Nitric acid is HNO3. Potassium carbonate is K2CO3. Nitric acid is an acid and potassium carbonate is a base, so this is an acid/base chemical reaction. The unbalanced chemical reaction is shown below.
HNO3 + K2CO3 --> KNO3 + H2CO3
Now we must balance the elements on each side of the equation. We have 2 potassiums on the left so we need another potassium on the right. This necessitates another molecule of HNO3 as well (also to balance the hydrogens). The balanced equation is shown below.
2HNO3 + K2CO3 --> 2KNO3 + H2CO3
The species on the far right is called carbonic acid (H2CO3). It is unstable and decomposes into water and carbon dioxide as shown below.
H2CO3 --> H2O + CO2
Taking this into account, the complete chemical equation is shown below:
2HNO3 + K2CO3 --> 2KNO3 + H2O + CO2