Question

What is E_cell (in volts) for a concentration cell at 25.0°C based off the redox reactions of X_(s) / X²⁺ _(aq) with the following conditions? Express your answer to 3 decimal places.

At both the anode and cathode the metal X is dipped in solutions containing X²⁺.

[X²⁺] (at the cathode) = 1.857 mol L^-1

[X²⁺] (at the anode) = 0.004 mol L^-1

Answer 1

For concentration cell, cathode and anode are same electrode

So, Eo = 0

Number of electron being transferred in balanced reaction is 2

So, n = 2

If E is positive anode will be the one with lower concentration

use:

E = Eo - (2.303*RT/nF) log {[X2+] at anode/[X2+]at cathode}

Here:

2.303*R*T/F

= 2.303*8.314*298.0/96500

= 0.0591

So, above expression becomes:

E = Eo - (0.0591/n) log {[X2+] at anode/[X2+]at cathode}

E = 0 - (0.0591/2) log (0.004/1.857)

E = 7.884*10^-2 V

Answer: 0.0788 V