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Starting from insoluble ZnO how would you obtain insoluble ZnCO3 by precipitation.

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ZnO (s) + 2HCl (aq) →  ZnCl2 (aq) + H2O(l) 

ZnCl2 (aq) + Na2CO3 (aq) → ZnCO3 (s) + 2NaCl (aq)

Dissolve zinc oxide in minimum quantity of dil. HCl. Add to it a saturated solution of Na2CO3 in water till no more precipitation takes place. Filter and dry the ZnCO3 so obtained.

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