The shell of an egg is basically calcium carbonate. So when it is placed in dilute HCl, the shell dissolves. Now the inner thin covering is exposed which acts as a semi-permeable membrane.
When this de-shelled egg is placed in water, it swells up. Water molecules move inside as a result of osmosis to maintain equilibrium. The surrounding medium has a higher concentration of water than that present in the egg. The surrounding solution is hypotonic. The water molecules move along the concentration gradient from a region of higher concentration to a region of lower concentration.
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