What is the balanced chemical equation when sodium bicarbonate is combined with silica and calcium carbonate?

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To the best of my knowledge there is no reaction between any of these species.  Let's look at each reagent.  Sodium bicarbonate (NaHCO3) will dissolve in water into sodium cations and bicarbonate anions.  The bicarbonate ion ((HCO3)-) can act as either a weak base or a very weak acid.  Silica is an oxide of silicon and has the formula SiO2.  It is not soluble to any extent in water.  Calcium carbonate (CaCO3) is a solid that will dissolve in water to give calcium cations and carbonate anions.  The carbonate ion ((CO3)2-) acts as a base and might deprotonate the bicarbonate to some extent but the product of that reaction is the same as the reagents!

(HCO3)- + (CO3)2- --> (CO3)2- + (HCO3)-

So if these reagents are added together in aqueous solution, the NaHCO3 and CaCO3 will not really react with each other and the silica will be totally unreactive.  It can react with strong acids and bases but neither of these is strong enough.  So I would say there is no reaction.

NaHCO3 + SiO2 + CaCO3 --> no reaction

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