Consider the above electrochemical cell where a metal electrode (M) is undergoing redox reaction by forming M ^ + ( M M ^ + + e ^ - ). The cation M ^ + is present in two different concentrations c_ 1 and c_ 2 as shown above. Which of the following statement is correct for generating a positive cell potential?
C. If c_ 1 is present at cathode, then c_ 1 >c_ 2 .
The given setup is a concentration cell with identical electrodes (M) and different electrolyte concentrations (c_1 and c_2). For a concentration cell, the standard cell potential E^0_ cell = 0. The cell reactions are: Anode: M(s) M^+(c_ anode ) + e^- Cathode: M^+(c_ cathode ) + e^- M(s) Net reaction: M^+(c_ cathode ) M^+(c_ anode ) Using the Nernst equation at 298 K : E_ cell = E^0_ cell - 0.0591 n c_ anode c_ cathode E_ cell = 0 - 0.0591 c_ anode c_ cathode For a positive cell potential (E_ cell > 0), the term c_ anode c_ cathode must be negative. This requires c_ anode c_ cathode c_ anode . If c_1 is present at the cathode and c_2 is at the anode, then for E_ cell > 0, we must have c_1 > c_2. Checking the options: (1) If c_1 is at cathode, c_1 (2) If c_1 is at anode, c_1 > c_2 (Incorrect, would require c_2 > c_1) (3) If c_1 is at cathode, c_1 > c_2 (Correct) (4) If c_1 is at anode, c_1 = c_2 (Incorrect, E_ cell would be zero)
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