Chemistry · Physical Chemistry

Electrochemistry formulas for JEE

Every Electrochemistry formula you need for JEE, grouped by concept.

FormulasRevision notes
26 formulas3 concepts
01Electrolytic Conductance02Electrochemical and Electrolytic Cells03Nernst Equation and Applications
01

Electrolytic Conductance

14 formulas

Conductivity (Specific Conductance)

κ=1ρ=1RlA=G∗R\kappa = \frac{1}{\rho} = \frac{1}{R} \frac{l}{A} = \frac{G^*}{R}

Inverse of resistivity, representing the conductance of a unit volume.

conductivitykappa

Kohlrausch's Law

Λm∘=ν+λ+∘+ν−λ−∘\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ

Limiting molar conductivity as the sum of independent ionic contributions.

applies whenAt infinite dilution (c approaches 0).
kohlrauschinfinite-dilution

Molar Conductivity (General)

Λm=κc\Lambda_m = \frac{\kappa}{c}

Conducting power of all ions produced by dissolving one mole of electrolyte.

applies whenUnits of volume must align with the concentration term.
molar-conductivityconcentration

Cell Constant

G∗=lA=RκG^* = \frac{l}{A} = R \kappa

A fixed geometric ratio for a specific conductivity cell.

applies whenRemains constant for a given physical conductivity cell.
cell-constantconductivity

Conductance

G=1R=Aρl=κAlG = \frac{1}{R} = \frac{A}{\rho l} = \kappa \frac{A}{l}

The ease with which current flows, defined as the inverse of resistance.

conductanceresistance

Variation of Molar Conductivity

Λm=Λm∘−Ac\Lambda_m = \Lambda_m^\circ - A \sqrt{c}

Linear decrease of molar conductivity with square root of concentration for strong electrolytes.

applies whenApplies strictly to strong electrolytes at low concentrations.
debye-huckel-onsagerstrong-electrolyte

Degree of Dissociation

α=ΛmΛm∘\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}

Approximation of dissociation extent using conductance data.

applies whenPrimarily for weak electrolytes.
dissociationweak-electrolyte

Ionic Mobility

μ=λ∘F\mu = \frac{\lambda^\circ}{F}

The velocity of an ion per unit electric field, related to ionic conductivity.

ionic-mobilityvelocityjee-advanced

Dissociation Constant via Conductance

Ka=cα21−α=cΛm2Λm∘(Λm∘−Λm)K_a = \frac{c \alpha^2}{1-\alpha} = \frac{c \Lambda_m^2}{\Lambda_m^\circ (\Lambda_m^\circ - \Lambda_m)}

Calculates K_a of a weak acid from molar conductivities.

applies whenWeak electrolytes forming 1:1 ions (like CH3COOH).
equilibrium-constantweak-acidostwald

Molar Conductivity (cm based)

Λm=κ×1000M\Lambda_m = \frac{\kappa \times 1000}{M}

Practical conversion formula yielding S cm^2 mol^-1.

applies whenk must be in S cm^-1 and M in mol L^-1.
molar-conductivityconversion

Molar Conductivity (m based)

Λm=κ1000×M\Lambda_m = \frac{\kappa}{1000 \times M}

Practical conversion formula yielding S m^2 mol^-1.

applies whenk must be in S m^-1 and M in mol L^-1.
molar-conductivityconversionsi-units

Electrical Resistance

R=ρlAR = \rho \frac{l}{A}

Resistance of an object or electrolytic solution column.

resistanceresistivityconductance

Transport Number

t+=λ+∘Λm∘=λ+∘λ+∘+λ−∘t_+ = \frac{\lambda_+^\circ}{\Lambda_m^\circ} = \frac{\lambda_+^\circ}{\lambda_+^\circ + \lambda_-^\circ}

The fraction of total current carried by a specific ion.

applies whenAt infinite dilution.
transport-numbertransferencejee-advanced

Wheatstone Bridge Unknown Resistance

R2=R1R4R3R_2 = \frac{R_1 R_4}{R_3}

Equation to calculate unknown resistance of an electrolyte using a balanced AC Wheatstone bridge.

applies whenBridge must be balanced (no current in detector).
wheatstoneresistancemeasurement
02

Electrochemical and Electrolytic Cells

4 formulas

Cell Potential

Ecell=Eright−Eleft=Ecathode−EanodeE_{cell} = E_{right} - E_{left} = E_{cathode} - E_{anode}

Standard convention for determining the EMF of a cell from half-cell potentials.

applies whenRight is cathode (reduction), left is anode (oxidation).
cellpotentialemf

Total Electric Charge

Q=I×tQ = I \times t

Charge passed through an electrolytic cell over time.

applies whenConstant current. Q in Coulombs, I in Amperes, t in seconds.
chargecurrentelectrolysis

Faraday's First Law

m=M×I×tn×Fm = \frac{M \times I \times t}{n \times F}

Mass of substance deposited or liberated at an electrode.

applies whenM = molar mass, n = valency factor/electrons exchanged.
faradayelectrolysismass

Faraday's Second Law

w1E1=w2E2\frac{w_1}{E_1} = \frac{w_2}{E_2}

Relates the mass of different substances deposited by the same charge to their equivalent weights.

applies whenSame charge passed through multiple cells in series.
faradayequivalent-weightjee-advanced
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03

Nernst Equation and Applications

8 formulas

Gibbs Energy and Cell EMF

ΔrG=−nFEcell\Delta_r G = -nF E_{cell}

Calculates the reversible electrical work or change in Gibbs free energy for a non-standard cell.

applies whenConstant temperature and pressure.
gibbsemfwork

Nernst Equation (General)

Ecell=Ecell∘−RTnFln⁡Q=Ecell∘−RTnFln⁡[C]c[D]d[A]a[B]bE_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q = E^\circ_{cell} - \frac{RT}{nF} \ln \frac{[C]^c [D]^d}{[A]^a [B]^b}

Calculates the EMF of a cell at any concentration or partial pressure.

applies whenNon-standard conditions. Pure solids and liquids are taken as unity.
nernstemfthermodynamics

Standard Gibbs Energy

ΔrG∘=−nFEcell∘=−RTln⁡Kc\Delta_r G^\circ = -nF E^\circ_{cell} = -RT \ln K_c

Relates standard Gibbs free energy to standard cell potential and equilibrium constant.

applies whenStandard conditions (1 M, 1 bar).
gibbsemfstandardequilibrium

Equilibrium Constant from EMF

Ecell∘=2.303RTnFlog⁡10KcE^\circ_{cell} = \frac{2.303 RT}{nF} \log_{10} K_c

Relationship between standard cell potential and the equilibrium constant of the reaction.

applies whenAt equilibrium (E_cell = 0).
equilibriumemfthermodynamics

Nernst Equation at 298 K

Ecell=Ecell∘−0.0591nlog⁡10QE_{cell} = E^\circ_{cell} - \frac{0.0591}{n} \log_{10} Q

Simplified Nernst equation using base 10 logarithm at standard room temperature.

applies whenT = 298 K (25 °C).
nernstemf298K

Nernst Equation for Half-Cell

EMn+/M=EMn+/M∘−RTnFln⁡1[Mn+]E_{M^{n+}/M} = E^\circ_{M^{n+}/M} - \frac{RT}{nF} \ln \frac{1}{[M^{n+}]}

Electrode potential for a specific reduction half-cell at non-standard concentrations.

applies whenFor metal electrodes; concentration of solid metal is 1.
nernsthalf-cellreduction

Enthalpy Change from EMF

ΔH=−nFEcell+nFT(∂Ecell∂T)P\Delta H = -nF E_{cell} + nFT \left( \frac{\partial E_{cell}}{\partial T} \right)_P

Determines the enthalpy change of a cell reaction via the Gibbs-Helmholtz equation.

applies whenConstant pressure.
enthalpytemperature-coefficientemfjee-advanced

Entropy Change from EMF

ΔS=nF(∂Ecell∂T)P\Delta S = nF \left( \frac{\partial E_{cell}}{\partial T} \right)_P

Determines the entropy change of a cell reaction using the temperature coefficient of the EMF.

applies whenConstant pressure.
entropytemperature-coefficientemfjee-advanced
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