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 3Å.​

Answer 1

Explanation:

The ideal gas equation relating pressure (P), volume (V), and absolute temperature (T) is given as:

PV = nRT

Where,

R is the universal gas constant = 8.314 J mol–1 K–1

n = Number of moles = 1

T = Standard temperature = 273 K

P = Standard pressure = 1 atm = 1.013 × 105 Nm–2

∴ V = nRT / P

= 1 × 8.314 × 273 / (1.013 × 105)

= 0.0224 m3

= 22.4 litres

Hence, the molar volume of a gas at STP is 22.4 litres.

Answer 2

Answer:

Diameter of O2 molecule = 3A°

So, radius of O2 ( r) = 1.5A°

So, volume of one O2 molecule = 4/3 πr³

= 4/3 × 22/7 × 1.5 A°³

In one mole = 6.023 × 10²³ molecule ,

So, volume of one mole of O2 molecules ( actual volume ) = 4/3 × 21/7 × 1.5 × 10^-30 × 6.023 × 10²³ = 8.51 × 10^-6 m³

= 8.51 × 10^-3 L

We know,

the volume of one mole of a gas at STP

= 22.4 L

So, fraction of molecular volume to actual volume = 8.51 × 10^-3/22.4

= 3.8 × 10^-4