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The soil provides for reactions that a tank of water can’t.
Minerals taken up from soil are usually due to combustion on the surface at some point in the past, or wood ash being dumped on the top and mixed in.
Puting ash in the tank is of no help, it sinks to the bottom or floats on the top.
Sorry, that’s not a helpful answer.
There must be some physical process involved to move soil minerals through the exterior cells of the roots.
And, once in the roots, if the mineral is not soluble, how does it circulate through plant, and deliver its vital nutrients to the cells that need them?