In prokaryotes, where is the respiratory electron transport chain located?

In the cellular membrane.

In eukaryotes the electron transport chain (ETC) is situated in the mitochondiral membrane. Prokaryotes do not have organelles such as mitochondria, but they do have an ETC.

A membrane is required for the ETC to work, otherwise it would not be possible to build a gradient of hydrogen atoms. The only membrane in prokaryotes is the cellular membrane, that is where the ETC is located.

On the top left corner the location of the ETC in prokaryotes, on the top right corner the situation in eukaryotes