Experimental measurements of density by X-ray absorption and of P-wave velocity by ultrasonic techniques of liquid Fe-(<17 wt%) Si-(<4.5 wt%) C alloys at pressures up to 5.8 GPa are presented. These data are used to construct an Fe-Si-C liquid mixing model and to characterize interior structure models of Mercury with liquid outer core composed of Fe-Si-C. The interior structure models are constrained by geodetic measurements of the planet, such as the obliquity and libration of Mercury. The results indicate that S and/or C with concentrations at the wt% level are likely required in Mercury's core to ensure the existence of an inner core with a radius (below ∼1,200 km) that is consistent with reported dynamo simulations for Mercury's magnetic field. Interior structure models with more than 14 wt% Si in the core, estimated for Mercury by assuming an EH chondrite-like bulk composition, are only feasible if the obliquity of Mercury is near the upper limit of observational uncertainties (2.12 arcmin) and the mantle is dense (3.43–3.68 g·cm−3). Interior structure models with the central obliquity value (2.04 arcmin) and less than 7.5 wt% Si in the core, consistent with estimates of Mercury's core composition from an assumed CB chondrite-like bulk composition, are compatible with 3.15–3.35 g·cm−3 mantle densities and an inner core radius below 1,200 km. Interior structure models with the obliquity of Mercury near the lower observational uncertainty limit (1.96 arcmin) have a low-density mantle (2.88–3.03 g·cm−3), less than 4 wt% Si in the core, and an inner core radius larger than 1,600 km.