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 1 mole of hydrogen? (Take the size of hydrogen molecule to be about ) Why is the ratio so large?
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# 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.
The large ratio indicates free space between hydrogen molecules.
# 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.
The large ratio indicates free space between hydrogen molecules.
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