edited from Wikipedia:
Baking powder is a dry chemical leavening agent used to increase the volume and lighten the texture of baked goods. It works by releasing carbon dioxide gas into a batter or dough, causing bubbles in the wet mixture to expand. It is used instead of yeast where the batter lacks the elastic structure to hold gas bubbles. Breads made by chemical leavening are called "quick breads" because the process is faster than fermentation.
Baking soda is the source of the carbon dioxide; when mixed with acid salts and water it produces a chemical reaction. "Fast-acting" acids (such as cream of tartar and monocalcium phosphate) work at room temperature, while "slow-acting" acids (sodium aluminum sulfate or sodium aluminum phosphate) will not react until heated in an oven. Baking powders that contain both fast- and slow-acting acids are called "double acting" because they providing a second rise in the oven, thus making baking time less critical.
The inert starch (usually cornflour) is primarily used to absorb moisture, and thus keep the alkaline and acidic components from reacting prematurely.
Before baking powder, people mixed baking soda with an acid such as sour milk, vinegar, lemon juice, or cream of tartar, which all reacted quickly so the batter had to be baked quickly before the gas escaped. Alfred Bird, a chemist, invented baking powder because he wanted to make bread for his wife, who was allergic to yeast. (She was also allergic to eggs, so he made Bird's custard.)
In pure water, there is an equal number of hydroxide (OH) and hydronium (H3O) ions, which is 10−7 moles per liter. The important thing there is the "7" which is why water has a pH ("power of hydrogen") of 7. If a substance has fewer hydrogen ions (pH < 7) it is an "acid" whereas if it has more (pH > 7) then it is "base." (Alkaline -- as in batteries -- refers to a set of metals that are naturally base.) When the two are mixed, a chemical reaction occurs to transfer the excess hydrogen from the acid to the base, which is (for obvious reasons) referred to as "neutralisation." Depending on the substances, this can be quite a violent reaction. In the case of baking soda and vinegar, the two end-products are carbon dioxide (CO2) and water (H2O), which is why it bubbles.
Why do you need to know this? Well, if you keep fish, you have to know that some prefer slightly acidic water, while others prefer slightly alkaline. Or if you want to know why your cake just fell, it might be helpful to understand what's going on at the molecular level.
Or if you read some nonsense about an acid/alkaline theory of disease, if might help you to understand why what they are saying is absurd. (This article also explains why if you eat excess protein, your body excretes calcium as well, and why cranberries help prevent urinary tract infections.)(By the way, this line of research started simply because I wanted to confirm that cornflour -- "cornstarch" to you Yanks -- didn't actually contain flour. It doesn't.)
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