Question

The ratio of the $RMS$ velocities of $S{O}_2$ and helium gas molecules at ${25}^{o}C$ is:

• A. 1:4
• B. 4 : 1
• C. 16:1
• D. 1 : 16

Answer 1

Answer: (A)

Root mean square velocity = $\sqrt{\frac{3RT}{M}}$

For $S{O}_2$ molecule, M = 64 g/mole

$U_{RMS}=\sqrt{\frac{3\times R\times T}{64}}$

For Helium gas molecule, M = 4 g/mole

$U_{RMS}=\sqrt{\frac{3\times R\times T}{4}}$

$\frac{{\left(U_{RMS}\right)}_{S{O}_2}}{{\left(U_{RMS}\right)}_{He}}=\sqrt{\frac{4}{64}}=\frac{1}{4}=1:4$