$360 \mathrm{~cm}^3$ of a hydrocarbon diffuses in 30 minutes, while under the same conditions $360 \mathrm{~cm}^3$ of $\mathrm{SO}_2$ gas diffuses in one hour. The molecular formula of the hydrocarbon is

An LPG (Liquified Petroleum Gas) cylinder weighs 15.0 kg when empty. When full, it weighs 30.0 kg and shows a pressure of 3.0 atm . In the course of usage at $27^{\circ} \mathrm{C}$, the mass of the full cylinder is reduced to $24 \cdot 2 \mathrm{~kg}$. The volume of the used gas in cubic metre at the normal usage condition ( atm and $27^{\circ} \mathrm{C}$ ) is (assume LPG to be normal butane and it behaves ideally)

The compressibility factor for a van der Waal gas at high pressure is

The root mean square (rms) speed of X$$_2$$ gas is x m/s at a given temperature. When the temperature is doubled, the X$$_2$$ molecules dissociated completely into atoms. The root mean square speed of the sample of gas then becomes (in m/s)