# “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?

## 1 Answer

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.
It does not matter what equation you write, since in the final analysis, the number of electrons taken are compensated by the power of the concentration term in the logarithm.