The average speed $(u_{avg})$ of $O_2$ gas at $\pi \times 10 \ bar$ pressure in an $8 \ m^3$ container containing $2 \ moles$ is:

The $RMS$ velocity $(u_{rms})$ of one mole of an ideal gas was measured at different temperatures and the following graph is obtained. What is the slope $(m)$ of the straight line?
($x$-axis $= T$ $(K)$; $y$-axis $= (u_{rms})^2$; $M =$ molar mass; $R =$ gas constant)

The volumes of ozone and chlorine gas diffusing in the same time are $35 \ mL$ and $29 \ mL$ respectively. If the molar mass of chlorine is $71$,calculate the molar mass of ozone. (in $.7$)

At what temperature $K$ will the $rms$ speed of $SO_2$ gas be equal to the $rms$ speed of $O_2$ gas at $303 \ K$?

If the mass of a gas at $3 \, atm$ pressure and $14.8 \, L$ volume is $15 \, g$,calculate the root mean square speed $(u_{rms})$ of the gas molecules. (Assume $T = 300 \, K$)

For a gaseous state,if the most probable speed is denoted by $C^*$,average speed by $\overline{C}$,and root mean square speed by $C$,then for a large number of molecules,the ratio of these speeds is: