Fnding the rms speed of hydrogen

  • #1

Homework Statement



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?



Homework Equations



Vrms


The Attempt at a Solution

 

Answers and Replies

  • #3
Finding the rms speed of hydrogen

Homework Statement



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?


Homework Equations



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



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?
 
  • #4
Delphi51
Homework Helper
3,407
11
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.
 

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