I understand that when salt dissolves in water the sodium and chlorine ions are broken by the charge of the water molecules and are surrounded by a shell of water molecules. However, I don't understand how the salt can retain its physical properties once the bonds are broken and the elements themselves are separated. I know that on its own, chlorine is a poisonous green gas, and sodium is a highly reactive silvery metal. If the bonds are being broken, how is this a physical change? I did a lab with my students in which we broke water into its elements by sending an electric current through the water. The result was bubbles of oxygen and hydrogen rising to the surface. How come it is different when the sodium chloride is broken? Does it have to do with the hydration?

You are confusing two types of bond here.

In water, hydrogen is covalently bound to oxygen. If you break apart the hydrogen from the oxygen you have a new substance: either hydrogen and oxygen gas (electrolysis) or "hydronium" and hydroxide ions. In either case, you don't have water any more, though of course you can re-form it. In the second instance, water exists in equilibrium with "hydronium hydroxide."

But sodium chloride is a collection of sodium ions and chloride ions. They are not bonded in the sense that no electrons are shared between them; they hang together purely by the attraction of opposite charges. The sodium ions and chloride ions remain chemically themselves whether they are surrounded by each other (bulk sodium chloride) or by water molecules (salt water). They can also freely combine with other ions in aqueous solution; this is seen in the test for chloride using silver:

ChloriNe is something chemically different from chloriDe. You can convert chloride to chlorine by electrolysis, just as you can convert water to hydrogen and oxygen; but simply dissolving chloride in water doesn't change its chemical character.

Dan Berger