The main chemical ingredients of baking soda and vinegar are sodium bicarbonate and acetic acid, respectively. These chemicals can be found in nature and have been used for a variety of purposes since ancient times.

Because they produce carbon dioxide bubbles when mixed, these and other similar chemicals have been used as chemical leavening agents in bread. The use of chemical leaveners appears to have been first documented as early as 1796 in a cookbook called "American Cookery". Although, I'm not sure whether or not it is known who was the very first person to put baking soda and vinegar together and observe their reaction.

I'm guessing that many people discovered the reaction of baking soda and vinegar, all over the world, over and over again. There's a book on the internet published in 1784 that talks about vinegar and soda. Baking soda has a high pH because it is basic or alkaline. Vinegar has a low pH because it's an acid. Acids and bases have strong reactions with each other that produce a lot of heat. Baking soda breaks down in acids to produce carbon dioxide gas.