ZnO is a wide band gap semiconductor with many applications such as in solar cells, varistors, and other electrical components. The ZnO material was synthesized using a sol-gel method. The material was characterized using X-Ray diffraction (XRD) and scanning electron microscopy (SEM). The material is pure and single phase. Electron conduction in ZnO nanomaterials was done using alternating current (ac) impedance. The frequency ranges of the measurements used were 1x 10-3 Hz to 1x 106 Hz and the ac impedance measurements were done within a temperature range of 60oC to 100oC. Nyquist plots were drawn and bulk resistances were obtained. Subsequently, conductivity values were calculated and the diffusion characteristics were obtained. From further analysis of the conductivities with temperature, the diffusion of electrons in the material was studied. It was found that the conductivity increased with the increase of temperature which meant that the rate of diffusion of the electrons through the materials also increased. An Arrhenius relation was concluded for the electron diffusion in the ZnO nanomaterials.