Why do the physical properties of an egg shell change when the egg shell is exposed to vinegar for a week? When an egg is kept in vinegar for one week, its hard calcium carbonate shell changes into a soft rubbery membrane. As vinegar is weak acetic acid, how does vinegar change calcium carbonate into a soft rubbery membrane? What is the reason for this?
It doesn't make calcium carbonate rubbery, it removes the calcium carbonate.  Egg shells are not purely calcium carbonate they are more like a composite with a continuous matrix of calcium carbonate and a smaller continuous matrix of protien.   When you put the egg in vinegar, you etch away this calcium carbonate matrix leaving the formerly less noticeable protein matrix as a gel filled with vinegar and creates a gel.