I read that the electrolytic refining of Silver is done using dilute Silver Nitratesilver nitrate as an electrolyte and a small percentage of free HNO3 $\ce{HNO3}$. The following reactions are possible at the anode:
$\ce{Ag ->Ag+ + e-}$
$\ce{ OH- -> 1/4O2 + 1/2H2O + e-}$$$\ce{Ag ->Ag+ + e-}$$ $$\ce{ OH- -> 1/4O2 + 1/2H2O + e-}$$
But the second reaction has $E^\circ = \pu{+0.4V}$ while the first reaction has $E^\circ = \pu{+0.8V}$. So why does Ag$\ce{Ag}$ of the anode get oxidised? Is it because of a low concentration of $\ce{OH-}$ ions due to poor dissociation? Or is there another reason?