Nernst Equation

Balance the cell reaction. Count total electrons transferred to get n. Write Q using aqueous and gaseous species only. Substitute concentrations with units converted consistently. Calculate the logarithm and interpret whether EMF rises or falls compared with standard EMF.

A diagram is not required. A flow chart from balanced reaction to Q to substitution is more useful for numerical accuracy.

A common wrong answer is using Q = [Cu2+]/[Zn2+] for the Daniell cell, which changes the sign of the correction term.

The Nernst equation relates the electrode potential or cell EMF to concentration, pressure, temperature, and reaction quotient for a redox reaction.

The Nernst equation relates the electrode potential or cell EMF to concentration, pressure, temperature, and reaction quotient for a redox reaction. At 298 K: E cell = E degree cell - (0.0591/n) log Q. For a half-cell Mn⁺ + ne- → M, E = E degree - (0.0591/n) log(1/[Mn+]), which can also be written as E = E degree + (0.0591/n) log[Mn+]. For Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s), Q = [Zn2+]/[Cu2+]. Therefore E cell = E degree cell - (0.0591/2) log([Zn2+]/[Cu2+]).

Standard EMF applies only under standard conditions. When ion concentrations change, the reaction quotient changes and the cell EMF also changes. At 298 K, the logarithmic form commonly used in Class 12 is E cell = E degree cell - (0.0591/n) log Q, where n is the number of electrons transferred and Q is the reaction quotient written from the balanced cell reaction. For pure solids and liquids, activity is taken as one, so they are not included in Q. At 298 K: E cell = E degree cell - (0.0591/n) log Q. For a half-cell Mn⁺ + ne- → M, E = E degree - (0.0591/n) log(1/[Mn+]), which can also be written as E = E degree + (0.0591/n) log[Mn+]. For Daniell cell at 298 K, E degree cell = 1.10 V, [Zn2+] = 0.10 M, [Cu2+] = 1.0 M, and n = 2. Q = 0.10/1.0 = 0.10. E cell = 1.10 - (0.0591/2) log(0.10). Since log(0.10) = -1, E cell = 1.10 + 0.02955 = 1.12955 V. The cell EMF increases because product ion concentration is lower relative to reactant ion concentration. Questions ask for EMF under non-standard concentration, equilibrium constant relation, concentration cell EMF, or effect of dilution on electrode potential. A common wrong answer is using Q = [Cu2+]/[Zn2+] for the Daniell cell, which changes the sign of the correction term.