Which of the following reactions takes place at the cathode of a dry…

The correct answer is Option (4) → \( \ce{MnO2 + NH4+ + e^- -> MnO(OH) + NH3} \)

• In the dry cell the zinc container is the anode and a carbon (graphite) rod surrounded by powdered manganese dioxide and carbon is the cathode. The space between them holds a moist paste of NH₄Cl and ZnCl₂.

• Reduction takes place at the cathode, and the species reduced is MnO₂:

      \( \displaystyle \ce{MnO2 + NH4+ + e^- -> MnO(OH) + NH3} \)

• Manganese goes from the +4 oxidation state in MnO₂ to +3 in MnO(OH), so one electron is taken up per MnO₂. The cell gives a potential of nearly 1.5 V.

Why the other options are incorrect

Option (1) \( \ce{Zn(s) -> Zn^2+ + 2e^-} \) — Incorrect. This is an oxidation; it takes place at the zinc container, the anode of the dry cell.

Option (2) \( \ce{Zn^2+ + 4NH3 -> [Zn(NH3)4]^2+} \) — Incorrect. The ammonia formed at the cathode does combine with Zn²⁺ to give this complex, but no electrons are taken up, so it is not the electrode reaction at the cathode.

Option (3) \( \ce{HgO + H2O + 2e^- -> Hg(l) + 2OH^-} \) — Incorrect. This is the cathode reaction of the mercury cell, whose cathode is a paste of HgO and carbon.

NCERT (2026-27 edition):
2.6.1 Primary Batteries – “…The cell consists of a zinc container that also acts as anode and the cathode is a carbon (graphite) rod surrounded by powdered manganese dioxide and carbon … The space between the electrodes is filled by a moist paste of ammonium chloride (NH₄Cl) and zinc chloride (ZnCl₂). The electrode reactions are complex, but they can be written approximately as follows:

    Anode: Zn(s) → Zn²⁺ + 2e^–

    Cathode: MnO₂ + NH₄⁺ + e^– → MnO(OH) + NH₃

In the reaction at cathode, manganese is reduced from the + 4 oxidation state to the +3 state. Ammonia produced in the reaction forms a complex with Zn²⁺ to give [Zn (NH₃)₄]²⁺. The cell has a potential of nearly 1.5 V.”