A closed vessel contains \( 10 \, \text{g} \) of an ideal gas \( X \) at \( 300 \, \text{K} \), which exerts \( 2 \, \text{atm} \) pressure. At the same temperature, \( 80 \, \text{g} \) of another ideal gas \( Y \) is added to it and the pressure becomes \( 6 \, \text{atm} \). The ratio of root mean square velocities of \( X \) and \( Y \) at \( 300 \, \text{K} \) is:
A gas has a compressibility factor of \( 0.5 \) and a molar volume of \( 0.4 \, \mathrm{dm^{3} \, mol^{-1}} \) at a temperature of \( 800 \, \mathrm{K} \) and pressure \( x \, \mathrm{atm} \). If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be \( y \, \mathrm{dm^{3} \, mol^{-1}} \). The value of \( x/y \) is _______.
[Use: Gas constant, \( R = 8 \times 10^{-2} \, \mathrm{L \, atm \, K^{-1} \, mol^{-1}} \)]
