# “Number of moles of electrons involved in the reaction” for hydrogen cell

I understand we can calculate the maximum work done by the electromotive force (driving electrons through a cell) by multiplying the potential of the cell with the charge of one mole of electrons (Faraday's constant) and with "the number of moles of electrons involved in the reaction". I thought that in the case of a hydrogen cell: the reaction $\ce{H2 - 2e- -> 2H+}$ involves two electrons but I can see on wikipedia that in the Nernst equation for the standard hydrogen electrode $z$ (the number of moles involved) is considered to be 1.

So what does this $z$, or expression "electrons involved" actually mean?

Nernst equation is used for finding the cell potential when the various reactants, i.e. anodic and cathodic electrolytes are not in their standard states ($298\text{K}, 1\text{mol l}^{-1}$). Thus, in such cases, you first write down any balanced form of equation, which for our hydrogen electrode, I choose to write down $\ce{3H2 -> 6H+ +6e-}$ and these electrons are used in a standard $\ce{H2}$ cell on the other electrode. Hence the Nernst equation would give the cell potential for this concentration cell as ($E^\circ=0$ since the the standard potentials of both sides is the same since the materials are same, and the non-standard hydrogen cell is the anode) $$E_{cell}=-\frac{RT}{6F}\ln\frac{[H^+]^6}{1}$$ By using the properties of logarithm, you can show this is equivalent to $-\frac{RT}{1F}\ln[H^+]^1$, and this is the equation if you took only 1 electron transfer in the reaction.