Question

The standard cell potential (E°) of a voltaic cell constructed using the cell reaction below is 0.76 V:

Zn(s) + 2H⁺(aq) → Zn²⁺(aq) + H₂(g)

With P_H2= 1.0 atm and [Zn²⁺] = 1.0 mol L^-1, the cell potential is 0.37 V. The concentration of H⁺ in the cathode compartment is ________ mol L^-1.

Answers:

2.6 × 10^-7

5.1 × 10^-4

0.686.6 × 10^-14

4.3 × 10^-27

Answer 1

Zn(s) + 2H⁺ Zn²⁺ + H₂(g)

Number of electrons transferred (n) = 2

[ Zn] = 1

Then

Nernst equation is

E_cell = E^o_cell - log{ [Zn²⁺] P(H₂) / [H⁺] }

0.37 = 0.76 - log (1*1)/[H⁺]²

Or, (0.37 - 0.76) = log [H⁺]²

Or, - 0.39 = 0.0295 log [ H⁺ ]²

^or, log [H⁺]² = (0.39/0.0296)

Or, 2 log [H⁺] = - 13.17

Or, log [H ⁺] = - 6.587

Or, [H⁺] = 10^-6.587 = 2.6 *10^-7 M

Hence, concentration of H⁺ = 2.6*10^-7 mol/L.