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Question : 17 of 33
Marks: +1, -0
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 1 Ã…). What is this ratio so large?
Solution:  
Atomic volume =43πR3×N=\frac{4}{3}\pi R^{3}\times N
=43π(0.5×10−10)3×6.023×1023=\frac{4}{3}\pi(0.5\times 10^{-10})^{3}\times 6.023\times 10^{23}
Molar volume =22.4=22.4 litre $ $
=22.4×10−3m−3=22.4\times10^{-3}\mathrm{m}^{-3}
Molar volumeAtomic volume\frac{\text{Molar volume}}{\text{Atomic volume}}
=22.4×10−33.15×10−7=\frac{22.4\times10^{-3}}{3.15\times10^{-7}}
=7.1×104=7.1\times10^{4}
The large value of ratio shows that the inter molecular separation in a gasis much larger than the size of a molecule.
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