Question

The RMS velocity of $CO$ gas molecules at $27^{\circ}$C is approximately $1000\, m/s$. For $N_2$ molecules at $600 \,K$ the RMS velocity is approximately

• A. 2000 m/s
• B. 1414 m/s
• C. 1000 m/s
• D. 1500 m/s

Answer 1

Answer: (B)

1414 m/s

Answer 2

As from the formula, $v_{ rms }=\sqrt{\frac{3 R T}{M}}$
Given that $\left(v_{ rms }\right)_{\infty}=1000\, m / s$
$( Temp .)_{ CO }=27^{\circ} C =300 K$
(Temp.) $_{ N _{2}}=600\, K$
Now putting the values, we get
$\frac{\left(v_{ rms }\right)_{ CO }}{\left(v_{ rms }\right)_{ N _{2}}}=\sqrt{\frac{3 R}{3 R} \times \frac{T_{ CO }}{M_{ CO }} \times \frac{M_{ N _{2}}}{T_{ N _{2}}}}$
$\frac{1000}{\left(v_{m s}\right)_{N_{2}}}=\sqrt{\frac{300}{28} \times \frac{28}{600}}$
$=\frac{1}{\sqrt{2}}$
or, $\left(v_{ ms }\right)_{ N _{2}}=1000 \times 1.414$
$=1414\, m / s$