  We evaluate the degree of disorder in electrolyte gating devices through the
transport measurements in graphene. By comparing the mobility in ion- and
standard metal-gated devices, we show that the deposition of the ionic liquid
introduces charged impurities with a density of approximately $6\times 10^{12}$
cm$^{-2}$; setting the upper limit of the mobility in graphene to 3000
cm$^2$/Vs. At higher temperature, phonons in the ionic liquid further reduce
the mobility, making its upper limit 2000 cm$^2$/Vs at room temperature. Since
the degree of disorder is independent of the base material, these results are
valuable towards understanding disorder effects in general devices using
electrolyte gating.
