Potash
Potassium carbonate, or potash, is a carbonate salt notable for its presence in wood ash and ease of extraction therefrom. Potash has several uses and is extremely simple to produce in large quantities even with the most basic of technology, this makes it a critical primitive chemical feedstock. It may be used to produce lye by a reaction with slaked lime (calcium hydroxide). It is a necessary compound for the production of saltpeter from organic material and may also be used in baking as a leavening agent.
Production
Potash is extremely simple to make, in fact it doesn't require the use of any chemical reaction, only a simple extraction. All that is needed are a piece of cloth, two containers (one wider than the other), and a lot of water. First, cut a hole in the bottom of the wider container and stuff the cloth down in the bottom to act as a filter. Next, place the wider container over top of the other container, so that any liquid from the top drains into the bottom. Now, fill the top container with wood ash and begin pouring water through the wood ash. Continue this until the water runs clear (or, relatively clear if energy is being conserved). Now, all that needs to be done is boiling down the liquid. This should be done in a non-metallic container (glazed pottery, glass, etc.) as potash is mildly caustic. What is left will be relatively pure potash which can be used for any of the above mentioned processes. If higher purity is needed, potash may be recrystallized from methanol or ethanol, but this is a very inconvenient process.