Answer:

Why can't electrons go to the positive terminal trough the battery but instead have to go around via a conductive wire?

Why can't electrons go to the positive terminal trough the battery but instead have to go around via a conductive wire?

The simple answer to this is that there’s no electron conductor between the terminals inside the battery and so nothing to carry electrons between the terminals. However I think this misses the point, because what’s significant in electric current is flow of charge, not necessarily charge carried by electrons.

So a more comprehensive answer is that charge cannot flow through the battery to discharge it because instead the battery is pumping charge in the opposite direction, against the voltage difference between the terminals. This is the very principle by which a battery works. It’s analogous to lifting mass from a low height to a high height, where that mass can then fall back down through the external circuit to deliver energy to that circuit. But instead of mass we have charge, and instead of height we have the electric potential of each terminal. The battery forces the charge to go from low potential to high potential by arranging for the charge carriers to be attracted to the high potential terminal, using a chemical attraction between these charge carriers and a material coating this terminal.

In practice the charge carriers between the terminals inside the battery are ions rather than electrons. An example is positively charged Lithium ions in Lithium ion batteries. The material between the terminals is a Lithium ion conductor which conducts current using free Lithium ions and not free electrons. The Lithium ions are attracted “uphill” to the positive terminal by an oxidising compound on the positive terminal with which the Lithium ions react. In other words the battery is converting the energy released by this reaction into electrical energy, by the reaction pumping the charge on the ions “uphill” to the higher potential terminal.