Question

The root mean square speed of oxygen molecule $\left(O_2\right)$ at a certain temperature is $v$. If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the rms speed would be

• A. $v$
• B. $\sqrt{2}v$
• C. $2v$
• D. $2\sqrt{2}v$

Answer 1

The correct option is C $2v$

The rms speed is given by
$v_{rms}=\sqrt{\frac{3RT}{M}}$
$(v_{rms}{)}_{O_2}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3RT}{M}}=v$
$(v_{rms}{)}_O=\sqrt{\frac{3R\left(2T\right)}{M/2}}=2\sqrt{\frac{3RT}{M}}=2v$.