Out of hydrogen and air,which will have a higher root mean square speed $(v_{\text{rms}})$?

The root mean square velocity of molecules of a gas is $200 \,m/s$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

For a gas at a temperature $T$,the root-mean-square velocity ${v_{rms}}$,the most probable speed ${v_{mp}}$,and the average speed ${v_{av}}$ obey the relationship:

$A$ gas is at a temperature of $0^{\circ}C$. To what temperature in $^{\circ}C$ must the gas be heated so that the $rms$ speed of its molecules becomes double?

Consider an ideal gas with the following distribution of speeds:

Speed $(m/s)$	$\%$ of molecules
$200$	$10$
$400$	$20$
$600$	$40$
$800$	$20$
$1000$	$10$

$(a)$ Calculate $v_{rms}$ and hence $T$. (Given mass of one molecule $m = 3.0 \times 10^{-26} \ kg$, Boltzmann constant $k_B = 1.38 \times 10^{-23} \ J/K$)
$(b)$ If all the molecules with speed $1000 \ m/s$ escape from the system, calculate the new $v_{rms}$ and hence the new $T$.

At what temperature $(^oC)$ will the $rms$ speed of hydrogen be double its value at $S.T.P.$? The pressure remains constant.