I'm not positive that there is a reaction. I know that Ca(HCO3)2 is soluble and I would therefore expect both Sr(HCO3)2 and Ba(HCO3)2 to be less soluble than that. I found one reference that the solubility of Ba(HCO3)2 tp be 0.73 g/100 mL H2O. So, if there IS a reaction it will be
2NaHCO3 + BaCl2 ===> Ba(HCO3)2 + 2NaCl. I would expect this reaction to occur only in higher concentrations AND with an excess of BaCl2 in order to bring into play the common ion effect.
Reaction between sodium bicarbonate and saturated solution of barium chloride
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