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

Explanation

Size of hydrogen atom
`=1A=10^-10 m=10^-8 cm`
`V_1`= Atomic volume = number of atoms `times` volume of atom.
One mole gas contains `n` molecules.
Avagadro Number n=`6.022 times10^23`
`V_1=1/3pir^3timesn`
`=4/3times22/7times[10^-8]^3times6.022times10^23`
`=25.23times10^-1`or 2.523 cc.
`V_2`= Molar volume of 1 mol. gas =22.4 lit
`=2.24 times 10^4 ` c.c
`because` 1lit =1000 c.c
`therefore` Ratio of molar volume to atomic volume
`=V_2:V_1`
`=2.24times10^4:2523=10^4m.`