Question

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). If the size of the hydrogen molecule is about $1 \AA$. What is the ratio of molar volume to the atomic volume of a mole of hydrogen?

Answer 1

Hii dear,

# Answer- 7.08×10^4.

# Given-
Radius of hydrogen atom, r = 0.5 Å = 0.5 × 10-10 m
Molar volume Vm = 22.4 L = 22.4×10^-3 m^3

# Formula-
Volume of hydrogen atom
= (4/3)πr^3
=(4/3)×(22/7)×(0.5×10^-10)^3
= 0.524×10^-30 m^3

Now, 1 mole of hydrogen contains 6.023×10^23 hydrogen atoms.
∴ Volume of 1 mole of hydrogen atoms,
Va = 6.023×10^23 × 0.524×10^–30
Va= 3.16×10^–7 m^3

Ratio of molar volume to total atomic volume
Vm/Va = (22.4×10^-3)/(3.16×10^–7)
Vm/Va = 7.08×10^4

Hence, Ratio of molar volume to total atomic volume is 7.08×10^4.