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Since calcium oxalate is 3000 times less soluble than calcium sulfate, would it be possible to concentrate sulfuric acid from let's say $\pu{50\%}$ solution using following steps? :

  1. adding calcium carbonate to cold dilute $\ce{H2SO4}$
  2. filtering off resulting $\ce{CaSO4}$
  3. mixing $\ce{CaSO4}$ with oxalic acid in 1:1 molar ratio
  4. adding just enough water to submerge the solids
  5. vacuum filtering off the now concentrated (hopefully) $\ce{H2SO4}$

My reasoning behind this is that even though at any given time there's only a small amount of $\ce{CaSO4}$ dissolved, the reaction producing sulfuric acid would eventually go to completion with high yield due to it's the massive kinetic favourability. The only problem I see is that the amount of water needed would limit the final concentration. Would adding merely enough water to wet all the solid still work, improving the final concentration?

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Calcium oxalate solubility depends on acidity, as the weak oxalic acid is protonated in highly acidic sulphuric acid.

Additionally, oxalic acid would be dehydrated if sulphuric acid was concentrated enough.

If we for convenience mark oxalate anion $\ce{(COO)2^2-}$ as $\ce{Ox^2-}$, then

$$\ce{CaOx <<=> Ca^2+ + Ox^2-}$$

$$\ce{Ox^2- + H+ <=>> HOx^-}$$

$$\ce{ HOx^- + H+ <=>> H2Ox}$$

$$\ce{ H2Ox ->[H2SO4] H2O + CO ^ + CO2 ^}$$

Therefore oxalic acid has no chance to create concentrated sulphuric acid.

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