Honey is acidic with a pH of 3.9- that's more acidic than some oranges. There is also quite a lot of honey in this recipe that will give the acid the baking soda needs to react.
In this recipe, both the egg whites and the baking soda are going to provide some leavening.
Without the soda the cake will undoubtedly be a little more dense.
Additionally, even when not contributing to leavening, raising the pH will promote browning of baked goods. I think the ground almonds will give nice color but the recipe may be a little paler without the soda.
There is no soda in angel food cake and I expect this cake will also be just fine without it.
Yes, I have found several sources that say that citric acid is about 4 times the strength of cream of tartar. So, mix 1 teaspoon of baking soda and 1/2 teaspoon of citric acid and use a 1/2 teaspoon of the mixture.
That should work. Let us know!
EDIT: Oops, I should have mentioned this before the OP accepted. Hopefully, he'll realize, or see this. That substitution will approximate single action baking powder, so don't dilly-dally before cooking! (Difference Between Double and Single Action Baking Powder)
2nd EDIT: Just to be extra confident, I compared the reaction (according to the method of David Lebovitz) of 1/4 tsp of my recommended mixture with boiling water and 1/2 tsp of new Rumford Baking Powder with boiling water. The results seemed identical.
3rd EDIT: I actually found this question pretty intriguing. While I could find plenty of evidence that it should work (including my own little water experiment), I couldn't find anything definitive that said it does work.
Well, it just so happens that I had some cream in the fridge, and I have been meaning to try America's Test Kitchen's cream biscuits. With nothing in them but flour, sugar, baking powder, salt and cream; they should be perfect for comparing real baking powder with the substitution.
SO:
I made biscuits.
They taste as identical as they look. (pretty yummy too)
I can now say with authority, the substitution works. 1 tsp fresh Rumford Brand Baking Powder = 1/2 tsp of a mixture of 1 tsp baking soda and 1/2 tsp citric acid.
Best Answer
They are different ingredients and one does not replace the other. Baking soda is an alkali which can react with acidic ingredients in a recipe to produce carbon dioxide which helps baked goods rise. Baking powder includes baking soda (or similar) and an acidic ingredient, so it is more 'self-contained' rather than relying on something else in the recipe. (Self-raising flour is basically flour with baking powder mixed in, to be even more self-contained.)
But you should just follow whatever is in the recipe you are making or adapting. If you have found a recipe you are trying to follow which does not make it clear you could post it in your question and we could try to work it out from the other ingredients.