One mole of nitrogen gas at 0.8 atm takes 38 s to diffuse through a pinhole. whereas one mole of an unknown compound of xenon with flourine at 1.6 atm takes 57 s to diffuse through the same hole. Calculate the molecular formula of the compound.

A 4 : 1 molar mixture of He and CH₄ is contained in a vessel at 20 bar pressure. Due to a hole in the vessel the gas mixture leaks out. What is the composition of the mixture effusing out initially?

An LPG (liquefied petroleum gas) cylinder weighs 14.8 kg when empty. When full, it weighs 29.0 kg and shows a pressure of 2.5 atm. In the course of use at 27^o C, the weight of the full cylinder reduces to 23.2 kg. Find out the volume of the gas in cubic meters used up at the normal usage conditions find the final pressure inside the cylinder. Assume LPG to be n-butane with normal boiling point of 0^o C.

A gas bulb of 1 litre capacity contains 2.0 $$\times$$ 10²¹ molecules of nitrogen exerting a pressure of 7.57 $$\times$$ 10³ Nm^-2. Calculate the root mean square (r.m.s) speed and the temparature of the gas molecules. If the ratio of the most probable speed to the root mean square speed is 0.82, calculate the most probable speed for these molecules at this temparature.