The pressure of H2 required to make the potential of H2-electrode zero in pure water at 298 K is:

2H⁺ + 2e⁻ → H₂
E = E⁰ - 0.0592/n log PH₂/[H⁺]²
In 1.0 M hydrogen ion solution with hydrogen pressure of 1 atm, E = 0
E = 0 - 0.0592/2 log 1/1²
E = 0 - 0.0592/2 log 1 = 0 - 0 = 0
In pure water, the hydrogen ion concentration is 10⁻⁷M, with hydrogen pressure of P atm,
E = E⁰ - 0.0592/n log PH₂/[H⁺]²
0 = 0 - 0.0592/2 log P/(10⁻⁷)²
0 = log P/(10⁻⁷)²
1 = P/(10⁻⁷)²
P = 10⁻¹⁴ atm