# Homework Help: Fnding the rms speed of hydrogen

1. Dec 9, 2011

### qspartan570

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. Dec 9, 2011

3. Dec 9, 2011

### qspartan570

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= $\sqrt{v2}$=$\sqrt{\frac{3kT}{m}}$

3. The attempt at a solution

mnitrogen=$\frac{28.0 g}{6.02 X 1023}$=4.65 X 10-26

mhydrogen=$\frac{2.0 g}{6.02 X 1023}$= 3.32 X 10-27

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

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

The answer is actually 1840 m/s.

What did I do wrong?

4. Dec 9, 2011

### Delphi51

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.