Gas Electrode Working
Standard Hydrogen Electrode

A SHE consists of four parts: a platinum lead wire, a platinum foil contact, an acid solution, and a hydrogen gas flow. The word standard refers to the fact that all concentrations and pressures are at standard state, thus the acid is 1M and the gas flow is 1 atm. At these conditions, the electrode has a potential of 0 V (this is how potential is defined). If there are any deviations from these values, the electrode is no longer considered a SHE. The potential can then be calculated using the Nernst equation.

The electrode is one half of an electrochemical circuit. The other half cell determines whether the SHE will behave as the cathode or the anode. If it is the anode, the electron flow comes from the external system to the platinum contact. 2 electrons reduce 2 acidic hydrogens from the solution to form one molecule of hydrogen, as in $2H^+ + 2e^- → H_2$. The molecular hydrogen then bubbles up above the solution. If the electrode is cathodic, hydrogen gas is absorbed on the platinum contact plate and oxidized to two acidic hydrogens which remain in solution. The electrons then flow to the external circuit. Electrons do not flow from hydrogen gas to the acid, or vice versa.

Reaction Quotient

The reaction quotient is indeed unitless. While it is common to use concentrations and pressures to calculate Q, it is more properly calculated by using activity of each species, which are also unitless. The activity is the apparent concentration or pressure of a species (can be viewed as a correction to concentration or pressure). Because in most chemical applications activity is very close numerically to concentration, using concentrations or pressures directly for calculations is a close approximation.