The potential of hydrogen electrode is a measure of the tendency of hydrogen ions (H+) to gain electrons and form hydrogen gas (H2). The potential of hydrogen electrode is used as a reference point to determine the potential of other electrodes in electrochemical cells.


The potential of hydrogen electrode can be calculated using the Nernst equation:
Eh = E°h − (RT/nF) ln [H+]

Where:
Eh = potential of hydrogen electrode
E°h = standard potential of hydrogen electrode (0 mV)
R = gas constant (8.314 J/mol K)
T = temperature in Kelvin
n = number of electrons transferred in the half-reaction (1 for hydrogen electrode)
F = Faraday constant (96,485 C/mol)
[H+] = concentration of hydrogen ions


Given that the potential of hydrogen electrode (Eh) is -118 mV, we can use the Nernst equation to calculate the concentration of hydrogen ions ([H+]):
-118 mV = 0 mV - (8.314 J/mol K)(298 K)/(1 mol e^-)(96,485 C/mol) ln [H+]
ln [H+] = -118 mV * (1 mol e^-)/(8.314 J/mol K)(298 K)/(96,485 C/mol)
ln [H+] = -0.000145
[H+] = e^-0.000145
[H+] = 0.999855 M

Therefore, the concentration of hydrogen ions is 0.999855 M.


The Nernst equation relates the potential of an electrochemical cell to the concentration of the ions involved in the reaction. In the case of hydrogen electrode, the half-reaction is: 2H+ + 2e^- → H2. The standard potential of hydrogen electrode is 0 mV, which means that at standard conditions (1 M hydrogen ions, 1 atm pressure of hydrogen gas, and 25°C), the potential of the hydrogen electrode is 0 mV. However, in practice, the concentration of hydrogen ions is rarely 1 M, and the temperature and pressure may vary from standard conditions. The Nernst equation allows us to calculate the potential of hydrogen electrode under non-standard conditions, and therefore, to determine the potential of other electrodes in electrochemical cells.