Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Fnding the rms speed of hydrogen

  1. Dec 9, 2011 #1
    1. The problem statement, all variables and given/known data

    The rms speed of nitrogen molecules in air at some temperature is 493 m/s. What is the rms speed of hydrogen molecules in air at the same temperature?



    2. Relevant equations

    Vrms


    3. The attempt at a solution
     
  2. jcsd
  3. Dec 9, 2011 #2

    Delphi51

    User Avatar
    Homework Helper

  4. Dec 9, 2011 #3
    Finding the rms speed of hydrogen

    1. The problem statement, all variables and given/known data

    The rms speed of nitrogen molecules in air at some temperature is 493 m/s. What is the rms speed of hydrogen molecules in air at some temperature?


    2. Relevant equations

    root-mean-square speedvrms= [itex]\sqrt{v2}[/itex]=[itex]\sqrt{\frac{3kT}{m}}[/itex]



    3. The attempt at a solution

    mnitrogen=[itex]\frac{28.0 g}{6.02 X 1023}[/itex]=4.65 X 10-26

    mhydrogen=[itex]\frac{2.0 g}{6.02 X 1023}[/itex]= 3.32 X 10-27

    493= [itex]\sqrt{\frac{(3)(1.38 X 10-23)(T)}{4.65 X 10-26}}[/itex]
    T= 233 K

    Vrms of hydrogen= [itex]\sqrt{\frac{(3)(1.38 X 10-23(T)}{3.32 X 10-27}}[/itex]=340.43 m/s

    The answer is actually 1840 m/s.

    What did I do wrong?
     
  5. Dec 9, 2011 #4

    Delphi51

    User Avatar
    Homework Helper

    Wow, all that work and it didn't come out right!
    Better to just think for a bit. The atomic mass for the H2 is lighter by a factor of 14.
    So the 3kT/m will be 14 times larger for the hydrogen. And its square root will be sqrt(14) times larger.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook