Question

If the rms velocity of nitrogen and oxygen molecule are same at two different temperature and same pressure then

• A. Average speed of molecules is also same.
• B. density (gm/lt.) 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)

most probable velocity of molecules is also equal.

As per question, $\left(u_{rms}\right)N_2=\left(u_{rms}\right)O_2$

$\sqrt{\frac{3R{T}_{N_2}}{M_{N_2}}}=\sqrt{\frac{3R{T}_{O_2}}{M_{O_2}}}$
$\Rightarrow \frac{T_{N_2}}{M_{N_2}}=\frac{T_{O_2}}{M_{O_2}}$

Then $u_{av}$ and $u_{mps}$ 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 $d_{N_2}=d_{O_2}$