Nitrogen Gas Molecule Speeds and Temperature Relationship

[weathercheck]

Homework Statement

Fractions of Molecules in an Ideal Gas with Speeds Less than Various Multiples of v/v_{\rm rms} in the textbook. The molar mass of {\rm{N}}_2 is 28.0 {\rm{ g/mol}}.


For a gas of nitrogen molecules {{\rm{N}}_2 } , what must the temperature be if 94.7\% of all the molecules have speeds less than 1500 \rm m/s?

Homework Equations

Vrms = sqrt(3kt/m)

The Attempt at a Solution

Really don't know where to start with the percentages and the relevance of the fracitons of molecules in an ideal gas with speeds less than various multiples etc??

Any help?

 

[Master J]

hmmmmmmmmm...

 

[kamerling]

I suppose there is a table in your book which tells you that 94.7% will have a speed smaller than 2x the rms velocity. You now know that 94.7% has a speed smaller than 1500m/s.
It should be easy to get the rms speed from that and then the temperature from your equation

 

[Master J]

I have tried it.

It says 94.7% have a speed less than (v/v_rms = 1.6). this is confsuing me. What does this mean? Clearly from that I can find v_rms, and plug it into the given equation above.

 

[weathercheck]

How would you use the figure that I am given to find the Vrms ??

 

[kamerling]

can you state exactly what is given in your book?