First, you need to know how these chemicals react with each other. Baking soda is the common name for the chemical sodium bicarbonate (NaHCO₃) and vinegar is an acetic acid solution.

A single molecule of sodium bicarbonate reacts one molecule of acetic acid to form one molecule each of water, carbon dioxide and sodium acetate. So, they react in a one-to-one ratio. This can be represented by the following formula, with the states of matter indicated in parentheses:

NaHCO₃ (s) + HC₂H₃O₂ (aq) → NaC₂H₃O₂ (aq) + H₂O (l) + CO₂ (g)

Baking soda and vinegar will react even if you mix them in an uneven ratio – there will just be some of the excess baking soda or vinegar left over. Now, we need to find a way to know how many molecules of baking soda and vinegar you have. There are many, many molecules in even the smallest amount of material that you can see, billions of billions of them. To deal with this, chemists define a unit called moles as 6.022 x 10²³ molecules – you can think of it like a chemists’ dozen and use them in the same ratio in the molecular formula above.

I usually use weight in the laboratory but, at home, it is easier to use volume, like you do in baking. You can convert the weight of baking soda and acetic acid into units of volume that you can easily measure at home or school. Start with the molecular weights of baking soda and acetic acid and use their density (you can find both on their Wikipedia pages) to convert to volume. (Note that vinegar is 5% acetic acid by weight in water, not pure acetic acid.)

Using that method, I found that one tablespoon of baking soda reacts with one cup of vinegar. Try it out – add vinegar to a tablespoon of baking soda slowly, keeping track of how much you add. At what volume did the mixture stop fizzing? Try it the other way – add baking soda in small amounts until 1 cup of vinegar stops fizzing. How much did you add?

They will react, always. They may react more if you give the perfect amounts to exactly cancel each-other, but any amount of vinegar will react with any amount of baking soda.

The chemical in vinegar that reacts with baking soda is acetic acid. One molecule of acetic acid will react with one molecule of baking soda to produce one molecule of water, one molecule of carbon dioxide (this is the bubbly-fizzy product), one ion of sodium, and one ion of acetate (a compound containing three hydrogen, two carbon, and two oxygen). However, the acetic acid in vinegar is dissolved in water, which does not react with baking soda, and you don't know how many acetic acid molecules there are in your bottle of vinegar. For this reason, you can't just calculate the right amount of each to use to get the largest reaction.