Answer:
You will get at first carbon dioxide by burning C:
C+O_2=CO_2
Burn hydrogen to obtain water:
H_2+\frac{1}{2}O_2=H_2O
Combine them:
CO_2+H_2O=H_2CO_3
Now react it with Ba:
Ba+H_2CO_3=BaCO_3+H_2
To sum up, the reaction is Ba+C+\frac{3}{2}O_2=BaCO_3, using hydrogen as a catalyst.
Step-by-step explanation: