To find the standard potential of M 3 + / M electrode, the following cell is constituted: Pt / M / M 3 + 0 .001 mol L - 1 / Ag + 0 .01 mol L - 1 / Ag The emf of the cell is found to be 0 . 421 volt at 298 K . The standard potential of half-reaction M 3 + + 3 e - → M at 298 K will be: (Given: E Ag + Ag ⊝ at 298 K = 0 . 80 volt )

Step-by-step solution

E cell = E o cell − 0 . 0591 n logQ ∴   Q = M 3 + Ag + 3   = 0 .001 ( 0 .01 ) 3 = 10 3 E cell = E o cell − 0 . 0591 3 log 10 3 E cell = E o cell − 0 . 0591 3 × 3 = 0 .421 E o cell − 0 .0591 = 0 . 421 E o cell = 0 . 48   V   = E o Ag + / Ag - E o M 3 + / M E o M 3 + / M = 0 . 80 - 0 . 48   =   0 . 32   V