volume to the actual volume of oxygen = $\sf \dfrac{8.51}{22400} = 3.8 \times 10^{-4}$