Soap equation using potash

I'm trying to understand the chemical formula of soap using potash ($\ce{K2CO3}$) as they did in antiquity instead of using sodium hydroxide ($\ce{NaOH}$) or potassium hydroxide ($\ce{KOH}$). I've found the formula for making soap with sodium hydroxide on the [Khan Academy](https://cdn.kastatic.org/ka-perseus-images/fa3d4e80684f15078d1444a1c861bfb1ef8216ed.png), but I didn't make much progress on my own.


[![soap](https://i.stack.imgur.com/iH97hm.jpg)](https://i.stack.imgur.com/iH97hm.jpg)


Can somebody help me understand how the soap and the glycerin molecule would look like?


Or is the saponification not possible and ancient soap makers first needed to create potassium hydroxide from potassium carbonate?




Ashes have been thoroughly studied more than $100$ years ago. See the Dictionnaire de chimie (in French) by A. Wurtz, Hachette ed., Paris, 1872, p. 787 - 789. Potassium hydroxyde $\ce{KOH}$ was never found in all ashes studied (Wood, fruits, vegetables) : in the presence of air, potassium hydroxide $\ce{KOH} $ is quickly transformed into potassium carbonate $\ce{K2CO3}$. The composition of wood ashes is $\ce{CaCO3}$ $5 - 50$%, $\ce{K2CO3}$ $12 - 32$%, $\ce{SiO2}$ $5 - 42$%, $\ce{Ca3(PO4)\_2}$ $5 - 15$%, $\ce{MgCO3}$ $2 - 6$%, and $\ce{FePO4}$ $0 - 2$%. So, wood ashes do not contain any $\ce{KOH}$, as the $\ce{OH-}$ ion is entirely transformed into carbonate in the presence of air. But, as mentioned by Oscar Lanzi, this $\ce{CO3^{2-}}$ ion is hydrolyzed in water and produced about $1$% $\ce{OH^-}$ ion, which is able to saponify the vegetable oils. But the yield is poor.


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> 
> Can somebody help me understand how the soap and the glycerin molecule would look like?
> 
> 
> 


Once you add water, you have potassium ions and hydroxide ions in solution, and the products look the same as with aqueous potassium hydroxide.


In contrast to the reaction with sodium hydroxide, which gives the sodium salts of the fatty acids, you would obtain the potassium salts of the fatty acids with potassium hydroxide or with potassium carbonate.


If you use potassium carbonate, there would be some form of carbonate as a side product. Depending on the final pH, it could be carbonate, hydrogen carbonate or carbon dioxide or some combination. According to [this source](https://classicbells.com/soap/woodAshLye.asp), traditional recipes used an excess of wood ash, so the pH would be fairly alkaline.


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Once you introduce water, potassium carbonate can generate potassium hydroxide through the hydrolysis reaction


$\ce{CO3^{2-} + H2O <=> HCO3^- +OH^-},$


and this reaction is fairly efficient because carbonate ion is a rather strong base ($\pu{pK\_b} = 3.75$ from the conjugate acid $\pu{pK\_a}$ reported by [Wikipedia](https://en.wikipedia.org/wiki/Potassium_carbonate)). That basicity combined with the good solubility of potassium carbonate in water allows a $\pu{pH}$ between $12$ and $13$ to be obtained.


In addition, the moderately strong-base carbonate ion can promote nucleophilic attack by the water itself, by acting as a base to remove a proton from the nucleophilic substitution product:


$\ce{RCOOR' + H2O -> RCOOH + R'OH}$


$\ce{RCOOH + CO3^{2-} -> RCO2^- + HCO3^-}$


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