Cell Potential question

Question

The standard electrode potential for Aluminum is found in Appendix 13 of the e-book (page 1107). Find the potential if the concentration of the ions in the solution is 0.546 M and the temperature is 12.7^oC. 

Answer 1

Assuming the question is related to the Standard Hydrogen Electrode (SHE), and that the conditions at the SHE remain constant, then we have ...

Al³⁺ + 3e- ==> Al(s) Eº = -1.66 V

2H⁺ + 2e- ==> H₂(g) Eº = 0

2Al(s) + 6H⁺(aq) ==> 2Al³⁺(aq) + 3H₂(g) overall reaction

Eº_cell = +1.66 V

Use the Nernst Equation:

E_cell = Eº_cell - RT/nF ln Q

Eº_cell = 1.66

R = 8.314 J/mol-K

T = temperature in K = 12.7C + 273.15 = 285.85K

Q = [Al³⁺]² / [H⁺]⁶

n = 6 mols electrons

F = Faraday constant = 96,500

E_cell = 1.66 - (8.314)(285.85) / (6)(96500) ln (0.546)²/(1.0)⁶

E_cell = 1.66 - 0.00410 ln 0.298

E_cell = 1.66 - 0.00410 x 1.347

E_cell = 1.66 - 0.0055

E_cell = 1.65 V

(be sure to check the math)