The chemical reaction is as follows:

Mg(OH)2 (magnesium hydroxide) + CO2 (carbon dioxide) -> MgCO3 (magnesium carbonate) + H2O (water)

MgCO3 (magnesium carbonate) + BaCl2 (barium chloride) -> BaCO3 (barium carbonate) + MgCl2 (magnesium chloride)

Therefore, the overall reaction is:

Mg(OH)2 + CO2 -> MgCO3 + H2O

MgCO3 + BaCl2 -> BaCO3 + MgCl2