The Nernst equation is one of the most important equations in electrochemistry.

Question

The Nernst equation is one of the most important equations in electrochemistry. To calculate the cell potential at non-standard-state conditions, the equation is

E=E??2.303RTnFlog10Q

where E is the potential in volts, E? is the standard potential in volts, R is the gas constant, T is the temperature in kelvins, n is the number of moles of electrons transferred, F is the Faraday constant, and Q is the reaction quotient. At standard temperature, 25 ?C or 298 K, the equation has the form

E=E??(0.0592n)logQ

The reaction quotient has the usual form

Q=[products]x[reactants]y

A table of standard reduction potentials gives the voltage at standard conditions, 1.00 M for all solutions and 1.00 atm for all gases. The Nernst equation allows for the calculation of the cell potential E at other conditions of concentration and pressure.

For the reaction

2Co3+(aq)+2Cl?(aq)?2Co2+(aq)+Cl2(g).  E?=0.71 V

what is the cell potential at 25 ?C if the concentrations are [Co3+]= 0.324M , [Co2+]= 0.174M , and [Cl?]= 0.407M and the pressure of Cl2 is PCl2= 5.30atm ?

Express your answer with the appropriate units.

Explanation / Answer

Ecell = Eocell + (0.0591/n) log Q

n = 2

Ecell = Eo - (0.0591/2) log [Co2+]2 PCl2 / [Co3+]2 [Cl-]2

E = 0.71- 0.02955 x log [(0.714)2 X 5.30)] / [(0.324)2 X (0.407)]

E = 0.71 - 0.02955 log 2.697 / 0.0423

E = 0.71 - 0.02955 X log 63.758

E = 0.71 - 0.02955 X 1.804

E = 0.71 - 0.0533 = 0.656 V

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