There are two steps to this reaction.
Step 1: Reaction between sulfuric acid and sodium sulfite.
First, sulfuric acid (`~H_2SO_4` ) reacts with sodium sulfite (`~Na_2SO_3` ) to produce sodium sulfate (`~Na_2SO_4` ) and sulfurous acid (`~H_2SO_3` ) as follows:
`~H_2SO_4` + `~Na_2SO_3` -> `~Na_2SO_4` + `~H_2SO_3`
This is an example of a double replacement reaction.
Step 2: Decomposition of sulfurous acid.
Second, the sulfurous acid product (`~H_2SO_3` ) is unstable and spontaneously decomposes into water (`~H_2O` ) and sulfur dioxide gas (`~SO_2` ) as follows:
`~H_2SO_3` -> `~H_2O` + `~SO_2`
This is an example of a decomposition reaction.
Therefore, the overall reaction between sulfuric acid and sodium sulfite is:
`~H_2SO_4` + `~Na_2SO_3` -> `~Na_2SO_4` + `~H_2O` + `~SO_2`
The number of each atom on both sides of the equation is the same, so the equation is already balanced.