  More than a third of all exoplanets can be classified as super-Earths based
on radius (1-2 $R_{\bigoplus}$) and mass (< 10 $M_{\bigoplus}$). Here we model
mass-radius relations based on silicate mantle and iron core equations of state
to infer to first order the structure and composition range of rocky
super-Earths assuming insignificant gas envelopes. We develop a new equation of
state of hexagonal close packed (hcp) iron for super-Earth conditions (SEOS)
based on density functional theory results for pressures up to 137~TPa. A
comparison of SEOS and extrapolated equations of state for iron from the
literature reveals differences in density of up to 4% at 1~TPa and up to 20% at
10~TPa. Such density differences change the derived mass by up to 10\% for
Earth-like super-Earths (core radius fraction of 0.5) and 20% for Mercury-like
super-Earths (core radius fraction of 0.8). We find that the effect of
temperature on mass (< 5%) is smaller than that resulting from the
extrapolation of the equations of state of iron and lower mantle temperatures
are too low to allow for rock and iron miscibility for R<1.75 $R_{\bigoplus}$.
We find that modeling uncertainties dominate over observational uncertainties
for many observed super-Earths. We illustrate these uncertainties explicitly
for Kepler-36b with well-constrained mass and radius. Assuming a core
composition of 0.8$\rho$ Fe (equivalent to 50 mol% S) instead of pure Fe leads
to an increase of the core radius fraction from 0.53 to 0.64. Using a mantle
composition of Mg$_{0.5}$Fe$_{0.5}$SiO$_3$ instead of MgSiO$_3$ leads to a
decrease of the core radius fraction to 0.33. Effects of thermal structure and
the choice of equation of state for the core material on the core radius of
Kepler-36b are small but non-negligible, reaching 2% and 5%, respectively.
