🚀 go-pugleaf

  How about this answer? When you have soap in the container with 
a certian amount of water it occupies an amount of space. When you 
shake the container the soap mixes with the water and expands which
compresses the air inside of the jug. To test this theory, I guess
you could fill a jug with soap suds, seal it tight and let it set 
until the suds settled back to basically just soapy water. When you
removed the cap, there should be a rush of air back into the bottle. 

  Another more scientific possibility would be that the soap could 
react with the water molecules and cause them to break up into their
hydrogen and oxygen components. Since a gas is more active than a liquid
the pressure would increase inside of the jug. 

  I like both of these answers so take your pick.