Fnding the rms speed of hydrogen

[qspartan570]

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

V_rms

The Attempt at a Solution

 

[Delphi51]

Better read this first: http://en.wikipedia.org/wiki/Root-mean-square_speed

 

[qspartan570]

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 speedv_rms= [itex]\sqrt{v²}[/itex]=$\sqrt{\frac{3kT}{m}}$

The Attempt at a Solution

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

m_hydrogen=[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

V_rms 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?

 

[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.

 

[asteriatic]

To find the rms speed of hydrogen molecules in air at the same temperature, we can use the equation Vrms = √(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass of the gas. In this case, the molar mass of hydrogen is 2 g/mol, and the temperature is the same as that of nitrogen molecules, so we can use the same value for R. Plugging in these values, we get Vrms = √(3*8.314 J/mol*K * T/2 g/mol), which simplifies to Vrms = √(4.157 J/mol * T). Therefore, at the given temperature, the rms speed of hydrogen molecules in air would be approximately 348 m/s.