Question

If nitrogen gas molecule goes straight up with its rms speed at $0^o$C from the surface of the earth and there are no collisions with other molecules, then it will rise to an approximate height of:

• A. $18$ km
• B. $15$ km
• C. $12.38$ km
• D. $8$ km

Answer 1

The correct option is C $12.38$ km

Molecular mass of Nitrogen molecule=$14$ g/mol

As nitrogen exists as $N_2$=28 g/mol=$0.028$ kg/mol

Also we know $v_{rms}=\sqrt{\frac{3RT}{M}}$ where R= gas constant=8.31 bar/(K mol)=8.31$\times {10}^5$ Pa/(K mol)

T= temperature=$0^0$ C=273 K

Also height $=\frac{V_{rms}^2}{2g}$

$=\frac{3\times 8.31\times {10}^5\times 273}{2\times 9.81\times 0.028}=12388m=12.38km$