Formula sheet: Electrochemistry

Electrochemistry12 min readLesson 1 of 7

1.1 Conventions first By convention the anode sits on the left of the cell diagram and the cathode on the right; the salt bridge appears as a double vertical line. Oxidation happens at the anode and reduction at the cathode. For a galvanic cell the cell potential is positive and the Gibbs energy change is negative; for an electrolytic cell an external supply forces the reverse. The standard hydrogen electrode is the reference and its potential is fixed at zero. 1.2 Potentials and Gibbs energy The cell potential is the difference of the two electrode potentials, and the standard value follows from the standard potentials. Gibbs energy connects the potential to the thermodynamics, and the equilibrium constant follows from the standard potential at 298 K.

E_{cell}^{0} = E_{cathode}^{0} - E_{anode}^{0}

Standard cell potential

Δ_{r} G = - n F E_{cell}, Δ_{r} G^{0} = - n F E_{cell}^{0}

Gibbs energy change of the cell reaction, n electrons and F = 96500 C mol^-1

E^{0} = \frac{0.0591}{n} lo g K_{c} (298 K)

Standard potential and equilibrium constant

E = E^{0} - \frac{0.0591}{n} lo g Q (298 K)

Nernst equation for the full cell, Q = reaction quotient

E_{cell} = E_{cell}^{0} - \frac{2.303 R T}{n F} lo g Q

General Nernst form; use 2.303RT/F = 0.0591 V at 298 K

1.3 Conductance Conductivity is the inverse of resistivity, and the cell constant converts a measured resistance into conductivity. Molar conductivity divides the conductivity by the concentration. For strong electrolytes molar conductivity falls slowly and linearly with the square root of concentration; for weak electrolytes it rises steeply on dilution as the degree of dissociation increases. Kohlrausch's law allows the limiting molar conductivity of a weak electrolyte to be built from the limiting values of strong electrolytes.

κ = \frac{1}{R} \times \frac{l}{A}

Conductivity from resistance; l/A is the cell constant in cm^-1

Λ_{m} = \frac{1000 κ}{M}

Molar conductivity, kappa in S cm^-1 and M in mol L^-1, result in S cm^2 mol^-1

Λ_{m} = Λ_{m}^{0} - A c

Strong electrolyte at low concentration

Λ_{m}^{0} = ν_{+} λ_{+}^{0} + ν_{-} λ_{-}^{0}

Kohlrausch law of independent migration of ions

α = \frac{Λ _{m}}{Λ _{m}^{0}}

Degree of dissociation of a weak electrolyte from molar conductivity

q = I t, n_{mol} = \frac{q}{z F}

Electric charge and amount deposited or liberated, z electrons per ion

1.4 Constants and checks F = 96500 C mol^-1. At 298 K, 2.303RT/F equals 0.0591 V, so the Nernst term is 0.0591 divided by n. Whenever the potential is in volts and the Gibbs energy in joules, n and F enter as a product. For a conductivity cell, a measured resistance in ohm times a cell constant in cm^-1 gives conductivity in S cm^-1. A positive E°cell means the reaction is feasible as written; a negative value means the reverse direction is feasible.

Exam

Write the anode and cathode half reactions separately before you use any formula. Most errors in this chapter come from a reversed electrode, not from the arithmetic.

1.5 Reaction quotient and cell notation The reaction quotient is written from the balanced cell reaction, with products in the numerator and reactants in the denominator, each raised to its coefficient. Pure solids and liquids, and the solvent in a dilute solution, are left out because their activity is taken as one. A gas enters as its pressure in bar. The cell diagram and the Nernst equation must describe the same reaction, so it is worth writing the two half reactions once and then building both from them. This single step prevents most sign and stoichiometry mistakes, and it also shows which species must be left out of the quotient because their activity is taken as one.

in hinglish

Electrochemistry mein pehla kaam cell likhna hai: left anode, right cathode, beech mein salt bridge. E°cell = E°cathode - E°anode, aur Nernst equation mein 0.0591/n ka term use hota hai (298 K par). ΔG = -nFE yaad rakho; negative ΔG matlab cell spontaneous hai. Conductivity resistance ka ulta hoti hai aur cell constant se judti hai. Molar conductivity Λm = 1000κ/M hoti hai; strong electrolyte ke liye yeh \sqrtc ke saath dheere girti hai, weak electrolyte ke liye tez badhti hai. Kohlrausch law se weak electrolyte ka Λm° nikalte hain. Faraday ke hisaab se 1 F = 96500 C, aur q = It. Numerical mein electrons count karna aur units match karna sabse zaroori hai. Aur cell diagram likhte waqt phases ka order mat badlo; galat order se poora answer galat ho jaata hai. Nernst ka 0.0591 sirf 298 K par valid hai.