Measurement of Electrode Potential

The overall redox reaction inside any electrochemical cell can always be split into two separate half-reactions — an oxidation and a reduction — and correspondingly, the overall cell emf can always be thought of as the sum of two separate electrode potentials, one at each electrode:

But there is a fundamental practical obstacle here: it is genuinely impossible to measure the potential of a single, isolated electrode with a voltmeter — a voltmeter can only ever measure the potential DIFFERENCE between two electrodes, i.e. a complete cell. What is needed, then, is one universally-agreed reference electrode of known (by convention, exactly zero) potential, against which every other electrode can be measured.

That reference is the Standard Hydrogen Electrode (SHE): a platinum electrode in contact with 1 M HCl solution, with hydrogen gas bubbled through at 1 atm pressure and 25°C, assigned an arbitrary but universally-adopted potential of exactly $E^{o} = 0$ V. The SHE can act as either a cathode (reduction: $2\text{H}^+\text{(aq,1M)} + 2e^- \rightarrow \text{H}_2\text{(g,1atm)}$, $E^{o}=0$ V) or an anode (oxidation: $\text{H}_2\text{(g,1atm)} \rightarrow 2\text{H}^+\text{(aq,1M)} + 2e^-$, $E^{o}=0$ V), depending on what it is paired against.

Worked illustration — finding the reduction potential of zinc. A galvanic cell is built pairing zinc against the SHE: $\text{Zn(s)} \mid \text{Zn}^{2+}\text{(aq,1M)}\ \|\ \text{H}^+\text{(aq,1M)} \mid \text{H}_2\text{(g,1atm)} \mid \text{Pt(s)}$. The measured emf of this cell is 0.76 V. Since $E_{cell} = E_{ox}(\text{Zn}\to\text{Zn}^{2+}) + E_{red}(\text{SHE})$, and $E_{red}(\text{SHE}) = 0$ exactly, the entire measured 0.76 V is attributed to zinc's own oxidation potential: $E^{o}_{ox}(\text{Zn}\to\text{Zn}^{2+}) = 0.76$ V. The far more commonly tabulated quantity, zinc's standard REDUCTION potential, is obtained just by reversing the half-reaction and flipping the sign: for $\text{Zn}^{2+} + 2e^- \rightarrow \text{Zn}$, $E^{o}_{red} = -0.76$ V. …