Electrochemistry — MHT-CET Chemistry Formulas and Traps

Cell Constant and Conductivity Measurements

Conductance, Conductivity and Their Units

Conductivity

\kappa = \frac{1}{\rho} = G\cdot\frac{l}{a} = \frac{1}{R}\cdot\frac{l}{a}

Cell Constant: l/a = κ × R

Cell constant

\frac{l}{a} = \kappa \times R

Conductivity From the Cell Constant and Resistance

Conductivity of the unknown

\kappa = \frac{\text{cell constant}}{R}

Common traps

Reading S cm² mol⁻¹ as the unit of conductivity

That is MOLAR conductivity. Conductivity is S cm⁻¹ (or S m⁻¹). The options always offer both; the one with mol⁻¹ in it belongs to Λ.

Dividing when the cell constant is asked

\kappa = (l/a)/R

, so

l/a = \kappa R

: MULTIPLY. Dividing gives

\kappa/R

, a number four orders too small — and it is offered as an option.

Trusting a printed exponent over the order of magnitude

One 2023 paper printed κ of 0.1 M KCl as

1.90 \times 10^{-6}

and keyed a cell constant of 218.5 cm⁻¹; the working needs κ = 1.90. When the arithmetic lands on no option, match the mantissa and let the sanity range decide the exponent.

Molar Conductivity, Kohlrausch's Law and Degree of Dissociation

Learn this subtopic in the notes

Molar Conductivity: Λ = 1000κ/c and Back

Molar conductivity

\Lambda = \frac{1000\,\kappa}{c},\qquad \kappa = \frac{\Lambda\,c}{1000}

Kohlrausch's Law: Λ₀ From the Ions

Kohlrausch's law

\Lambda_0 = \nu_+\,\lambda_+^0 + \nu_-\,\lambda_-^0

Degree of Dissociation: α = Λ/Λ₀

Degree of dissociation

\alpha = \frac{\Lambda_c}{\Lambda_0}

Common traps

Dropping the 1000

\kappa/c

with c in mol L⁻¹ is a thousand times too small. The factor converts litres to cm³ because κ is per cm. Options are set one factor of 1000 apart to catch exactly this.

Adding all three values

The third electrolyte supplies the ions you must REMOVE, so it is subtracted. 4.2 + 1.1 + 1.5 = 6.8 is nowhere near an option; 4.2 + 1.1 − 1.5 = 3.8 is the key.

Inverting the ratio

α is the SMALL number over the big one and must come out below 1. Λ₀/Λ_c gives 23.7 for acetic acid — no option, but a sign the fraction is upside down.

Faraday's Laws of Electrolysis

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What Forms at Each Electrode: Molten Versus Aqueous NaCl

Electrode reactions

\text{cathode: } M^{n+} + n e^- \to M;\qquad \text{anode: } 2X^- \to X_2 + 2e^-

Faraday's First Law: W = ItM/nF

Faraday's first law

W = \frac{I\,t\,M}{n\,F},\qquad Q = I\,t,\qquad F = 96500\ \text{C mol}^{-1}

Charge for a Redox Change, and Cells in Series

Charge for n electrons; series cells

Q = \text{mol} \times n \times F,\qquad \frac{W_1}{W_2} = \frac{M_1/n_1}{M_2/n_2}

Common traps

Sodium at the cathode from BRINE

Water is reduced before Na⁺ is. Aqueous NaCl gives H₂ (and OH⁻) at the cathode; only the MOLTEN salt gives sodium metal.

Using n = 1 for a divalent metal

Cu²⁺, Mg²⁺, Ca²⁺, Zn²⁺ each take TWO electrons, so a given charge deposits half a mole per faraday. The n = 1 answer (double the true mass) is always among the options.

n = 3 for dichromate

Each Cr goes +6 → +3, but Cr₂O₇²⁻ carries TWO chromiums: n = 6 per formula unit. Half the correct charge is always an option.

Galvanic Cells, EMF, Nernst Equation and Thermodynamics

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Reading a Cell: Anode Left, Cathode Right

Cell notation

\text{anode (–)}\ \big|\ \text{anode ion}\ \big\|\ \text{cathode ion}\ \big|\ \text{cathode (+)}

E°cell = E°cathode − E°anode

Standard emf

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

The Electrochemical Series: Who Reduces, Who Oxidises, Who Deposits

Spontaneity test

E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} > 0 \iff \text{spontaneous}

The Nernst Equation: E = E° − (0.0592/n) log Q

Nernst equation (298 K)

E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0592}{n}\log_{10} Q

Potential of One Electrode at a Given Concentration

Oxidation electrode potential

E_{\text{ox}} = -E^\circ_{\text{red}} - \frac{0.0592}{n}\log[\text{M}^{n+}]

ΔG° = −nFE° and the Bridge to K

Gibbs energy and K

\Delta G^\circ = -nFE^\circ,\qquad E^\circ = \frac{0.0592}{n}\log_{10} K

Common traps

Anode = positive

That is true in an ELECTROLYTIC cell only. In a galvanic cell electrons leave the anode, so it is negative; the cathode, where they arrive, is positive.

Adding the two potentials

E^\circ_{\text{anode}} + E^\circ_{\text{cathode}}

is offered as a 'relation' and as a number. Reduction potentials are SUBTRACTED; for Zn/Cd that gives 0.36 V, not −1.17 V.

Picking F⁻ as the strongest oxidising agent

F⁻ is already reduced — it can only be oxidised. The oxidising agent is the species that GETS reduced: F₂. Likewise Li (the metal), not Li⁺, is the reducing agent.

Forgetting the square on [Ag⁺]

Two Ag⁺ per Zn, so Q carries

[\text{Ag}^+]^2

. Dropping Ag⁺ to 0.1 M multiplies Q by 100, a two-decade shift of 0.0592 V — twice the 0.0296 V that dropping Zn²⁺ gives.

Doubling E° when the equation is doubled

Electrode potential is intensive — it does not scale with the amount. 2Zn → 2Zn²⁺ + 4e⁻ is still +0.76 V; +1.52 V and −1.52 V are the planted options.

Losing the minus sign

E^\circ = \Delta G^\circ/nF

without the minus is the planted FALSE relation, and −ΔG° written as ΔG° flips the sign of a spontaneous cell's 'work'. A positive E° always goes with a negative ΔG°.

Batteries, Primary, Secondary and Fuel Cells

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The Hydrogen–Oxygen Fuel Cell

Fuel cell net reaction

2\text{H}_2(g) + \text{O}_2(g) \to 2\text{H}_2\text{O}(l),\qquad E^\circ = 1.23\ \text{V}

Dry Cell, Lead Accumulator and Nickel–Cadmium Cell

Cell	Type	Anode (−)	Cathode (+)	Note
Dry cell	Primary	Zn → Zn²⁺ + 2e⁻	MnO₂ → Mn₂O₃ (reduced); NH₄⁺ → NH₃ + H₂	1.5 V; n = 2
Mercury cell	Primary	Zn(Hg) → Zn²⁺	HgO → Hg	1.35 V, steady PRIMARY — the 2022 paper's key called only the dry cell primary; the textbook counts the mercury cell too.
Lead accumulator (discharge)	Secondary	Pb → PbSO₄	PbO₂ → PbSO₄	H₂SO₄ consumed, water formed
Lead accumulator (recharge)	Secondary	PbSO₄ → Pb (reduced)	PbSO₄ → PbO₂ (oxidised)	Electrolysis: an external source drives it On recharge the POSITIVE plate is oxidised — the reverse of normal cathode behaviour.
Ni–Cd	Secondary	Cd → Cd(OH)₂	NiO(OH) → Ni(OH)₂	KOH electrolyte

Discharge is galvanic (spontaneous); recharge is electrolytic (driven).

Common traps

Swapping discharge and recharge at the positive plate

On DISCHARGE the positive plate reduces PbO₂ → PbSO₄. On RECHARGE the same plate oxidises PbSO₄ → PbO₂. The paper asks for one and offers the other.

Calling H₂ the oxidising agent because it 'burns'

Burning IS oxidation — of the hydrogen. The species that is oxidised is the reducing agent. H₂ reduces; O₂ oxidises.

Electrochemistry formulas

Cell Constant and Conductivity Measurements

Conductance, Conductivity and Their Units

Cell Constant: l/a = κ × R

Conductivity From the Cell Constant and Resistance

Common traps

Molar Conductivity, Kohlrausch's Law and Degree of Dissociation

Molar Conductivity: Λ = 1000κ/c and Back

Kohlrausch's Law: Λ₀ From the Ions

Degree of Dissociation: α = Λ/Λ₀

Common traps

Faraday's Laws of Electrolysis

What Forms at Each Electrode: Molten Versus Aqueous NaCl

Faraday's First Law: W = ItM/nF

Charge for a Redox Change, and Cells in Series

Common traps

Galvanic Cells, EMF, Nernst Equation and Thermodynamics

Reading a Cell: Anode Left, Cathode Right

E°cell = E°cathode − E°anode

The Electrochemical Series: Who Reduces, Who Oxidises, Who Deposits

The Nernst Equation: E = E° − (0.0592/n) log Q

Potential of One Electrode at a Given Concentration

ΔG° = −nFE° and the Bridge to K

Common traps

Batteries, Primary, Secondary and Fuel Cells

The Hydrogen–Oxygen Fuel Cell

Dry Cell, Lead Accumulator and Nickel–Cadmium Cell

Common traps

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