Question

If the RMS velocity of nitrogen and oxygen molecule is same at two different temperatures and same pressure, then:

• A. average speed of molecules is also the same
• B. density (gm/L) of nitrogen and oxygen is also equal
• C. number of moles of each gas is also equal
• D. most probable velocity of molecules is also equal

Answer 1

Answer: (A), (B), (D)

average speed of molecules is also the same
most probable velocity of molecules is also equal
density (gm/L) of nitrogen and oxygen is also equal

$(V_{rms}{)}_{N_2}=(V_{rms}{)}_{O_2}$
$\sqrt{\frac{3R{T}_{N_2}}{M_{N_2}}}=\sqrt{\frac{3R{T}_{O_2}}{M_{O_2}}}\frac{T_{N_2}}{M_{N_2}}=\frac{T_{O_2}}{M_{O_2}}$
Then, $V_{av}$ and $V_{mps}$ is also same.
$d_{N_2}=\frac{P_{N_2}{M}_{N_2}}{R{T}_{N_2}}{d}_{O_2}=\frac{P_{O_2}{M}_{N_2}}{R{T}_{O_2}}$
If $P_{N_2}=P_{O_2}$, then $d_{N_2}=d_{O_2}$.