\(n_{CO_2}=\dfrac{2,24}{22,4}=0,1\left(mol\right)\\ PTHH:CO_2+Ba\left(OH\right)_2\rightarrow BaCO_3\downarrow+H_2O\\ \Rightarrow n_{Ba\left(OH\right)_2}=n_{BaCO_3}=0,1\left(mol\right)\\ \Rightarrow C_{M_{Ba\left(OH\right)_2}}=\dfrac{0,1}{0,2}=0,5M\\ m_{BaCO_3}=0,1\cdot197=19,7\left(g\right)\)