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 Å). Why is this ratio so large?

Solution

Diameter space of space hydrogen space atom comma space straight D space equals space 0.5 space straight A with straight o on top space equals space 0.5 cross times 10 to the power of negative 10 space end exponent straight m Volume comma space straight V space equals space 4 over 3 straight pi space open parentheses straight D over 2 close parentheses cubed space space equals space 5.238 space cross times space 10 to the power of negative 31 end exponent space straight m cubed space Ratio space of space molar space volume space to space volume space of space one space atom space is comma space fraction numerator 22.4 over denominator 5.238 cross times 10 to the power of negative 28 end exponent end fraction space equals space 4.276 space cross times space 10 to the power of 28 space Ratio space os space large space because semicolon space straight i right parenthesis thin space No. space of space atoms space in space straight a space mlole space of space gas space is space large. space ii right parenthesis thin space Distance space between space hydrogen space molecules space almost equal to space 10 space straight A with 0 on top

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