Primitive cells had to divide using very few biological mechanisms. This work proposes physicochemical mechanisms, based upon nanoscale electrostatics, which explain and unify the motions of chromosomes during prometaphase, metaphase, and anaphase A. In the cytoplasmic medium that exists in biological cells, electrostatic fields are subject to strong attenuation by ionic screening, and therefore decrease rapidly over a distance equal to several Debye lengths. However, the presence of microtubules within cells completely changes the situation. Microtubule dimer subunits are electric dipolar structures, and can act as intermediaries that extend the reach of the electrostatic interaction over cellular distances. Experimental studies have shown that intracellular pH rises to a peak at mitosis, then decreases through cytokinesis. This result, in conjunction with the electric dipole nature of microtubule subunits, is sufficient to explain the dynamics of the above mitotic motions, including their timing and sequencing. The physicochemical mechanisms utilized by primitive eukaryotic cells could provide important clues regarding our understanding of cell division in modern eukaryotic cells.