GATE Electroanalytical Methods — Potentiometry, Voltammetry and Coulometry

By Aniket Bhardwaj · 15 September 2026 · GATE Chemistry

Electroanalytical chemistry is the part of the analytical syllabus where a measured electrical quantity — a potential, a current or a charge — is converted into a concentration. For GATE it is a high-value area because the questions are formula-driven: you are given a potential and asked for a concentration, or given a current and a time and asked for a mass deposited. This guide covers the four families of methods, the equations that connect them, and three worked numericals with every step of the arithmetic shown.

As always, confirm the examinable syllabus from the official GATE notification for your year. Do not take any website's word for the pattern or the marks.

The four families in one view

Family	Measured quantity	Held constant / controlled	Typical technique
Potentiometry	Cell potential at essentially zero current	No net current drawn	pH electrode, ion-selective electrodes, potentiometric titration
Voltammetry	Current as a function of applied potential	Potential is swept	Polarography, cyclic voltammetry, stripping analysis
Amperometry	Current at one fixed potential	Potential fixed	Amperometric titration, Clark oxygen electrode
Coulometry	Total charge passed	Current or potential controlled	Constant-current and controlled-potential coulometry, Karl Fischer

Conductometry — measuring the conductance of a solution — is sometimes grouped here too, but it is not selective for a particular ion, so it is treated separately.

Potentiometry — the Nernst equation is the whole method

E = E° − (2.303 RT / nF) log Q → E = E° − (0.0592/n) log Q at 298 K

E — the measured electrode or cell potential in volts.
E° — the standard potential of the couple, in volts.
n — number of electrons transferred in the half-reaction.
R = 8.314 J K⁻¹ mol⁻¹, F = 96,485 C mol⁻¹, T = absolute temperature in kelvin.
Q — reaction quotient, written with activities (approximated by concentrations in dilute solution).

The number 0.0592 V is only valid at 298 K. It comes from 2.303 × 8.314 × 298 ÷ 96,485. If a question specifies another temperature, you must recompute that factor; at 310 K, for instance, it becomes about 0.0615 V.

An ion-selective electrode responds to one ion with the same logarithmic form. A glass pH electrode gives E = constant + 0.0592 pH at 25 °C, which is why a pH meter must be calibrated with buffers: the "constant" includes the asymmetry potential and the reference junction potential, neither of which you can calculate. Selectivity is described by the Nikolsky–Eisenman selectivity coefficient — a smaller coefficient means less interference from the competing ion.

Worked example 1 — an ion-selective electrode reading

A silver electrode is used as an ISE for Ag⁺. Given E°(Ag⁺/Ag) = +0.799 V and a measured potential of the half-cell against the standard hydrogen electrode, find E when [Ag⁺] = 1.0 × 10⁻⁴ M at 298 K.

Half-reaction: Ag⁺ + e⁻ → Ag, so n = 1.

E = E° + (0.0592/1) log [Ag⁺]
log (1.0 × 10⁻⁴) = −4
0.0592 × (−4) = −0.2368
E = 0.799 − 0.2368 = +0.562 V

Reading the result: the potential falls by 59.2 mV for every ten-fold dilution of a singly charged ion. For a doubly charged ion (n = 2) the same ten-fold change moves the potential by only 29.6 mV. That "slope per decade" is the single most useful number in potentiometry.

Voltammetry — current tells you concentration

In voltammetry the potential is swept and the resulting current is recorded. In classical polarography at a dropping mercury electrode, the diffusion-limited current is given by the Ilkovic equation:

i_d = 708 n D^1/2 m^2/3 t^1/6 C

with i_d in µA, D the diffusion coefficient in cm² s⁻¹, m the mercury flow rate in mg s⁻¹, t the drop time in s and C the concentration in mmol dm⁻³. The essential point for an exam is the proportionality: i_d ∝ C, which is what makes the method quantitative. The potential at which the current is half of its limiting value, the half-wave potential E_1/2, is characteristic of the species and is nearly independent of concentration — so E_1/2 identifies, i_d quantifies.

For cyclic voltammetry at a planar electrode with a freely diffusing species, the peak current at 25 °C follows the Randles–Sevcik equation:

i_p = 2.69 × 10⁵ · n^3/2 · A · D^1/2 · C · v^1/2

where A is the electrode area in cm², C is in mol cm⁻³ and v is the scan rate in V s⁻¹. Two diagnostic tests follow directly and are asked repeatedly:

i_p ∝ v^1/2 — a straight line through the origin when i_p is plotted against √v means the species is diffusing freely in solution. If i_p ∝ v instead, the species is adsorbed on the electrode surface.
ΔE_p = E_pa − E_pc ≈ 59/n mV at 25 °C for an electrochemically reversible couple, together with a peak current ratio i_pa/i_pc ≈ 1 that does not change with scan rate. A ΔE_p much larger than 59/n mV, growing as the scan rate increases, indicates a quasi-reversible or irreversible process.

Worked example 2 — reading a cyclic voltammogram

A one-electron couple gives ΔE_p = 61 mV at 25 °C and i_pa/i_pc = 0.99. The peak current at a scan rate of 25 mV s⁻¹ is 12.0 µA. Predict i_p at 100 mV s⁻¹.

Step 1 — is it reversible? For n = 1 the expected ΔE_p is 59 mV. The observed 61 mV and a current ratio of essentially 1 are consistent with a reversible one-electron transfer, so the Randles–Sevcik proportionality applies.

Step 2 — apply i_p ∝ v^1/2.
i_p2 / i_p1 = √(v₂ / v₁) = √(100 ÷ 25) = √4 = 2
i_p2 = 12.0 × 2 = 24.0 µA

Cross-check: scan rate went up four-fold and the current only doubled. If a candidate answered 48.0 µA, they used i_p ∝ v — the mistake that separates a diffusing species from an adsorbed one.

Coulometry — counting electrons directly

Coulometry is the only electroanalytical method that is absolute: you do not need a calibration curve, because Faraday's laws convert charge into moles exactly.

Q = ∫ i dt (= i × t for constant current) and n(substance) = Q / (nF) so mass = Q M / (nF)

Controlled-potential coulometry holds the working electrode at a potential where only the analyte reacts and integrates the decaying current to exhaustion. Constant-current coulometry generates a titrant electrically — the Karl Fischer determination of water is the best-known industrial example. Current efficiency must be 100% for the result to be valid, which is why the supporting electrolyte and the potential window are chosen so carefully.

Worked example 3 — controlled-potential coulometry

A constant current of 25.0 mA is passed for 5.00 minutes to deposit copper from a solution containing Cu²⁺. Calculate the mass of copper deposited. (M(Cu) = 63.546 g/mol, F = 96,485 C/mol.)

Step 1 — charge.
i = 25.0 mA = 0.0250 A; t = 5.00 min = 300 s
Q = i t = 0.0250 × 300 = 7.50 C

Step 2 — moles of Cu. Cu²⁺ + 2e⁻ → Cu, so n = 2.
moles = Q ÷ (nF) = 7.50 ÷ (2 × 96,485) = 7.50 ÷ 192,970 = 3.887 × 10⁻⁵ mol

Step 3 — mass.
mass = 3.887 × 10⁻⁵ × 63.546 = 2.470 × 10⁻³ g = 2.47 mg

Sanity check: one faraday (96,485 C) would deposit half a mole of copper, about 31.8 g. We passed 7.50 C, which is 7.50/96,485 = 7.773 × 10⁻⁵ faraday, so we expect 7.773 × 10⁻⁵ × 31.773 = 2.470 × 10⁻³ g. The two routes agree.

Standard addition — the method that beats matrix effects

Real samples contain other substances that change the response of an electrode. Standard addition solves this by adding a known amount of analyte to the sample itself, so the matrix is the same in both measurements.

A voltammetric measurement on 25.0 mL of a sample gives a peak current of 0.240 µA. Adding 1.00 mL of 0.0500 M standard raises it to 0.400 µA. Find the original concentration C_x.

Step 1 — write both signals. Signal = k × concentration.
Before: 0.240 = k C_x
After: total volume = 26.0 mL, so the new concentration is (25.0 C_x + 1.00 × 0.0500) ÷ 26.0, and 0.400 = k × that.

Step 2 — divide to remove k.
0.400 ÷ 0.240 = 1.6667
(25.0 C_x + 0.0500) ÷ 26.0 = 1.6667 C_x
25.0 C_x + 0.0500 = 43.333 C_x
0.0500 = 18.333 C_x
C_x = 0.0500 ÷ 18.333 = 2.73 × 10⁻³ M

Check by substitution: after addition the concentration is (25.0 × 2.727 × 10⁻³ + 0.0500) ÷ 26.0 = (0.06818 + 0.0500) ÷ 26.0 = 4.545 × 10⁻³ M, which is 1.667 times the original — exactly the observed signal ratio.

Common mistakes that cost marks

Using 0.0592 at a temperature other than 25 °C. Recompute 2.303RT/F if the question changes T.
Mixing ln and log. The RT/nF form takes ln Q; the 0.0592/n form takes log₁₀ Q. The factor 2.303 is the bridge between them.
Forgetting the sign convention. Write the Nernst equation for the reduction as it is given, and keep Q as products over reactants for that reaction.
Assuming i_p ∝ v in cyclic voltammetry. It is v^1/2 for a diffusing species; linear in v means adsorption.
Treating E_1/2 as concentration-dependent. It identifies the species; the limiting current measures how much there is.
Ignoring current efficiency in coulometry. If the solvent or supporting electrolyte also reacts, the charge you counted did not all go to the analyte, and the answer is wrong however neat the arithmetic.
Forgetting the dilution in standard addition. The added volume changes the total volume; using 25.0 mL instead of 26.0 mL after the spike is the single most common slip in this calculation.

Where these methods appear in GATE preparation

Topic	Typical question style	What to drill
Nernst equation and ISEs	Potential from concentration, or the reverse	The 59.2/n mV per decade rule
Polarography	Identify E_1/2, use i_d ∝ C	What each Ilkovic term controls
Cyclic voltammetry	Reversibility diagnosis, scan-rate dependence	ΔE_p = 59/n mV and i_p ∝ √v
Coulometry	Mass or moles from charge	Faraday's laws; getting n right
Calibration and standard addition	Concentration of an unknown	Dilution bookkeeping; least-squares fitting
Stripping voltammetry	Why it detects trace metals	Pre-concentration step, then stripping scan

Practise the Nernst step until it is automatic. Almost every potentiometry question — and the reversibility criteria in voltammetry — reduces to applying E = E° − (0.0592/n) log Q correctly at the right temperature. The free Nernst Equation calculator lets you enter E°, n, temperature and the concentration terms and returns the cell potential, so you can check a batch of practice problems in a few minutes and see immediately where a sign or a factor went wrong.

Open the Nernst Equation Calculator →

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