How to extract pure potassium carbonate from ash? In our village, lots of ash is produced which is thrown off. I want to extract pure potassium carbonate from that ash. I am able to extract the potassium compound and a soluble compound by recrystallizing and evaporating but I found impurities. The first test I performed is electrolysis. This test confirmed the presence of chlorine gas which is able to change the litmus paper to white. The second test I performed is flame test. During the flame test, I got a yellowish orange color while my expectation was bluish violet. So, I assume there is sodium. How can I extract the pure compound?
To conclude, there is a small amount of potassium chloride, sodium chloride, sodium carbonate which are the impurities.
The composition of the wood ashes varies with the nature and the origin of the wood. In the average, it is a mixture of $40$ % - $70$ % $\ce{CaCO3}$, $5$% - $10$% $\ce{MgCO3}$, $5$% - $10$% $\ce{K2CO3}$, $5$% - $10$% $\ce{Na2CO3}$, $2$% - $5$% $\ce{SiO2}$, $2$% - $5$% $\ce{Ca3(PO4)2}$, $0.5$% -$2$% $\ce{Al2O3}$, &lt;$1$% $\ce{NaCl}$, &lt;$1$% $\ce{KCl}$, plus traces of manganese and iron. So it is difficult to purify, and/or to extract any of these compounds, as a lot of these compounds are insoluble in water: $\ce{CaCO3, MgCO3}$, $\ce{SiO2, Ca3(PO4)2, Al2O3}$. The only soluble compounds are $\ce{K2CO3}$ and $\ce{Na2CO3}$, plus traces of $\ce{NaCl}$ and $\ce{KCl}$, and they form less than $20$% of the total mass of the ashes. The solution obtained from washing the wood ashes is a mixture of sodium and potassium carbonate. The problem is how to separate those two carbonates. Fractional crystallization does not seem easy. I would rather transform them into nitrates by adding nitric acid : at $0°$C, $\ce{KNO3}$ is  not very soluble ($5$ g/$100$ mL), which is much less than $\ce{NaNO3}$ ($73$ g/$100$ mL). So obtaining $\ce{KNO3}$ from the mixture by cooling a hot solution should be relatively easy.
Ref.: J. Hartwig, Ann. der Chem. u. Pharm. XLVI, p. 97. A. Wurtz, Dictionnaire de chimie pure et appliquée, Vol. 1, p. 641 (1891).