Baking soda (bicarb) makes a cake lighter and fluffier. According to About you can substitute 2–3 times the baking powder for the baking soda because baking powder is 2 parts cream of tartar to one part baking soda. The question is, what does that much cream of tartar do to a cake? Apparently it solidifies the egg whites in a recipe. Quite frankly, have you thought about going to a neighbor and borrowing some baking soda? It would be much easier. I will add that if you are not good at baking, and don’t have the right ingredients, combining recipes is not a good idea if you expect to eat the results or unless you are baking because you are bored and don’t mind wasting the ingredients you do have.