A concentration cell is constructed using two silver electrodes at 298 K . The anode compartment contains a saturated aqueous solution of AgCl , while the cathode compartment contains a 0.1 M aqueous solution of AgNO ₃ . The cell potential is measured to be 0.24 V . If the solubility product ( K_ sp ) of AgCl at this temperature is 10^ -x , the value of x is _______. (Given: 2.303RT F = 0.06 V )

Step-by-step solution

For a concentration cell, both electrodes are made of the same material, so the standard cell potential E^ _ cell = 0 V . The half-cell reactions are: Anode: Ag ( s ) Ag ^+( anode ) + e ^- Cathode: Ag ^+( cathode ) + e ^- Ag ( s ) Overall: Ag ^+( cathode ) Ag ^+( anode ) The number of electrons transferred, n = 1 . Using the Nernst equation: E_ cell = E^ _ cell - 0.06 1 [ Ag ^+]_ anode [ Ag ^+]_ cathode Substitute the given values: 0.24 = 0 - 0.06 [ Ag ^+]_ anode 0.1 [ Ag ^+]_ anode 0.1 = - 0.24 0.06 = -4 [ Ag ^+]_