It is not my equation it is one from an internet search on what happens when you dissolve Potassium Carbonate in water.
I leached my wood ash and boiled the leachate to concentrate then set it aside to cool. I filtered the leachate to remove particulate that formed when it cooled, I repeated that process and then set the remainder of the liquid aside to evaporate to dryness. I now have a powder that I believe is Potassium Carbonate or a mixture that could be considered potash.
I think you are suggesting that I could leach wood ash, and add Lime (CaO), filter the particulate and then evaporate to dryness and I would have a powder that is KOH.
I might try that sometime. I think I can use mortar for Lime.
Tim