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When plant based solid fuels, such as firewood, coal etc. are burned, their potassium and phosphorus content stay in the solid ashes. Quick search on the net shows ashes contain about 4% potassium and 1-2% phosphorus.

What chemical methods exist to separate potassium-something, something-phosphate out of ashes?

It seems mixing ashes with water will dissolve potassium salts, but still unsure what can we do the get the phosphorus out.

(I find the question interesting because currently both potash and phosphate are mined, and thus non-renewable. So if we want to be sustainable, we will need a way to recover these nutrients from organic waste and ashes.)

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    $\begingroup$ Why would you want to separate them from ashes? $\endgroup$ 2 days ago
  • $\begingroup$ Search for they recovery, you should find quite some material. Urine can be a relatively good source for phosphates. Ex sciencedirect.com/science/article/abs/pii/S1385894719326944 $\endgroup$
    – Alchimista
    2 days ago
  • $\begingroup$ @IvanNeretin Because I think ashes contain a few simple inorganic compounds rather than a lot of complex organic ones. Perhaps it's easier to reason about. $\endgroup$
    – Calmarius
    2 days ago
  • $\begingroup$ With my comment I wanted also to say that it is done. I do not know the scale of that industry, but recovering for fertiliser is done, at least for phosphates. Just the source are so that the phosphate is already concentrated by living animals and, yes, humans too. $\endgroup$
    – Alchimista
    2 days ago
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    $\begingroup$ If you want to use these compounds as fertilizers, ashes are good enough as is, without any separation. On the other hand, if you want to do some chemistry, this source is too dirty anyway. $\endgroup$ 2 days ago
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Ashes are made of

$30 - 70$% $\ce{CaCO3}$,

$5 - 12$% $\ce{K2CO3}$,

$5 - 12$% $\ce{Na2CO3}$,

$5 -10$% $\ce{MgCO3}$,

$2 - 15$% $\ce{SiO2}$,

$2 - 5$% $\ce{Ca3(PO4)2}$,

$2 - 5$% $\ce{Mg3(PO4)2}$,

$2 - 3$% $\ce{K2SO4}$,

$< 2$% $\ce{AlPO4}$,

$< 2$% $\ce{FePO4}$,

plus less than $1$% oligoelements. Water will dissolve the sodium and potassium compounds. Adding then acidic solutions will extract the calcium, magnesium and iron compounds. It will not be easy to separate potassium and phosphorus compounds out of these solutions.

Ref.: http://gallica.bnf.fr/ark/12148/bpt6K33845.image.r=Dictionnaire+de+chimie.f181.langFR

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