For 1 mole of H2 (g) produced, how many moles of electrons are transferred in the electrolysis of water?

In the electrolysis of water, it breaks down into oxygen and hydrogen. The well-balanced chemical equation for this reaction can be written as:

`2H_2O (l) -> 2H_2 (g) + O_2 (g)`

Using stoichiometry, 2 moles of water produces 2 moles of hydrogen gas and 1 mole of oxygen gas. 

This reaction takes place in an electrolytic cell. 

Hydrogen has an oxidation state of +1 in water and after electrolysis, it attains an oxidation state of 0, that is, it gains an electron. The half-cell reaction for hydrogen reduction can be written as:

`2H^+ + 2e^(-) -> H_2`

That is, 2 electrons are transferred for making 1 molecules of hydrogen gas, from protons. In other words, 2 moles of electrons are transferred for making 1 mole of hydrogen gas. 

These electrons are donated by oxygen during its oxidation, as per the following reaction:

`H_2O -> 1/2 O_2 + 2H^(+) + 2e^-`

Adding the two half reactions together, we get:

`H_2O -> 1/2 O_2 + H_2`

which is the same as the equation for electrolysis of water. 

Thus, 2 moles of electrons are transferred from oxygen to hydrogen for each mole of hydrogen gas produced.

Hope this helps.