My textbook says that for a metal dipped in a solution of one of its electrolytes, the potential difference between the two at equilibrium is the electrode potential and it depends on the nature of the metal, its ions and the concentration of the ions.
However, for a combination of two half cells, as the reaction proceeds, they don't consider the effect of the salt bridge ions that move into the respective compartments but instead consider only the ions of the metal of which the electrode is made up of in the Nernst equation and say that the cell ultimately reaches an equilibrium at which cell potential becomes zero. Why is that so? I get that the salt bridge ions don't react with the initial electrolyte but they would definitely affect the tendency of the anode metal to oxidize right?
Also, consider a solution of ZnSO4 with a Zn electrode. Why can't we just use ZnSO4 in the salt bridge?
Also, in order to measure the potential of a HALF cell why can't we just use a potentiometer? Even if no displacement of charges can occur, a potentiometer can be used to find the potential difference. Granted, it would of no practical use as we would require a reference to generalize the values but it wouldn't it be incorrect to say we couldn't measure the electrode potential of a half cell?