The law of the conservation of matter requires that the number of atoms of each element on each side of a chemical equation. This is done by adding coefficients in front of the formulas in the equation. A chemical formula should never be changed, only the amount.
AgI+Fe2(CO3)3→FeI3+Ag2CO3
First notice that there is a polyatomic ion, the carbonate ion, CO2−3 that occurs on both sides. When there is a polyatomic ion, it is treated as a single entity. So there are three carbonate ions on the left side and one on the right. So a coefficient of 3 is needed in front of Ag2CO3
AgI+Fe2(CO3)3→FeI3+3Ag2CO3
Now there are six Ag atoms on the right side, but one on the left. So a coefficient of 6 needs to be added in front of the compound AgI.
6AgI+Fe2(CO3)3→FeI3+3Ag2CO3
Now there are six AgI, which gives us six I atoms on the left side, but three on the right. So a coefficient of 2 is needed in front of the compound FeI3.
6AgI+Fe2(CO3)3→2FeI3+3Ag2CO3
This also balanced the Fe atoms. So the balanced equation is
6AgI+Fe2(CO3)3→2FeI3+3Ag2CO3
