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Don't read any further in this thread. Wood ash typically amounts to 1-2% of the original woods mass prior to burning. assuming that all of the cellulose lost all of it's water of hydration (CH + O -> C + h2O) and got converted to charcoal (carbon) and then all of the carbon got enough air and heat to combust ( C+O2 -> CO2) then all you will be left with are non-combustable salts of Calcium, Sodium, Potassium, and Magnesium with trace amounts of others. completing the salts are chloride, carbonate, sulfate sulfite, nitrate, Oxide and phosphate. The mix will vary depending on what you are burning, how hot it was, and how much air was able to get to it. some of the salts are soluble in water, some are not.
Nice answer, but you will be left with oxides of these salts, at least while still very hot, and some will be quite soluble, others not. See post 67 for some more facts.
BTW, if the wood is burnt in chamber "starved" for O2, there will lot of carbon left as coke or charcoal provided you let it cool before extracting it.* In Brazil this chamber is often made from sun-dried mud bricks, with walls many "bricks" thick and each layer of slightly smaller radius - a dome shaped chamber. The inner layer is sold as are not bad bricks, and the next time a new chamber is built, new sun dried bricks form the outer layers. Usually this is done near the edge of a road in rural areas as the smoldering makes lots of smog.
* You can tell when the charcoal and bricks are (or soon will be) ready for sale if you drive that road daily - no smoke rising and dome may be half gone. I don't know, and it depends on the weather some, but think the production cycle takes about a month, so usually there are at least two, "out of phase" ovens. There is always a large array of bricks drying in the sun, and full time work, often for the children of the area making these bricks. - It is a way of life, not entirely legal as cutting trees is illegal. They are usually cut some miles from where the field of drying bricks is during the night.
I had a cattle farm for a decade and at least twice some of my trees were stolen. The cutters were kind - did not clear cut, but were selective in their cutting. Every month or so, a government plane flies over your farm taking photos. A neighbor did slightly and slowly expand his pasture into the adjoining woods, of his land. They finally caught him - I think he did both jail time and paid a big fine. Brazil has probably the world's tightests environmental laws and enforcements in the world.
There are a few trees in pastures - left for cows /steer to have shade to rest in. One in my pasture had toxic leaves that a strong wind blew off. Several of my steers got sick and one died. I only visited the farm for a couple of week-ends each month as had very honest smart field man.** He "came with the land" when I bought it - had worked there since a child and almost knew every blade of grass by name. When I arrived, and learned what had happen, I said: "Cut that damn tree down and burn it." He explained: You don't want to do that, but knew what to do and had already done it. Cut a deep grove thru the bark all around the trunk. The government's photographing plane would see tree dying and after standing dead for few years we could safely cut it down.
** A leader of the local community and very intelligent and honest - a politician once gave him a new steel door, just for every day wearing the a political T-shirt the month before election. He was naturally gifted in personal relationships - I think most of the valley voted as that T-shirt said to. He was also nearly illiterate, so Brazil lost potentially one of the best diplomats it could have had. He never knew what day I would come, but was always up in the field with his hoe when I arrived. The cattle make Darwinian selection favoring the weeds when eating the good grass - he did the opposite - selectively killed weeds to keep the pasture in good shape.
I paid him the local equivalent of $100/ month for his 44 hour work week (Half day on Saturday). That got other "absentee" owners mad at me. Their workers wanted better pay too. The whole valley lived self-sufficient out side the cash economy. Grew their own coffee, tobacco, food, made cooking *** lard from the pigs, had lots of chickens, a productive garden, clean unpolluted water, fresh milk every day, etc. No one had a refrigerator, so if they killed an old cow not giving much milk any more, all came to share the "beef feast." No one ever ate even just a samwich in the presence of another without offering to share. My hired man, offered to me part of his lunch (beans & rice) during his lunch breaks if I went outside my small house there, so I rarely did. A few times, just to be polite, I accepted his offer, returned to get a small bowl, and ate some with him. I usually then gave him a can of Vienna sausages or sardines I had for him to later share with his wife (after confirming he did have a rarely used can opener).
*** Their wood fire stove is clever design, with only three or four holes (covered by lids or with pots) in one small piece of flat steel. It has an "entrance table" and burns logs from the end - no need to cut the dry fallen limbs used as fuel. Just jump on them supported at ends by two rocks until the pieces are not more than about 6 or 7 feet long. The cook feeds them into the combustion part of the stove as needed to regulate the heat.
They will all be still doing well, when the "advanced world" collapses under its growing, unpayable debt, with no food in your local grocery store etc.