Which of the following reactions does a common alkaline battery, such as those used in portable tape players (think 1990s), utilize?

Zn(s) + MgO(s) → ZnO(s) + Mg(s)
ZnO(s) + Mg(s) → Zn(s) + MgO(s)
2 Zn(s) + 2 MnO₂(s) → 2 ZnO(s) + Mn₂O₃(s)
Zn(s) + HgO(s) → Hg(l) + ZnO(s)

To determine which reaction a common alkaline battery utilizes, such as those used in portable tape players, we need to understand how an alkaline battery works.

Alkaline batteries are a type of primary battery that uses a reaction between zinc and manganese dioxide. The anode (negative electrode) of the battery is made of zinc metal, while the cathode (positive electrode) is made of manganese dioxide mixed with an alkaline electrolyte, usually a potassium hydroxide (KOH) solution.

Based on the given options, the reaction that represents the operation of a common alkaline battery is:

2 Zn(s) + 2 MnO₂(s) → 2 ZnO(s) + Mn₂O₃(s)

In this reaction, zinc (Zn) is oxidized at the anode, releasing two electrons. Meanwhile, the manganese dioxide (MnO₂) at the cathode accepts the electrons, causing a reduction reaction. The overall chemical reaction produces zinc oxide (ZnO) and manganese (III) oxide (Mn₂O₃).

It's important to note that the other provided reactions do not accurately represent the reaction occurring in an alkaline battery.