Question

Which of the following is the correct value of the root mean square speed of $O_2$ gas when average transition kinetic energy of $O_2$ gas is 10J/mol?

• A. $\sqrt{5}/2\sqrt{2}$ $m{s}^{-}1$
• B. 25 $m{s}^{-}1$
• C. 1.25 $m{s}^{-}1$
• D. 625$m{s}^{-}1$

Answer 1

The correct option is A $\sqrt{5}/2\sqrt{2}$ $m{s}^{-}1$

$\begin{array}{c}K.E_{av}=\frac{3}{2}RT=10J\Rightarrow 3RT=20J\\ V_{RMS}=\sqrt{\frac{3RT}{M}}\Rightarrow \sqrt{\frac{20}{32}}\Rightarrow \sqrt{\frac{5}{8}}\Rightarrow \frac{1}{2}\sqrt{\frac{5}{2}}M/S\\ V_{rms}=\frac{\sqrt{5}}{2\sqrt{2}}M/S\end{array}$