Electrochemistry — JEE Mains Chemistry Formulas and Traps

Galvanic Cells and Electrode Potentials

Setting up a galvanic cell

Standard cell potential

E^\circ_{cell}=E^\circ_{cathode}-E^\circ_{anode}

$E^\circ_{cathode}$ reduction potential of the couple that is reduced (higher)
$E^\circ_{anode}$ reduction potential of the couple that is oxidised (lower)

The electrochemical series

Couple	E° at 298 K (V)	What it tells you
$\mathrm{Li^+/Li}$	$-3.05$	Li is the strongest reducing agent in water
$\mathrm{Na^+/Na}$	$-2.71$	Na ionises more easily than Li, yet its E° is higher
$\mathrm{Mg^{2+}/Mg}$	$-2.37$	Mg displaces almost every metal ion from water
$\mathrm{Al^{3+}/Al}$	$-1.66$	Al is a strong reducing agent
$\mathrm{Zn^{2+}/Zn}$	$-0.76$	Zn is the anode of the Daniell cell
$\mathrm{Cr^{3+}/Cr}$	$-0.74$	Cr is a reducing agent close to Zn
$\mathrm{Fe^{2+}/Fe}$	$-0.44$	Fe dissolves in dilute acid and gives H₂
$\mathrm{H^+/\tfrac12 H_2}$	$0.00$	The zero of the scale, by definition
$\mathrm{Cu^{2+}/Cu}$	$+0.34$	Cu does not release H₂ from dilute acid
$\mathrm{I_2/I^-}$	$+0.54$	I⁻ is a fairly good reducing agent
$\mathrm{Fe^{3+}/Fe^{2+}}$	$+0.77$	Fe³⁺ oxidises I⁻ to I₂
$\mathrm{Ag^+/Ag}$	$+0.80$	Ag is oxidised by nitric acid
$\mathrm{NO_3^-/NO}$	$+0.97$	Nitrate in acid oxidises Ag but not Au
$\mathrm{Cr_2O_7^{2-}/Cr^{3+}}$	$+1.33$	Dichromate in acid oxidises Ag and Fe²⁺
$\mathrm{Cl_2/Cl^-}$	$+1.36$	Cl₂ oxidises Br⁻ and I⁻
$\mathrm{Au^{3+}/Au}$	$+1.40$	Au resists every common oxidant here
$\mathrm{MnO_4^-/Mn^{2+}}$	$+1.51$	Permanganate in acid oxidises Cl⁻
$\mathrm{F_2/F^-}$	$+2.87$	F₂ is the strongest oxidising agent

Read down the table for stronger oxidising agents (the left-hand species); read up for stronger reducing agents (the right-hand species).

Common traps

Picking the oxidised form as the reducing agent

From

\mathrm{Co^{3+}/Co^{2+}}

the candidate reducing agent is

\mathrm{Co^{2+}}

, not

\mathrm{Co^{3+}}

. Always read the right-hand species of a reduction couple when ranking reducing agents.

Reading the sign backwards

A more negative

E^\circ

means a STRONGER reducing agent, not a weaker one. Lithium, at

-3.05

V, is the strongest of all.

Adding the two potentials

E^\circ_{cell}

is a difference of two reduction potentials. Flipping the anode's sign and then adding gives the same number, but adding the two tabulated values does not.

Scaling E° with the equation

Balancing electrons may double a half-reaction. Its

\Delta G^\circ

doubles; its

E^\circ

does not, because

E^\circ

is intensive.

Nernst Equation and Concentration Effects

Learn this subtopic in the notes

Cell emf from the Nernst equation

Nernst equation at 298 K

E_{cell}=E^\circ_{cell}-\frac{0.059}{n}\log Q

$Q$ reaction quotient: products over reactants, powers from the balanced equation
$n$ electrons transferred in the balanced reaction

Solving the Nernst equation for an unknown

Nernst equation, rearranged

\log Q=\frac{n\left(E^\circ_{cell}-E_{cell}\right)}{0.059}

Electrodes that depend on pH

Hydrogen electrode

E_{H^+/H_2}=-0.059\,\mathrm{pH}-\frac{0.059}{2}\log p_{H_2}

Common traps

Dropping the powers in Q

In

\mathrm{Zn+2Ag^+}

, the silver ion is squared in

Q

. The same balancing that fixes

n

fixes the powers, so do both from one balanced equation.

Q upside down

Q

is products over reactants. Writing it the other way flips the sign of the log term and moves the answer by twice the correction.

Losing the sign of the log

If the measured

E

is ABOVE

E^\circ

,

\log Q

must be negative. Check this before you take the antilog; a sign slip turns 0.01 M into 100 M.

Square root forgotten

When

Q=1/x^2

, the log gives

x^2

. Take the square root at the end.

Electrode potential is not the cell emf

"Potential of the hydrogen electrode" means the single electrode's reduction potential,

-0.059\,\mathrm{pH}

. It is not an

E_{cell}

, and no second electrode is subtracted.

Forgetting the pressure term

A hydrogen electrode at 2 atm or 0.1 bar needs

-0.0295\log p_{H_2}

as well as the pH term.

Gibbs Energy, Equilibrium Constant and Combining Potentials

Learn this subtopic in the notes

Gibbs energy, K and work from E°

Gibbs energy and equilibrium constant

\Delta G^\circ=-nFE^\circ_{cell},\qquad \log K=\frac{nE^\circ_{cell}}{0.059}

Combining electrode potentials

Combining two steps

n_3E^\circ_3=n_1E^\circ_1\pm n_2E^\circ_2

Common traps

Work as charge divided by potential

Electrical work is

Q\times E

, in joules. A statement that puts

E

in the denominator is the incorrect one.

Joules against kilojoules

nFE

comes out in joules. A blank asking for kJ mol⁻¹ needs a division by 1000 first.

Subtracting potentials directly

E^\circ(\mathrm{Fe^{3+}/Fe})-E^\circ(\mathrm{Fe^{2+}/Fe})

is not

E^\circ(\mathrm{Fe^{3+}/Fe^{2+}})

. Weight each potential by its electrons first.

Averaging a Latimer diagram

Two steps of 1 and 2 electrons are not averaged 50:50. Divide the electron-weighted sum by the TOTAL electrons.

Conductivity, Cell Constant and Molar Conductivity

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Cell constant, conductivity and molar conductivity

From resistance to molar conductivity

\kappa=\frac{G^*}{R},\qquad \Lambda_m=\frac{1000\,\kappa}{c}

$G^*$ cell constant l/A (cm⁻¹)
$c$ concentration in mol L⁻¹

What conductance depends on

Ion	λ° at 298 K (S cm² mol⁻¹)	Why
$\mathrm{H^+}$	$349.6$	Proton hopping along hydrogen bonds
$\mathrm{OH^-}$	$199.1$	Proton hopping, in reverse
$\mathrm{SO_4^{2-}}$	$160.0$	Double charge carries twice the current
$\mathrm{Ca^{2+}}$	$119.0$	Double charge
$\mathrm{Mg^{2+}}$	$106.0$	Double charge, but a smaller ion is more hydrated than Ca²⁺
$\mathrm{Br^-}$	$78.1$	Large anion, lightly hydrated
$\mathrm{Cl^-}$	$76.3$	Close to K⁺, which is why KCl is the standard
$\mathrm{K^+}$	$73.5$	Least hydrated of Li⁺, Na⁺, K⁺
$\mathrm{Na^+}$	$50.1$	More hydrated than K⁺
$\mathrm{CH_3COO^-}$	$40.9$	Large, bulky organic anion
$\mathrm{Li^+}$	$38.7$	Smallest bare ion, largest hydrated ion

Values are per mole of the ion as written.

Common traps

Mixing unit systems

The factor 1000 belongs with S cm⁻¹ and mol L⁻¹. In SI, convert

c

to mol m⁻³ (multiply mol L⁻¹ by 1000) and drop the factor.

Resistivity used as conductivity

A resistivity in Ω cm must be inverted to get

\kappa

before anything else.

Bare size against hydrated size

\mathrm{Li^+}

is the smallest bare ion but the slowest in water. What moves is the ion with its shell of water.

κ and Λm move opposite ways

"Conductivity always decreases on dilution" is true. "Molar conductivity decreases on dilution" is false.

Molar Conductivity, Dilution and Kohlrausch's Law

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Strong and weak electrolytes on dilution

Debye–Hückel–Onsager (strong electrolytes)

\Lambda_m=\Lambda_m^\circ-A\sqrt c

Kohlrausch's law of independent migration

Kohlrausch's law

\Lambda_m^\circ=\nu_+\lambda_+^\circ+\nu_-\lambda_-^\circ

Degree of dissociation, Ka and solubility

Degree of dissociation

\alpha=\frac{\Lambda_m}{\Lambda_m^\circ},\qquad K_a=\frac{c\alpha^2}{1-\alpha}

Common traps

Extrapolating a weak electrolyte

Only a strong electrolyte gives a straight line to read

\Lambda_m^\circ

from. For a weak one the curve is nearly vertical near zero, so there is no intercept to read.

Plotting against c instead of √c

The straight line is against

\sqrt c

. Taking the slope from

c

values gives the wrong

A

.

Doubling a divalent salt

\mathrm{MgSO_4}

has one

\mathrm{Mg^{2+}}

and one

\mathrm{SO_4^{2-}}

. Its

\Lambda_m^\circ

is

\lambda_+^\circ+\lambda_-^\circ

, not twice that.

Leaving an ion uncancelled

Write the ions of every salt you add and subtract. The ions left over must be exactly those of the target, with the right counts.

Dropping the 1000

With

\kappa

in S cm⁻¹ and

c

in mol L⁻¹, the 1000 converts litres to cm³. Leave it out and every answer is off by a thousand.

The wrong Ksp expression

K_{sp}=s^2

only for a 1:1 salt. For

\mathrm{A_2X_3}

,

K_{sp}=(2s)^2(3s)^3=108s^5

.

Electrolysis and Faraday's Laws

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Faraday's laws of electrolysis

Faraday's first law

m=\frac{M\,I\,t}{n\,F}

$M$ molar mass of the substance
$n$ electrons needed per particle
$F$ 96500 C per mole of electrons

Products of electrolysis

Electrolyte	Electrodes	Cathode	Anode
Molten NaCl	Inert	Na	$\mathrm{Cl_2}$
Aqueous NaCl (brine)	Inert	$\mathrm{H_2}$ , with $\mathrm{OH^-}$ left in solution	$\mathrm{Cl_2}$
Aqueous $\mathrm{AgNO_3}$	Pt	Ag	$\mathrm{O_2}$
Aqueous $\mathrm{AgNO_3}$	Ag	Ag	Ag dissolves as $\mathrm{Ag^+}$
Aqueous $\mathrm{CuSO_4}$	Pt	Cu	$\mathrm{O_2}$
Aqueous $\mathrm{CuSO_4}$	Cu	Cu	Cu dissolves as $\mathrm{Cu^{2+}}$
Dilute $\mathrm{H_2SO_4}$	Pt	$\mathrm{H_2}$	$\mathrm{O_2}$
Concentrated $\mathrm{H_2SO_4}$	Pt	$\mathrm{H_2}$	$\mathrm{S_2O_8^{2-}}$

An active anode dissolves; an inert anode oxidises an anion or water.

Common traps

Four electrons for oxygen

\mathrm{2H_2O\to O_2+4H^++4e^-}

. One mole of

\mathrm{O_2}

needs 4 F, not 2 F.

Minutes left as minutes

Charge is

I\times t

with

t

in seconds. Convert minutes and hours before multiplying.

The charge on a complex ion's metal

Gold in

\mathrm{AuCl_4^-}

is +3, so each Au atom needs 3 electrons. Read the metal's oxidation state, not the ion's charge.

Depositing sodium from water

Water is reduced long before

\mathrm{Na^+}

or

\mathrm{Mg^{2+}}

. From an aqueous solution the cathode gives

\mathrm{H_2}

, never the metal.

Forgetting an active anode

With silver or copper electrodes, the anode metal dissolves. An option that gives

\mathrm{O_2}

there is wrong.

Batteries, Fuel Cells and Corrosion

Learn this subtopic in the notes

Primary and secondary batteries

Cell	Anode	Cathode	Electrolyte	Type and use
Dry (Leclanché) cell	Zn container	Graphite rod in $\mathrm{MnO_2}$ and carbon	Paste of $\mathrm{NH_4Cl}$ and $\mathrm{ZnCl_2}$	Primary; clocks, transistors, torches
Mercury cell	Zn–Hg amalgam	Paste of HgO and carbon	Paste of KOH and ZnO	Primary; hearing aids, watches; steady voltage
Lead storage battery	Pb	$\mathrm{PbO_2}$ packed on a lead grid	About 38% $\mathrm{H_2SO_4}$	Secondary; cars and inverters
Nickel–cadmium cell	Cd	$\mathrm{Ni(OH)_3}$	KOH	Secondary; long life, rechargeable devices
$\mathrm{H_2}$ – $\mathrm{O_2}$ fuel cell	Porous carbon with $\mathrm{H_2}$ fed in	Porous carbon with $\mathrm{O_2}$ fed in	Concentrated aqueous NaOH or KOH	Continuous feed; Apollo space programme

Primary: used once. Secondary: recharged. Fuel cell: reactants fed in continuously.

Fuel cells and corrosion

Statement	Verdict	Reason
The H₂–O₂ fuel cell was used in the Apollo space programme	True	Its water was drunk by the crew
The H₂–O₂ fuel cell is about 40% efficient	False	About 70%, far above a thermal power plant
Its electrodes use aluminium as a catalyst	False	Finely divided Pt or Pd on porous carbon
Reactants are fed in at one go	False	They are fed in continuously
A fuel cell is a galvanic cell	True	A spontaneous reaction gives electricity
In a methanol fuel cell, methanol is oxidised at the anode	True	The fuel is always the anode's reactant
Rusting is an electrochemical process	True	Anodic and cathodic spots on one piece of iron
Rusting is faster in alkaline water than in acid	False	$\mathrm{H^+}$ drives the cathode reaction; above pH 9 to 10 rusting stops
A tin coat protects iron even after it peels	False	Iron is below tin in the series, so exposed iron corrodes faster
A scratched zinc coat still protects iron	True	Zinc is oxidised first, as a sacrificial anode

Common traps

Renaming the plates on charging

When a lead battery is charged, NCERT still calls the Pb plate the anode and the

\mathrm{PbO_2}

plate the cathode. Keys follow that naming.

Why the mercury cell is steady

Its overall reaction has only solids on both sides. Nothing in solution changes, so the Nernst term never moves.

Oxygen at the anode

In a fuel cell

\mathrm{O_2}

is consumed at the cathode. It is neither formed nor consumed at the anode.

Tin protects like zinc

Tin is a barrier only. Once it breaks, iron is the anode of the tin–iron couple and rusts faster than bare iron.

Electrochemistry formulas

Galvanic Cells and Electrode Potentials

Setting up a galvanic cell

The electrochemical series

Common traps

Nernst Equation and Concentration Effects

Cell emf from the Nernst equation

Solving the Nernst equation for an unknown

Electrodes that depend on pH

Common traps

Gibbs Energy, Equilibrium Constant and Combining Potentials

Gibbs energy, K and work from E°

Combining electrode potentials

Common traps

Conductivity, Cell Constant and Molar Conductivity

Cell constant, conductivity and molar conductivity

What conductance depends on

Common traps

Molar Conductivity, Dilution and Kohlrausch's Law

Strong and weak electrolytes on dilution

Kohlrausch's law of independent migration

Degree of dissociation, Ka and solubility

Common traps

Electrolysis and Faraday's Laws

Faraday's laws of electrolysis

Products of electrolysis

Common traps

Batteries, Fuel Cells and Corrosion

Primary and secondary batteries

Fuel cells and corrosion

Common traps

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