The Hugoniot equation of state of KFeS2 (initial density 2.663 g/cm3) has been determined for pressures up to 110 GPa. The Hugoniot data demonstrate a transformation at 13¿1 GPa to a phase with an apparent zero-pressure density of 3.7¿0.2 g/cm3. A comparison of the inferred isentrope of KFeS2 (high-pressure phase) with those of Fe, Fe0.9S, and FeS2 indicates that the atomic volume of potassium in KFeS2 is approximately twice that of iron at 75 GPa. In the temperature and pressure range of the experiments, potassium fails to meet the empirical Hume-Rothery and Raynor (HRR) criterion for solubility of an element in iron, namely, that the molar volume of the element should not exceed that of iron by a factor greater than ~1.4. However, both the applicability of the HRR solubility criterion and the infrared isotrope of KFeS2 at high pressure are uncertain. Thermochemical calculations of the partitioning of K between a sulfide and silicate phase (e.g., KFeS2 and KAlSiO4 or KAlSi3O8 (hollandite)) indicate that pressure does not have a pronounced effect on the relative stability of solid KFeS2 and potassium aluminosilicate high-pressure phases. The calculations suggest that the high-pressure phase of KFeS2 would not be stable in relation to KAlSiO4 (kalsilite) in the upper mantle, or in relation to KAlSi3O8 (hollandite) in the lower mantle. However, the calculations do not bear directly on the question of partitioning of K into an iron sulfide melt from lower mantle aluminosilicate phases. Although the present results cannot absolutely rule out the hypothesis that a large fraction of the terrestrial potassium budget has dissolved into a molten iron sulfide-bearing core, the present analysis of the pressure-volume relation for potassium, iron, iron sulfides, potassium aluminosilicate, and potassium iron sulfide yields no evidence in support of this hypothesis.