Why Electrochemistry Needs a Reference
At every electrode-electrolyte interface a separation of charge develops. Metal ions from the solution tend to deposit on the metal, while metal atoms tend to dissolve as ions and leave electrons behind. At equilibrium the electrode acquires a definite potential difference with respect to the solution — its electrode potential. When all species in the half-cell are at unit concentration (and gases at 1 bar, 298 K), this becomes the standard electrode potential, $E^\circ$. By IUPAC convention, standard reduction potentials are now simply called standard electrode potentials.
The problem is fundamental: the potential of a single half-cell cannot be measured. Any voltmeter needs two terminals, so any measurement records the difference between two electrode potentials, i.e. the cell emf. As NCERT puts it, we can measure only the difference between two half-cell potentials. The cure is to fix one electrode arbitrarily as a universal zero and quote every other potential relative to it. That fixed reference is the standard hydrogen electrode.
For a galvanic cell written with the anode on the left and the cathode on the right, the cell emf is the right-hand reduction potential minus the left-hand one:
$E_{cell} = E_{right} - E_{left} = E_{cathode} - E_{anode}$
"Absolute" vs "relative" electrode potential
Students often assume each tabulated $E^\circ$ is an absolute, measurable voltage of that one electrode. It is not. Every value in the table is a difference, measured against the SHE benchmark of zero. The table is a ladder of relative numbers, not a set of standalone measurements.
Rule: the potential of a lone half-cell is unmeasurable; only $E_{cell}=E_{cathode}-E_{anode}$ is observable.
Building the Standard Hydrogen Electrode
The standard hydrogen electrode (SHE), also called the normal hydrogen electrode, is represented as $\ce{Pt(s) | H2(g) | H+(aq)}$. NCERT and NIOS describe its construction identically: a platinum electrode coated with platinum black is dipped into an acidic solution, and pure hydrogen gas is bubbled through it. The platinum black is a finely divided coating that adsorbs hydrogen and catalyses the establishment of the half-reaction equilibrium quickly; platinum itself is inert and merely provides a surface for electron exchange.
The electrode reaction, written as a reduction, is:
$\ce{H+(aq) + e- <=> 1/2 H2(g)}$
For the conditions to be "standard", the activities of both the oxidised form ($\ce{H+}$) and the reduced form ($\ce{H2}$) must be unity. In practice this means a hydrogen-ion concentration of 1 M, a hydrogen-gas pressure of 1 bar, and a temperature of 298 K. The SHE can act as anode or cathode depending on the other electrode: paired against a more easily reduced couple it is the anode (oxidation, $\ce{H2 -> 2H+ + 2e-}$); paired against a more easily oxidised metal it is the cathode (reduction).
Why E° of the SHE Is Zero
There is no deep physical reason the hydrogen electrode "should" have zero potential. It is a convention. By assigning $E^\circ_{\ce{H+/H2}} = 0.00\ \text{V}$ at all temperatures, chemists create a fixed origin against which all other half-cells can be calibrated. Hydrogen is chosen because it is reproducible, reversible, and sits conveniently in the middle of the redox range, separating species that are reduced more readily than $\ce{H+}$ from those that are not.
Because the SHE is the left-hand reference half-cell, when it is paired with another half-cell the cell emf collapses directly onto the other electrode's standard potential:
$E^\circ_{cell} = E^\circ_R - E^\circ_L = E^\circ_R - 0 = E^\circ_R$
In other words, the measured emf of the cell is the standard electrode potential of the unknown half-cell. This is the engine that lets a single arbitrary zero generate an entire quantitative table.
Measuring a Standard Electrode Potential
To measure the standard electrode potential of an unknown couple, build a cell with the SHE on one side and the unknown half-cell (all species at unit activity) on the other, then read the emf on a high-resistance voltmeter so that effectively no current flows. NCERT gives two textbook cells.
For copper:
$\ce{Pt(s) | H2(g, 1 bar) | H+(aq, 1 M) || Cu^2+(aq, 1 M) | Cu}$
The measured emf is $+0.34\ \text{V}$, which is therefore $E^\circ$ for $\ce{Cu^2+ + 2e- -> Cu}$. For zinc:
$\ce{Pt(s) | H2(g, 1 bar) | H+(aq, 1 M) || Zn^2+(aq, 1 M) | Zn}$
here the measured value is $-0.76\ \text{V}$, which is $E^\circ$ for $\ce{Zn^2+ + 2e- -> Zn}$. The sign is decided by which way electrons actually flow; if the metal is more easily oxidised than hydrogen, the SHE behaves as the cathode and the metal couple gets a negative value.
Q. The cell $\ce{Pt | H2(1 bar) | H+(1 M) || Zn^2+(1 M) | Zn}$ reads 0.76 V with the zinc electrode as the negative terminal. What is $E^\circ_{\ce{Zn^2+/Zn}}$?
Because zinc is the negative terminal, oxidation occurs there, so zinc is the anode and the SHE is the cathode. Writing the cell with the anode on the left would reverse the convention, so as drawn (SHE left, Zn right) the right-hand couple reduces less readily than hydrogen. The standard electrode potential of the $\ce{Zn^2+/Zn}$ couple is therefore $-0.76\ \text{V}$ — negative, signalling that zinc is more easily oxidised than hydrogen.
What the Sign of E° Means
Once values are tabulated against the SHE, the sign carries direct chemical meaning. NCERT states the interpretation crisply:
If the standard electrode potential of an electrode is greater than zero then its reduced form is more stable compared to hydrogen gas. If the standard electrode potential is negative then hydrogen gas is more stable than the reduced form of the species.
A positive $E^\circ$ (e.g. $\ce{Cu^2+/Cu}$, $+0.34\ \text{V}$) means the oxidised form is reduced more readily than $\ce{H+}$. That is why copper does not dissolve in dilute HCl: $\ce{H+}$ cannot oxidise copper. A negative $E^\circ$ (e.g. $\ce{Zn^2+/Zn}$, $-0.76\ \text{V}$) means hydrogen ions can oxidise the metal — zinc reduces $\ce{H+}$, so zinc dissolves in acid and liberates $\ce{H2}$. NIOS frames the same idea as two summary rules, captured below.
| Sign of E° | Reduced form vs H₂ | Reducing power of couple | Worked consequence |
|---|---|---|---|
E° > 0 | Reduced form more stable than H₂ | Weaker reducing agent than H⁺/H₂ | Cu does not displace H₂ from dilute HCl |
E° < 0 | H₂ more stable than reduced form | Stronger reducing agent than H⁺/H₂ | Zn displaces H₂ from dilute HCl |
The Electrochemical Series
When a large number of standard electrode potentials are arranged in order, the result is the electrochemical series (also called the activity or electrochemical activity series). Conventionally it is listed with the most negative potential at the top and the most positive at the bottom. The table below reproduces representative values from the NCERT Table 2.1 / NIOS Table 13.2 ordering. Reading the trends down the table is the single most examined skill in this subtopic.
| Reduction half-reaction | E° / V | Reading |
|---|---|---|
| $\ce{Li+ + e- -> Li}$ | −3.05 | Strongest reducing agent (Li metal) |
| $\ce{K+ + e- -> K}$ | −2.93 | Very easily oxidised |
| $\ce{Ca^2+ + 2e- -> Ca}$ | −2.87 | |
| $\ce{Mg^2+ + 2e- -> Mg}$ | −2.37 | |
| $\ce{Al^3+ + 3e- -> Al}$ | −1.66 | |
| $\ce{Zn^2+ + 2e- -> Zn}$ | −0.76 | Displaces H₂ from acid |
| $\ce{Fe^2+ + 2e- -> Fe}$ | −0.44 | |
| $\ce{2H+ + 2e- -> H2}$ | 0.00 | Reference (SHE) |
| $\ce{Cu^2+ + 2e- -> Cu}$ | +0.34 | Below H; does not displace H₂ |
| $\ce{Fe^3+ + e- -> Fe^2+}$ | +0.77 | |
| $\ce{Ag+ + e- -> Ag}$ | +0.80 | |
| $\ce{Br2 + 2e- -> 2Br-}$ | +1.07 | |
| $\ce{Cr2O7^2- + 14H+ + 6e- -> 2Cr^3+ + 7H2O}$ | +1.33 | Strong oxidiser |
| $\ce{Cl2 + 2e- -> 2Cl-}$ | +1.36 | |
| $\ce{F2 + 2e- -> 2F-}$ | +2.87 | Strongest oxidising agent (F₂) |
NCERT summarises the directional trend exactly: as we go from top to bottom in the table the standard electrode potential increases, the oxidising power of the species on the left increases, and the reducing power of the species on the right decreases. Fluorine, with the highest $E^\circ$, is the strongest oxidising agent and fluoride is the weakest reducing agent; lithium, with the lowest, is the most powerful reducing agent while $\ce{Li+}$ is the weakest oxidising agent.
These standard potentials power the cell-emf machinery. See how they assemble into a working cell in Galvanic Cells & Electrode Potential.
Applying the Series
The series is examined almost entirely through four predictions. Each reduces to comparing positions or computing $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$ and checking the sign.
1. Predicting spontaneity / feasibility
Split the reaction into a reduction half (cathode) and an oxidation half (anode). Compute $E^\circ_{cell}$. A positive $E^\circ_{cell}$ means the reaction is spontaneous under standard conditions; a negative value means it is non-spontaneous and the reverse runs instead. This works because $\Delta_r G^\circ = -nF E^\circ_{cell}$, so positive emf is negative free-energy change.
Q. Is $\ce{Cu^2+(aq) + 2Ag(s) -> Cu(s) + 2Ag+(aq)}$ feasible? Given $E^\circ_{\ce{Ag+/Ag}}=+0.80\ \text{V}$, $E^\circ_{\ce{Cu^2+/Cu}}=+0.34\ \text{V}$.
Reduction (cathode) is $\ce{Cu^2+ + 2e- -> Cu}$; oxidation (anode) is $\ce{Ag -> Ag+ + e-}$. So $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} = 0.34 - 0.80 = -0.46\ \text{V}$. The negative value means the reaction will not occur — silver cannot displace copper. The reverse reaction (copper displacing silver) is the spontaneous one, consistent with copper lying above silver in the series.
2. Displacement of metals
A metal will displace from solution any metal ion below it in the series, because the higher metal is the stronger reducing agent. Thus the standard ordering of reducing strength for common metals is $\ce{Mg > Al > Zn > Fe > Cu}$. Zinc displaces copper from $\ce{CuSO4}$ ($E^\circ_{cell}=1.10\ \text{V}$), but copper cannot displace zinc.
3. Displacement of hydrogen from acids
Any metal above hydrogen in the series — that is, with a negative $E^\circ$ — is a better reducing agent than hydrogen and liberates $\ce{H2}$ from dilute HCl or $\ce{H2SO4}$. Zinc, magnesium, iron and calcium qualify; copper and silver, sitting below hydrogen with positive potentials, do not.
4. Comparing oxidising and reducing strength
The left-hand species of a low-lying (high $E^\circ$) couple is a strong oxidising agent; the right-hand species of a high-lying (low $E^\circ$) couple is a strong reducing agent. So $\ce{F2}$ is the best oxidant and $\ce{Li}$ the best reductant in aqueous solution. To rank reducing power of metals, simply order them by increasing $E^\circ$ — the lower the potential, the stronger the reducing agent.
Do not flip E° when you reverse a half-reaction in the cell formula
When applying $E^\circ_{cell}=E^\circ_{cathode}-E^\circ_{anode}$, both potentials are taken as reduction potentials straight from the table. You subtract the anode's reduction potential — you do not change its sign first and then add. Reversing a half-reaction's sign and then also subtracting double-counts the inversion and gives the wrong emf.
Rule: read both as reduction potentials, then $E^\circ_{cell}=E^\circ_{cathode}-E^\circ_{anode}$. A positive result = spontaneous.
One subtlety worth holding: standard electrode potential is an intensive property — multiplying a half-reaction by any factor does not change $E^\circ$. The extensive quantity is $\Delta_r G^\circ = -nF E^\circ_{cell}$, which scales with $n$. This distinction is itself a recurring assertion-reason theme in the chapter, and is developed further alongside the concentration dependence in the Nernst Equation.
Lock these in
- A single electrode potential is unmeasurable; only $E_{cell}=E_{cathode}-E_{anode}$ is observable.
- SHE: $\ce{Pt(s)|H2(g, 1 bar)|H+(aq, 1 M)}$ at 298 K, platinised Pt; assigned $E^\circ = 0$ at all temperatures by convention.
- Pairing the SHE with an unknown half-cell gives $E^\circ_{cell}=E^\circ_R$, so the measured emf is the unknown's standard electrode potential.
- $E^\circ > 0$: reduced form more stable than H₂, weaker reductant (Cu won't displace H₂). $E^\circ < 0$: opposite (Zn displaces H₂).
- Down the series: $E^\circ$ increases, oxidising power (left) increases, reducing power (right) decreases. F₂ strongest oxidant, Li strongest reductant.
- Feasibility: positive $E^\circ_{cell}$ = spontaneous; a metal displaces ions of any metal below it; metals above H₂ liberate H₂ from dilute acids.