Here's the explaination regarding baking soda, water, and an electrical current. To quote:
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This Week's Experiment - #115 Cleaning the Silver
This week's experiment is in honor of all of the mothers on the list. It is a simple chemistry experiment that you can use to clean the silver. I do ask you to get permission before doing this. While it may seem a nice surprise, some silver is not to be cleaned, so be sure to ask before you do this experiment.
You will need:
some aluminum foil baking soda boiling water some tarnished silver
What causes silver to tarnish? It starts all bright and shiny and soon turns dark and dull. The tarnish is a chemical change which takes place when sulfur compounds in the air combine with the silver to make silver sulfide. Silver sulfide is black.
Some silver polishes actually grind away the silver sulfide. This makes the silver nice and shiny, but it also removes a bit of the silver. This is especially serious for silver plated items, as years of polishing will wear away the silver, revealing the metal underneath.
With this experiment, we will change the silver sulfide back into silver, leaving in place instead of removing it. To do that, we need to remove the sulfur. By knowing a bit about electricity and chemicals, we can do this easily.
Line a large pot or your sink with aluminum foil. Sprinkle about a cup of baking soda over the foil. Pour in a couple of quarts of boiling water. Add the silver, being careful not to burn your fingers. The silver should be in contact with the foil. Within minutes, you should see the tarnish begin to vanish. At the same time, the foil will darken.
What is happening? The sulfur from the silver sulfide (Its formula is Ag2S) is moving to join with the aluminum to form aluminum sulfide (Al2S3). The sulfur is being moved by electricity. Two different metals in a conducting solution (water and baking soda) can produce an electric current. As the current flows, it removes the sulfur from the silver and bonds it to the aluminum. If you have an electric volt meter, you can connect one lead to the handle of a silver fork and the other to the edge of the foil. When the fork is brought into contact with the foil, the volt meter should show about half a volt. Not a lot of electricity, but enough to carry the sulfur and clean the silver.