為何碳鋅電池不能充電?

A chemical cell can be rechargeable only if the reactions at the electrodes are reversible.

Consider the reactions of a zinc-carbon cell:
Anode: Zn(s) → Zn2+(aq) + 2e-
Cathode: 2NH4^+(aq) + 2MnO2(s) + 2e^- → 2NH3(aq) + Mn2O3(s)

The cathodic reaction above is irreversible. Besides, the zinc ions flow away from the anode and thus the backward reaction of the anodic reaction also cannot occur.