Setup:
(A) An air filled balloon is placed in liquid nitrogen
(B) A Helium filled balloon is place in liquid nitrogen,

Observations:  

• The pressure of the gas in the balloon is close to the that of air pressure of the room, especially when the balloon collapses.
• The boiling point of Nitrogen is 77.3 K. If thermal equilibrium were completely established then the air in the balloon would also be at 77.7K.
• Using the ideal gas law alone the volume of the gas in the balloon should only contract to about 1/4 its volume because of the drop in temperature, Boiling point of Nitrogen/ Room Temp = 77K/ 294 = .261.
• The air filled balloon's final volume is much smaller than 1/4 because some of the Nitrogen and Oxygen condenses out - changes phase from gas to liquid. The boiling point of Oxygen is 90.2K so most of the oxygen freezes out. It is possible to submerge all the balloon into liquid nitrogen and the balloon's volume will go to nearly zero as the rest of the Nitrogen freezes out.
• When Helium is used as a gas the volume does not get less that 1/4 it original volume because the boiling point of helium ( 3K) is much lower that of liquid nitrogen.