Question

At ${27}^{o}C$, the ratio of R.M.S velocity of ozone to oxygen is:

• A. $\frac{\sqrt{3}}{5}$
• B. $\frac{\sqrt{4}}{3}$
• C. $\sqrt{\frac{2}{3}}$
• D. $0.25$

Answer 1

The correct option is C $\sqrt{\frac{2}{3}}$

Root mean square velocity of the gas is = $\sqrt{\frac{3RT}{M}}$

For ozone gas, M = 48 g/mole T = 300 K

For oxygen gas, M = 32 g/mole T = 300 K

$\frac{{\left(U_{RMS}\right)}_{ozone}}{{\left(U_{RMS}\right)}_{oxygen}}=\frac{\sqrt{\frac{3\times R\times 300}{48}}}{\sqrt{\frac{3\times R\times 300}{32}}}=\sqrt{\frac{32}{48}}=\sqrt{\frac{2}{3}}$