Question

The rms speed of oxygen at room temperature is about 500ml.the rms speed of hydrogen at the same temperature is about

Answer 1

$\Large\boxed{\sf{2000\ m\ s^{-1}}}$

We know that RMS velocity is given by,

$\longrightarrow\sf{v=\sqrt{\dfrac{3RT}{M}}}$

At a constant or same temperature,

$\longrightarrow\sf{v\propto\dfrac{1}{\sqrt M}}$

Therefore,

$\longrightarrow\sf{\dfrac{v_2}{v_1}=\sqrt{\dfrac{M_1}{M_2}}}$

Here,

$\sf{v_1=500\ m\ s^{-1}}$ (RMS velocity of Oxygen)

$\sf{M_1=32\ g}$ (Molecular mass of Oxygen)

$\sf{M_2=2\ g}$ (Molecular mass of Hydrogen)

Then RMS velocity of Hydrogen is,

$\longrightarrow\sf{v_2=v_1\sqrt{\dfrac{M_1}{M_2}}}$

$\longrightarrow\sf{v_2=500\sqrt{\dfrac{32}{2}}}$

$\longrightarrow\sf{\underline{\underline{v_2=2000\ m\ s^{-1}}}}$