 Solution

Bulk electroneutrality gives $\boxed{[\mathrm{N}{\mathrm{O}}_3^{-}]=[{\mathrm{H}}^{+}]+2[\mathrm{Z}{\mathrm{n}}^{2+}]}$. Each dissolved zinc ion contributes two positive elementary charges, whereas each nitrate contributes one negative charge.

This assumes complete nitric acid dissociation, only ${\mathrm{H}}^{+}$ and $\mathrm{Z}{\mathrm{n}}^{2+}$ as significant cations, and only nitrate as a significant anion. It neglects $\mathrm{O}{\mathrm{H}}^{-}$ at acidic pH, other dissolved salts, zinc complexes and additional ionic nitrogen products. It is a bulk charge balance; a thin charged electrode interface does not invalidate bulk electroneutrality.