Yeast fermentation in baking:

   Sugars (CxHyOz) + O2 -> CO2 (g) + H2O

The released CO2 causes baked goods like bread to rise.

Chemical versions of yeast:

Baking soda is sodium bicarbonate NaHCO3

Upon heating NaHCO3 decomposes to CO2 and sodium carbonate Na2CO3
This also causes baked goods (like cakes or breads) to rise.

Can you balance the above reaction?

This process, however, is less than desirable since sodium carbonate (washing soda) has a soapy taste (why?) not desirable in baked goods.

We know from playing around as kids that baking soda reacts with vinegar (an acid) to form CO2 (remember the balloons and rockets?).

Can you balance a reaction of baking soda with vinegar (CH3COOH)?

Baking soda is used as a leavening agent in recipes which are already acidic (containing, for example, sour cream or buttermilk).

Anyone who has baked often knows that baking powder is different than baking soda. Why use baking powder?

Baking powder is a mixture of baking soda and an acid and cornstarch to absorb moisture and keep the baking soda and acid dry (why?).

Fast acting baking powder contains tartaric acid or monocalcium phosphate monohydrate, which dissolve rapidly in cold water.
Slow acting baking powder contains sodium aluminum sulfate or anhydrous monocalcium phosphate), which dissolve slowly in water (but dissolve better as the solution heats up in the oven)
Double acting baking power contains a mixture of both, to provide CO2 production over a longer baking time.

Information from "Cookwise : The Hows and Whys of Successful Cooking," by Shirley O. Corriher, William Morrow & Company, 1997 (ISBN: 0688102298)