Here are a few things that you can easily do at home with eggs to explore Chemistry and Biology. I originally saw this experiment done while I was in Biology, however I didn't understand what was going on until I was in Chemistry.

These are safe to do at home and could be a fun thing to do with children, either just for fun or a fun way of explaining diffusion or how a cell works (more on these later). Here I will show not only the setup of the original experiment that I saw, I will include the extra step that I did out of curiosity. So, here is a list of the things that I used for this experiment.

Vinegar - any vinegar should work, I used white vinegar.
Egg(s) - the number of eggs you use will depend on the number of things you are testing (more on this later). I ended up using more than I was testing, so it is best to have a few extras.
Containers - you should have a container for each of the things you are testing plus one for the vinegar. The container for the vinegar should be large enough to fit all the eggs in at once.
Water - I used the water for two tests but you could do it by itself.
Salt - this was the extra step I took to see what would happen.
Corn syrup/sugar water/any syrup - I used corn syrup but I believe the first time I saw this experiment they had used imitation maple syrup (the cheap kind for pancakes).
Gloves (optional) - these are not needed but it may make your life easier during cleanup.

At the end I will discuss what is going on and how you could make this experiment your own, for all of those who are interested. I know not everyone is interested in reading how they can take the experiment one step further while also reading how to do the experiment.

Step 1: Making "Naked Eggs"

The first step is to take all the eggs you are going to experiment with and prepare them. Eggs are made up of several different things, the first layer is a shell made up of calcium carbonate; the second layer is a thin membrane made of keratin; inside the membrane is the egg white, the yolk, and an air pocket. In this step we are going to remove the shell but leave the membrane and everything in the membrane intact.

First, find a container to put all your eggs in. Then pour your vinegar into the container being sure to cover all the eggs with about an inch or so extra vinegar. After you pour in the vinegar it becomes a waiting game, walk away and do something else. If you think of it you can occasionally stir the eggs around gently. You will notice there are bubbles forming and possibly a white foam at the top, the bubble are CO2 and the foam is from the shells dissolving in the vinegar (more on that at the end).

I would leave these overnight to do this while mixing them whenever I walk by. If you feel the need, you could refrigerate this setup but keep in mind it could take a lot longer to finish. Also if you would like to reduce the vinegar smell you could wrap the top off the container with plastic wrap.

After you are done with dissolving the egg shell, you can either go to the next step immediately or you can store your eggs in the fridge until you are ready to move on. That being said, I'm not sure how long these eggs will last.

Pictures:

The pictures in order are as follows. A top view of an egg in vinegar, a bottle with the top cut off with two eggs in the vinegar (later I changed this to only have one egg as it worked better with only one egg per container), the foam produced from the process, an egg with the shell fully dissolved but still covered with a white powder that I was washing off, two eggs with their shells fully dissolved (one before cleaning the white powder cleaned off and one after), an egg with the shell and white powder completely removed, just the membrane of the egg (after making a mistake, I popped the egg).

*When handling the eggs make sure the skin stays moist* If the membrane drys, the egg can and probably will pop. I learned this the hard way.

Step 2: Experiment

Here is the time to have some fun, it is another waiting game but the results are really cool. I experimented with water, salt water, and corn syrup. I used tap water because I didn't have any distilled water on hand, that being said my tap water results could be different than the distilled water results (I may do this later). The process is the same for each experiment so just repeat the process for each.

Take a container and put one of the naked eggs in it, then pour the substance that you are testing into the container making sure to completely cover the egg with about an inch of extra fluid. If you have multiple substances that look alike (i.e. salt water and water) it might be a good idea to label the containers, this is especially true if you want to know for sure what each substance does to the egg.

Then you wait, you can check back in an hour, a day, or a week. The only things to keep in mind are the facts that the egg could go bad if you leave it out too long, if you don't wait long enough there might not be a noticeable difference, and finally there is a point at which the process will stop.

I made an interesting observation while doing this experiment: if you look at the picture, the egg on the right (in corn syrup) has this swirly effect over the top. This is caused by there being two different densities of liquid, the water in or around the egg is trying to float to the top (because it is less dense) and that is what you are seeing.

Step 3: Clean-up

The worst part of almost any experiment. To dispose of the liquids you tested, you can just wash those down the drain. Keep in mind that vinegar is acidic, so when washing it down the drain it may be a good idea to use a lot of water to do so. Also keep in mind that if the substance you used is not a household material that you should check if it is okay to wash it down the drain, some substances are illegal to do so with. And as for the eggs, I put the eggs in a container and used a knife to pop them then flushed then down the toilet. I mostly did it that way because I didn't want to deal with trying to wash the yolks down the drain and the garbage was just taken out so I didn't want to have to smell rotten eggs later.

Step 4: Results

I want to start this off by saying that my results were a little unexpected. I was expecting the egg in the water to become slightly bigger, the one in salt water to give up some of the water inside the membrane and become somewhat empty, and the one in corn syrup to be the same as the salt water.

The first picture shows all the egg side by side, including the one which was only in vinegar.

The next picture shows the egg that was just in vinegar, as you can see it doesn't have a shell but otherwise is the same size and shape as an egg.

The next picture is of the egg I soaked in water. Though you may not be able to tell from the picture, the egg is more round and swollen than it was before it was in the water. As a side note, this egg was also a little more firm than the rest.

The next picture is of the egg that was soaked in salt water. This gave me an unexpected result, I though the egg would deflate. The egg deflated a very small amount but not nearly as much as I thought it would. I think the confusing result was caused by the fact that I put this in the fridge, when the water got cold it was unable to dissolve as much salt as it would be able to while warm.

the last picture shows the egg that was soaked in corn syrup. This was the egg that left me waiting for longer than expected. This did exactly as I expected, but took far longer than intended. As a side note, describing the feeling of holding this egg in your hand is beyond words but interestingly the yolk was hard; if anyone know why the yolk becomes hard from this, please let me know as I am very interested in knowing.

Step 5: What Is Going On? - Dissolving the Shell

During the first part, we put the whole egg in vinegar and after a while the egg shell was gone. This process happens because the shell is made up of calcium carbonate which is a base and vinegar contains acetic acid. Calcium carbonate and baking soda share a similar reaction when it comes into contact with vinegar. The vinegar breaks down the calcium carbonate crystals and the calcium ions are free to dissolve into the water/vinegar. This releases CO2 (from the "carbonate" part), those are the bubbles you see forming on the surface of the shell. The inside of the shell has a membrane made from keratin (the protein in human hair), this doesn't get dissolved by the vinegar. So you remove the shell without harming the membrane or anything in the membrane.

Step 6: Whats Going On? - the Tests

The process that takes place when you put the naked eggs into the different liquids is called diffusion but it can be explained by comparing it to a process called osmosis (or something very similar).

Osmosis is the process that a cell uses to transport water in and out of its membrane without using any energy. This could easily be used as a demo for how a cell works. In fact, an egg is very similar to a cell: a cell has a membrane, doesn't use energy to transport water in and out of it, and has a nucleus (the yolk). The cell doesn't have to use any energy because the membrane is made of a semi-permeable membrane, a substance that has small holes in the surface that are small enough for water molecules to enter but nothing that is larger can get in.

Diffusion is the process in which a high concentration of a substance tries to spread to lower concentrations. A good example of this process would be taking a glass of water and carefully adding a drop of food coloring without disturbing the water. Once the drop has been added to the water, the drop will slowly start to spread. The drop spreads from the high concentration (where it first entered the water) to the lower concentration (where there is no food coloring).

Step 7: Taking This a Step Farther

You could easily continue experimenting with different substances. I chose the liquids I did because I had everything I needed. You could try water/distilled water, then add food coloring or salt to see if that changes the results. You could also try honey or shampoo. Really, you could try any liquid that you could submerge the egg in. If anyone tries something, feel free to let everyone know what you tried (extra points if its something odd). Also if anyone tries this, please post pictures in the comments.