Question

If the density of hydrogen gas at NTP is $0.0000893g/c{m}^3$, then the root mean square velocity of molecules of hydrogen molecules at NTP is:

• A. 1840 cm/s
• B. 184.0 cm/s
• C. 1840 m/s
• D. 184.0 m/s

Answer 1

Answer: (C)

The root mean square velocity $\left(v_{rms}\right)$ is by
$v_{rms}=\sqrt{\frac{3P}{\rho }}$
where $P$ is pressure and $p$ the density.
Given, $P=1.013\times 10^3$ At.
$\rho =0.0000893g/c{m}^3$
$\rho =0.0000893\times 1000kg/m^3$
$\therefore v_{rms}=\sqrt{\frac{3\times 1.013\times 10^5}{0.0000893\times 1000}}$
$v_{rms}\approx 1840m/s$