The commercial method of preparation of potassium by reduction of molten $\mathrm{KCl}$ with metallic sodium at 850° C is based on the fact that:

sodium has less affinity to chloride ions in the presence of potassium ion

potassium is solid and sodium distils off at 850° C

potassium being more volatile and distils off thus shifting the reaction forward

sodium is more reactive than potassium at 850° C