General Chemistry Electrochemistry Math Question 9

Question

At 25 C, the standard hydrogen electrode (SHE) has a half-cell potential that is defined to be 0.00 volts. If the pH is increased at this electrode (keeping everything else the same), at what pH will the half-cell potential be equal to -0.462 volts?

Answer 1

2H⁺ + 2e- ==> H₂

Nernst equation:

E = Eº - RT/nF ln K

At 25ºC E = Eº - 0.059/n log K

-0.462 = 0 - 0.059/2 log K

-0.462 = -0.0295 log K

log K = 15.66

K = 4.6x10¹⁵ = 1/[H⁺]²

(4.6x10¹⁵)([H⁺]² = 1

[H⁺] = 1.5x10^-8

pH = -log 1.5x10^-8

pH = 7.83