Baking Soda on Passover
In short — baking soda is kosher for Passover. It’s a chemical leavening agent, it doesn’t work through fermentation like yeast (which is prohibited). Additionally, matzah, once baked, is kosher for Passover, and simply cannot be made “unkosher” for Passover by the introduction of seltzer, eggs, or baking soda. (Note that there are folks who avoid “gebrokts” — matzah that has been prepared with liquid.)
While any year-round baking soda is acceptable on Passover (so long as it’s a new box), baking powder is not acceptable unless it is made without cornstarch and thus specifically marked kosher for Passover.
Of course, especially on Passover, if you’re uncertain about what’s okay and what isn’t, ask your local halachic authority.
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According to Rav Abadi’s Pesah list, baking powder without a specific hechsher is OK even for ashkenazim, although in a Q&A he says at least that brand for sephardim. Could be an issue of bitul, an inconsistency, or a makhloket.
I have never seen a Pesach recipe that uses baking soda. I was under the (mistaken, perhaps?) impression that baking soda was only used for cleaning on Pesach.