At 298 K , a flask ' $A$ ' of unknown volume $(V)$ contains oxygen at 5 atm . Another flask ' $B$ ' of volume 2 L contains helium at 3 atm . Two flasks are connected together by a small tube of zero volume. After the two gases are completely mixed, if the resulting mixture is found to have the mole fraction of oxygen as 0.2 , the volume of flask ' $A$ ' (in L ) is

(Assume oxygen and helium as ideal gases)

At $T(\mathrm{~K})$ root mean square (rms) velocity of argon (molar mass $40 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is $20 \mathrm{~ms}^{-1}$. The average kinetic energy of the same gas at $T(\mathrm{~K})$ (in $\mathrm{J} \mathrm{mol}^{-1}$ ) is

Two vessels are filled with ideal gases $A$ and $B$ and are connected through a pipe of zero volume as shown in figure. The stop cock is opened and the gases are allowed to mix homogeneously and the temperature is

kept constant. The partial pressures of $A$ and $B$ respectively ( in atm ) are

The RMS velocity of dihydrogen is $\sqrt{7}$ times more than that of dinitrogen. If $T_{\mathrm{H}_2}$ and $T_{\mathrm{N}_2}$ are the temperatures of dihydrogen and dinitrogen, then the correct relationship between them is