[smithbryanf2]

I'm thinking about producing nitric acid by reacting potassium nitrate with sulfuric acid.
2KNO3 + H2SO4 ----->  2HNO3 + K2SO4

my question is since potassium is higher in the reactivity series of metals, why does this reaction go forward instead of backwards?

[smithbryanf2]

I'm trying to get better at predicting reactions, and hopefully i can get some insight into why this might happen.

[Borek]

Potassium cation is just a spectator here, it doesn't change during the reaction.

[Zyklonb]

Double displacement reactions don't work that way. All you will have in a solution of ions. The only way to drive a DD reaction to the right, is by removing one of the products as the reaction proceeds. The common ways to do this are: precipitating one of the salts and boiling off the most volatile liquid.
In the case of the specific reaction you suggested, only the later can be used. Simply distill the solution, works like a charm.
There is a way to do it without distillation, using the other way to drive equilibrium: precipitation. Use calcium, barium or strontium nitrate, add this to the stoichoimetric quantity of conc. sulfuric acid. XSO₄ will percipitate, and nitric acid will remain in solution.