Reduced graphene oxide (RGO) is an electronically hybrid material that displays remarkable chemical sensing properties. Here, we present a quantitative analysis of the chemical gating effects in RGO-based chemical sensors. The gas sensing devices are patterned in a field-effect transistor geometry, by dielectrophoretic assembly of RGO platelets between gold electrodes deposited on SiO2/Si substrates. We show that these sensors display highly selective and reversible responses to the measured analytes, as well as fast response and recovery times (tens of seconds). We use combined electronic transport/Kelvin probe microscopy measurements to quantify the amount of charge transferred to RGO due to chemical doping when the device is exposed to electron-acceptor (acetone) and electron-donor (ammonia) analytes. We demonstrate that this method allows us to obtain high-resolution maps of the surface potential and local charge distribution both before and after chemical doping, to identify local gate-susceptible areas on the RGO surface, and to directly extract the contact resistance between the RGO and the metallic electrodes. The method presented is general, suggesting that these results have important implications for building graphene and other nanomaterial-based chemical sensors.