One mole of an ideal gas at standard tem | Class 11 Physics Chapter Unit and measurment, Unit and measurment NCERT Solutions

Question:

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen? (Take the size of hydrogen molecule to be about 1Å). Why is this ratio so large?

Answer:

Radius of hydrogen atom, r = 0.5 Å = 0.5 × 10-10 m

Volume of hydrogen atom = 4/3 π r3

= 4/3 x 22/7 x (0.5 x 10-10)3

= 0.524 x 1030 m3

1 mole of hydrogen contains 6.023 × 1023 hydrogen atoms.

∴ Volume of 1 mole of hydrogen atoms = 6.023 × 1023 × 0.524 × 10-30

= 3.16 × 10-7 m3

Molar volume of 1 mole of hydrogen atoms at STP,

Vm = 22.4 L = 22.4 × 10-3 m3

∴ Vm / Va  =  22.4 x 10-3  /   3.16 × 10-7  =  7.08 × 104

Hence, the molar volume is 7.08 × 104 times higher than the atomic volume. For this reason, the inter-atomic separation in hydrogen gas is much larger than the size of a hydrogen atom.

 


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Welcome to the NCERT Solutions for Class 11 Physics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 17: One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What i....