Question

. At 27°C the ratio of the R.M.S. velocities of
ozone and oxygen molecules is​

Answer 1

Answer:

2/3

At 27 degree celsius the ratio of rms velocities of ozone to oxygen is √2/3. It is essential to know that the ratio of a root mean square velocity of O3 to O2 is calculated as. Finally, we can get the ratio of RMS velocity of Ozone to oxygen as √2/3. The remaining values are constant.

Answer 2

The RMS velocity is given by,

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

where,

$\longrightarrow\sf{R}$ = universal gas constant.

$\longrightarrow\sf{T}$ = temperature.

$\longrightarrow\sf{M}$ = molecular mass.

At the same temperature,

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

Therefore,

$\longrightarrow\sf{\dfrac{u_1}{u_2}=\sqrt{\dfrac{M_2}{M_1}}}$

We know that,

• mass of ozone molecule,

$\longrightarrow\sf{M_1=48\ g}$

• mass of oxygen molecule,

$\longrightarrow\sf{M_2=32\ g}$

Thus,

$\longrightarrow\sf{\dfrac{u_1}{u_2}=\sqrt{\dfrac{32}{48}}}\\\\\\\longrightarrow\underline{\underline {\sf{\dfrac{u_1}{u_2}=\sqrt{\dfrac{2}{3}}}}}$

Or,

$\longrightarrow\underline {\underline {\sf{\dfrac{u_1}{u_2}=\dfrac{\sqrt{2}}{\sqrt{3}}}}}$