A hydrogen gas electrode is made by dipping platinum wire in a solution of HCl of pH = 4 and passing hydrogen gas around the platinum wire at one atm pressure and at 298 K. The reduction potential of the hydrogen electrode would be

Solution:

The reduction half-reaction for a hydrogen electrode is:

2H⁺(aq) + 2e⁻ → H₂(g)

The Nernst equation for this reaction at 298 K is:

E_red = E°_red - (0.059 / n) * log([P_H₂] / [H⁺]²)

Given:

pH = 4, which means [H⁺] = 10⁻⁴ M

P_H₂ = 1 atm

n = 2 (number of electrons transferred)

E°_red (Standard Hydrogen Electrode) = 0.00 V

Substitute the values into the Nernst equation:

E_red = 0.00 - (0.059 / 2) * log(1 / (10⁻⁴)²)

E_red = 0.00 - (0.0295) * log(1 / 10⁻⁸)

E_red = 0.00 - (0.0295) * log(10⁸)

E_red = 0.00 - (0.0295) * 8

E_red = 0.00 - 0.236

E_red = -0.236 V

Thus, the reduction potential of the hydrogen electrode would be -0.236 V.