Q. 173.7( 39 Votes )

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?

Answer :

Given,

Volume of one mole of ideal gas at STP, Vm=22.4L=22.4 × 10-3 m3


Radius of hydrogen atom, r = 1 Å / 2 = 0.5 Å = 0.5 × 10-10 m


Volume of the hydrogen atom, V = (4/3)πr3


V = (4/3)×3.14×(0.5×10-10 m)3


V = = 5.24 × 10-31 m3


One mole of hydrogen atom contains NA = 6.023 × 1023 atoms.


Where, NA is Avogadro’s number.


So, Volume of one mole of hydrogen atom,


Vt = 6.023 × 1023 × 5.24 × 10-31 m3


Vt = 3.16 × 10-7 m3


The ratio of molar volume to atomic volume is



Vm �/Vt = 7.089 × 104


This ratio is very high due to the fact that the inter-atomic distance is very high as compared to the size of atoms in hydrogen gas.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Analyse Dimensional Analysis Through Live QuizAnalyse Dimensional Analysis Through Live QuizAnalyse Dimensional Analysis Through Live Quiz44 mins
Introduction To Cell DivisionIntroduction To Cell DivisionIntroduction To Cell Division60 mins
Cell - The unit of Life - 02Cell - The unit of Life - 02Cell - The unit of Life - 0268 mins
All about Enzymes | A thorough lectureAll about Enzymes | A thorough lectureAll about Enzymes | A thorough lecture47 mins
Stem and its modificationsStem and its modificationsStem and its modifications47 mins
Dicot and Monocot rootDicot and Monocot rootDicot and Monocot root35 mins
Vision NEET | Lets go deep into our "Eye"Vision NEET | Lets go deep into our "Eye"Vision NEET | Lets go deep into our "Eye"46 mins
Digestion & Absorption | Quiz/Test TimeDigestion & Absorption | Quiz/Test TimeDigestion & Absorption | Quiz/Test TimeFREE Class
NCERT Exemplar| Locomotion and Movement Part 1NCERT Exemplar| Locomotion and Movement Part 1NCERT Exemplar| Locomotion and Movement Part 130 mins
NCERT Exemplar | Breating & Exchange of Gases Part 2NCERT Exemplar | Breating & Exchange of Gases Part 2NCERT Exemplar | Breating & Exchange of Gases Part 222 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :