General Chemistry Electrochemistry Math Question 4

Question

A standard hydrogen electrode has a half-cell reduction potential of zero at 25 C. Calculate the potential of the half-cell when the pH is 7.5 and the pressure of H₂ is 4.7 bar.

Answer 1

2H⁺ + 2e- ==> H₂

pH = 7.5 therefore [H⁺] = 1x10^-7.5 = 3.16x10^-8 M

K = P_H2 / [H⁺]² = 4.6 atm / (3.16x10^-8)² = 4.6x10¹⁵ (changed 4.7 bar to 4.6 atm)

Nernst equation:

E = Eº - RT/nF ln K and @ 25º we have

E = Eº - 0.059/n log K = 0 - 0.059/2 log 4.6x10¹⁵

E = -0.0295 x -15.6

E = 0.46 V